Bismillah ar-Rahman ar-Rahim. So just repeat after me. I'll do the Arabic and then the English. I'll do the Arabic three times and then the English. I testify that there is no deity except Allah and I testify that Muhammad is the Messenger of Allah. Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest Allah is the greatest is the greatest is the greatest Allah is the greatest Allah is the greatest is the greatest Allah is Alhamdulillah, all praise be to God Almighty, you are like the day you were born without any sin and so this is the this is the most beautiful day of your life and we are so honored to be here with you and so remember us in your prayers pray for us and if you have any anything we can do to serve you inshaAllah the community we're here to serve you any questions any support we can provide Alhamdulillah sorry okay yeah bismillah well yeah I mean guess I'll tell so yeah it's been it's it's been a journey coming into Islam I didn't grow up religious but I was always into spirituality in high school I dabbled in Catholicism and Christianity just didn't resonate too much with me as I carried on to college I did psychology and took a bunch of world religions classes and philosophy classes just dabbling more like getting into Eastern philosophies you know dabbling to Taoism and Hinduism Unitarianism I feel like I like deliberately like skip the class on Islam because of the whole Islamophobia and everything stuff for a law as I carried on I ended up going to grad school and getting my master's in holistic marriage and family therapy with an emphasis on Buddhist psychology so it was just like really into like the Eastern stuff that was in 2015 in 2017 I was just randomly in another city then I lived and I walked into a bank and this guy greeted me and he was like super nice and respectful and I would I was just thinking to myself like why is this guy so respectful like so nice and he just kept looking at me he was like I know you from somewhere and so he kept asking questions and then he was like we finally figured it out we were best friends in elementary school this was 20 years later that we're reunited he's a he was a poor Muslim so we like just embraced right there in the bank and like hugged and like got each other's numbers and that's when kind of like my journey to Islam began and I know it's just been on stages so 2017 I just you know started learning about it like researching it at first it was like trying to like prove it wrong and like see what's wrong with it but it backfired a little bit in the best way possible right so it just it just turned around I just fell in love with they was like it was like all the stuff that I loved about all the other face that I had dabbled into it was like Islam had all of it put into one right it was like the balance of all the other face combined so I you know and it just I it just everything made sense it answered all the questions that I had about things and so it's it had been like a you know a journey so in 2019 I participated in Ramadan for the first time I read a bunch of pamphlets I fasted and I like read a bunch of pamphlets that I had like randomly received in Europe on a trip that like I come across as like Islamic booth and like he gave me all this stuff and then 2020 Ramadan I fasted I I read the Quran in English and and prayed every day but not always five times and then 2020 I took my my first Shahada was at Eid of 2020 but you see it was like it's a journey so it was like I I didn't fully like rid myself of all the vices right so there's still like stuff that I was you know participate like I was I knew the faith I had read so much and like I learned about it but I wasn't applying everything right so this this past Ramadan is when I I really like cut loose all the the prior vices and really like started applying the pit the faith fully praying every day you know and just do it like trying to live by it by the Prophet's ways peace be upon him and and and then it was just like life just kind of like change like drastically like exponentially right like so once once started applying in and just thinking of you know a loss upon a what's all I just like just you know health got better family got better you know work got better I started attracting like amazing people into my life like may they be rewarded for for the goodness that they brought and like the catalyst for you know just enhancing my you know Iman and I know that it's a journey like it's not like you know it's not always easy not just because I join this faith that now everything is all you know butterflies the rainbows like it's it's it's a challenge and it's you know ongoing and like it's a I know it's a lifelong journey but it's like anything is just better as we're closer to Allah like it just makes everything better everything more easy like just knowing that you know we have this like support that's always there no matter where you are and you don't need anybody to talk to him you can talk to him whenever and so that's that's where I'm at I just feel like I'm just much more grounded in the faith and just say it was time to get make it make it more thank you thank you thank you for sharing welcome to our community I know all of them will be greeting you know All right so we'll get COVID friendly hugs and kiss pumps to brother Chad inshallah and then in the conference room inshallah we have another shahada so after Suna let's go there inshallah


What's up guys, today we're going to be doing an absolutely epic battle against Yu-Gi-Mou. We've done six battles and now we are on game seven. We've split three wins to three wins. We have a twilight edition, light and dark. This is going to be absolutely crazy. I think there's like ten special editions in here with a light of destruction, fan of darkness and tactical evolution packs. Like it can't get much better than this. This is going to be crazy. And speaking of much better than this, we have a giveaway. I'll be giving away a Mystical Knight of Jackal from Veronica. A Secret Rare Miserdevil and a Secret Rare Dark Magician from the 2003-10. Pretty happy giveaway, right? But Yu-Gi-Mou sent his own giveaway. So he'll be giving away, why he taped this, he'll be giving away a Stardust Dragon Assault Mode and a Hidden Arsenal pack. So you guys have a chance to win like four different awesome cards and a booster pack. All you gotta do is like this video, be subscribed and let me know who won the battle between me and Yu-Gi-Mou. If you don't say me, you can't win. I'm just kidding. Let's get into it. Yu-Gi-Mou with four ghost pulls in the last three. He's LeBron James. I mean, that's a, that's a good thing. And then Ruxing going up three and no impact battle. So LeBron with that classic block. Look, if he, if he wants to be LeBron, then I can respect that. So let's, let's get into this opening. This is going to be crazy. I'm pretty hyped about this. We've lost three in a row. We are on the verge of becoming the first NBA team to ever blow three of the, oh wait, this isn't the NBA. Sorry. All I know is that we're going to win. That's all that matters. That's, that's all we care about at this point. I think this is European print or something like that. European edition. I don't know. All I know is that if we pull a ghost share, he's pulled four ghost shares, as he said in his IRL meme. We're going to pull more. All right. Here we go. Here we go. Let's check this sucker out. Twilight edition, light and dark. We, this is going to be a lot of packaging, probably going to be a lot of cutting in this video. I'm going to be cutting through all this stuff. I'm definitely not going to make y'all watch it. Guys, that was insane. That took like seven minutes to open everything up and I didn't even throw the trash away. I just threw it on the ground. It took like seven full minutes. This stuff like, it's like soap. There's, they just, they just slide everywhere. So let's just open this stuff up. Let's start off. Oh yeah. I got to show you. We got 10 honest. I haven't slid these up yet, but we have 10 honest in nice condition, which is really cool. So I'm going to set those aside. I don't want to damage anything. Let's start the opening. It says we're nine minutes in, but we're probably two minutes in right now in the actual video. We're trying to destroy Yu-Gi-Moh. By the way, if you don't know who Yu-Gi-Moh is, he has an Epic Yu-Gi-Oh channel. His video will be in the description. Make sure you go check it out and let us know who had better pulls from this video. It's huge. Cause this is game seven. All the marbles, all the monkeys, the stuff here. Volcanic rat. Here we go. Phalanx pike, bad start. I think it actually comes after the rare in these, then a swap and flintlock. Yeah. This stuff is so like slick. I'm telling you guys, Phalanx pike is that good? I can't remember. Okay. So these are just going to be going everywhere. The whole video. I don't, I don't know what to do about it other than that, but yeah.  I don't want to spoil what they are because they're pretty crazy, but it's going to be pretty good. It's going to be pretty awesome. Rainbow path. All right. Phanum darkness. What can we get out of here? We can pull dark arm dragon. We can pull Gosher rainbow neos. We can pull crazy stuff. Doesn't he already departed? Cool. Cry havoc. All right. So far nothing regenerating rose. That's okay. Dark crusade.  That's sitting down for. So we have 10 of each pack because we had 10 special editions and that's why it took so long to open.  It was crazy. It was like gold series. It just took forever, except longer because gold series is only a few packs. All right. Arcana force six. Yeah. So we got to learn our Roman numerals and get a little bit of work there. Interplanetary invader a light barrier rare goblin recon spot. Oh, nice. Summon limit. I forgot about this. That is a nice like one or two dollar card. It has been reprinted several times. So I'm sure it's gone down a little bit, but it's going to be worth something. All right. Taxical evolution. So far we're 0 for three. We do have a nice common. Oh, that just worked really weird. You know what that means? Gosher. Gosher rainbow dragon. Hey, hey, summon them. We got a rainbow dragon back there. We got two ghosts back there. We need some luck. Here we go. Venom serpent. Neospatian marine dolphin. Double summon. Very good rare. So if that aside, counter counter, Venom swamp and gruvatic orb. I forgot this was a battle and now, um, yeah, I now remember we are getting killed right now. We have no foils. Nothing in the battle. We need something good. He already recorded is. I don't know what he pulled. So could be good. Could be bad. Loanfire blossom. Oh, do we get something? Doomsday horror. Isn't it? Wait. Loanfire blossom is good. That's a good card. Okay. Doomsday horror. Super rare. That's pretty cool. Isn't this the guy that's like based on your bandish monsters or dark cars in the graveyard? No, remove from play dark. Okay. Cool. Yeah. That's a cool card. Pretty cool card. I mean, it's not going to win us any battles, but it's pretty cool. Maybe it would win us a duel, but not a battle, you know. All right. Light of destruction. Here we go. Let's destruct. You know, he already, if you guys didn't see, he had a video. He pulled dark armed. It was crazy. So that, yeah, hopefully that doesn't happen again for him. Maybe for us. That'd be sweet. Yeah. Oh, wait. What just happened? Oh. Substitute. Okay. A rare. And a wolf. Lightsworn beast. Super rare. Super rare. I'm a little nervous about these super rares. I mean, if that's all we're going to get, we're not, we're in big trouble. This is game seven. You know, we got to step it up. All right. Here we go. Back to tactical evolution. Rainbow dragon. We need you. We're going to need you big time to give us something good. Euro print rainbow ghost rare. That'd be pretty cool. Volcanic rat. Goggle Golem. I feel like this is a decent car for some reason. Snake whistle. Venom boa. Hunter dragon. That's a rare. Elemental hero. Neos alias. We have pulled this a lot in super rare in the first edition. We've also pulled the alternate rare once or twice. At least once. It's a pretty cool card. Super rare. So we have three super rares. Some of the ambition classic, but we don't have anything better than a super rare. So what is the issue here? Oh, these packs are ripping like crazy. They're very easy to open. I like it. Obsidian dragon. Come on. Gladiator beast. Darius. We're going to need some luck guys. You guys are going to have to hit the like button. Let's do it. Double tag team. Shadow priestess of own. Look at that headdress. It looks like Queen Amidala and the Phantom Menace. Okay. And then it recedes. That's a weird looking card. Okay. Okay. So that was Phantom Darkness. This is not going well guys. This is not going well. But I'm not nervous. I know we're going to pull something big. I know we're going to pull something big. Ghost rare. I mean, why not? Spell gear. What else could you need? Just get the ghost rare. Out of here it would be honest. We already had 10 honest. Why not get an 11th? Glorious illusion. Oh. I called it again and honest, but it's a secret rare. It's not the ghost rare. I was actually thinking in my head. Well, we could get the secret version. I called it. Why not get an 11th honest? We get it. Secret rare. That's our first big bull. That's actually a really awesome one. Secret rare. So we have 10 ultra rares or super rares. No, ultra rares. 10 ultra rares and one secret rare. Now we just need the ghost. How about it? That'd be so crazy. First big bull against Yu-Gi-Mou. I'm feeling a lot better about this. If we can get some big ultimate rare or like a ghost, obviously we'd be in great shape. But now we're sitting pretty. We have a secret rare. I want to say ghost. I really just wanted it to be a ghost. It looks really nice as a secret though. I've never actually owned that card. All right. Cocoon Vale. I've never had the ghost rare either. So that'd be pretty cool. Venom Serpent. Venom Snake. I don't care if it's unlimited. Just give it to me. Cocoon Party. I need unlimited rainbow. Or in Neo's Rare. Light effigy. Dark effigy. Okay. That's cool. King Pyron and Venom Swap. All right. Here we go. Okay. We've already pulled honest. It's time. What's the cover card? What's this guy called? The... Ubell. The ultimate. The Terran Carnant or the Ultimate Nightmare? Ultimate Nightmare, I think. Terran Carnant is the middle one, right? Black Velossi. Fire Trooper. Alchemy Cycle. Aztec Apeed the Worm Warrior. Dark Horus Ultra Rare. Okay. That's pretty cool. That's a cool Ultra Rare. I will take that. That card looks really good. I mean, just check that out. That card looks incredible. So, that's a decent pull. I know the value on it's not too great. I know a lot of you guys, by the way, in our last battle against Rhymesaw, you know we're trying to give them the win. Come on, guys. You gotta be going for me. That's all I'm saying. Especially when I pull a $200 card, you guys gotta be on my side. All right. Spogier. Here we go. Hero Mask. That's kind of weird. Dice Try. Disc Blade Rider. Oh. And Light of Redemption. The Foils always get stuffed to the back. I mean, it makes sense, but also it's kind of weird. Light of Redemption. Man, these foils are really clean. I like them. Light Spiral and Volcanic Queen. So, we have about what? Okay, we have exactly half of this left. So, we've pulled one big pull. We've had a decent Ultra Rare pull.  We're overflowing Super Ares, which is kind of crazy. So, let's see if we can pull something else big. We're gonna need something big to win. Game 7. Reverse of Neos. Rise of Snake Deity. Shadow Delver. Okay, why does this look like a foil? Summoner's Art. Cool. And a Venom Shot. O'jama Knight is actually a nice common. Unlimited probably not worth as much. I think it was like a dollar in First Edition. That's pretty good. Okay. Venom Darkness. So far, you've given us an Ultra Rare. That's not bad. But we're looking for... How about a Goature at Rainbow Neos? I don't think I've ever had that one either. Black Velocity. We get a Twinkle Moss. Spell Chronicle. Chain Summoning. Dark Spirit Art. Greed. And a Cyber Auroboros. Gemini Lancer. And Unleash Your Power. Okay, okay. Wait, did I not open one of these at one point? No, I was wrong. We're not even half way. We've only opened like... We'd only opened 12 and I thought we'd open half. What am I thinking? We have more chances than I thought. Alright, Arcana Call. Come on, give us something good. Give us a secret. Give us an ultimate. Give us a ghost. Oh. Oh. A maniacal servant. That's a cool card. And Wetlands. Summon Limit. There we go. We'll take that all day. It's a nice Summon Limit. Okay, we're on to Tactical. Now we are halfway through. We should be. Unless I've miscounted again, which is entirely possible. Entirely possible. I have no idea how long this video is, really, because I'm going to have to cut out so many minutes of me opening this stuff. Cocoon Rebirth. Rise of this negativity. Crystal is cheeky. And a Grass Chopper. Phantom Cricket. King Byron. Gift card. That's actually like two or three dollars in first edition. I don't probably unlimited it a little less, but it's still pretty good. Yeah, Tactical Evolution has some nice, nice value in the comments. I'm not sure if, I don't think gift card's been re-printed, so it's probably still worth something. Gladiator Beast. Archvene Shield. The Calculator. Destiny Hero Departed. Cybernetic Zoom. Future Samurai. Oh! Secret Rare. Belial. Marquee of Darkness. I've never seen this card before. So that's pretty cool. Probably doesn't mean it's worth that much, but that card looks absolutely awesome. Sick. Two Secret Rares. Okay, that's pretty strong. That's pretty strong, but just the number of Secret Rares does not make us win. We're going to, like, if you pull something huge, we're going to be in trouble, so we need to pull a Ghost Rare to guarantee it. Yeah, if we pulled Ghost Rare, I would feel pretty good. Like, having an honest Secret Rare and a Ghost Rare, that would be almost impossible to beat. Not impossible, but almost. Battery and Micro Cell. What? Garof. Raging Cloudion. Nimble Massasubi. Massasabi. Light of Redemption again, okay. Another Super Rare. Light of Redemption. Cool. We have pulled a lot of foils. That's all I know. Miracle Flipper. So now we're down to 12 packs. So far we have two secrets. Out of 18 packs. That's good. That's really good, actually. No Ultimates and no Ghosts. I mean, Ghosts is very unlikely. Ultimates, I feel like, we should hopefully pull one, I hope. Cocoon Veil. We're going to need it, probably. Cocoon Party. Lots of Cocoons. Cover Contact. Snake Rain. That's a very good Rare. And a Ritual Raven. Creature Seizure. And Gravatic Orb. Phantom Darkness. Here we go. Here we go. Phantom Darkness. We're putting up a decent performance so far, but we're going to need something big. That's all I'm saying to win this. Win this series. We've played seven games. Seven pack battles. Make sure you check out Yugi Mo in his video. And make sure you spam in the comments. Bruxen won. Yeah, because he always comes over here, and he starts telling everybody that he won. I want you guys to go over there. I want you to tell him that we won. By we, I mean me, you. Everyone but Yugi Mo. We all won. Alright, Deep Forza. Let's go. Let's get a Ghost Rare. Raging Cloudion. Come on. Cloudion Storm Cloud. Lots of Clouds. Arcane of Force III. Smork, the bird of Ancestry. Shortcut Circuit. Space Gift. The Lady and White. That actually used to be a good card. I think you got reprinted. It's probably less now. Nine more packs. Come on. Get something huge. Let's do this. I want something huge so much. Alright. Cocoon Party. I mean, honest Secret Rare is pretty awesome. That's going to be pretty tough to beat. Venom Snake. Venom Bow. But also, we're going to need more. Snake Rain, yes. That'll add up. Ritual Raven. Ringe. Doddbreak. And Venom Burn. We need it guys. Come on. We need the power. We need the luck. We need the fire. Here we go. Earth Effigy. Come on. Oh, Spell Chronicle. These are going crazy. And all. What is that? Imprisoned Green Archfiend. Alright. Imprisoned Green Archfiend. Dark Crusader looks amazing. Immortal. Man, there's some really cool looking cards in here. Very good artwork. Very good common selection. And some really good cards. Cross Porter. Light of Destruction. Cup of Ace. Quick Charger. Uniforob. Come on. Come on. Flame Spirit. Ignis. Arcana Force 21. Is that 21? Yep. The World. Arcana Force 21. The World. I've actually pulled this in Ultimate once. I think it was out of one of these. Which is crazy. So that's a nice Ultra Rare. I think it's actually worth like five bucks. Which is not bad for an Ultra Rare. In a set where they have ghost secrets.  It's like the fourth best rarity. So it's actually pretty valuable. For what it is. So I will take that. I will take that. But I will also take an Ultimate Rare. Right here. Ultimate Rare Rainbow Dragon. Just kidding. That doesn't exist. I'm just kidding. I know. Snake Deities Command. Oh, Elemental Hero Dark Bright. Boo. Oh, sorry. That was just... That's the outro. You guys will see that later. But yeah. Elemental Hero Dark Bright Ultra Rare. Nice card. But in Ultra he's not too crazy. But he's still really cool. And definitely get ammunition for the battle. So I will take that. Elemental Hero Dark Bright. I like it. I like it. I like it. I'm just... Come on.  We're getting like a lot of good stuff. Like decent.  Just saying. Instant Neo Space. Some Saralotus. Come on. We need something super poly. I forgot I was in here. That's a huge Rare. Okay. That's good. It's probably only worth like two, three bucks now. But even that is still pretty strong. Like we're pulling a lot of very good Rare value and common value. Okay. So overall I think our number for what we pulled will be pretty decent. I mean we haven't pulled anything worth too much. I guess we'll be worth like 20 bucks maybe. Dice try? Not totally sure. Oh. Okay. Illuminal Lights were on Summoner. That didn't mean to do that. Jane Lights were on Paladin. Okay. So we have one of each Pac-Love guys. We have pulled well. We've not pulled incredible. So Yu-Gi-Moh has a chance to win. I don't like to say that. This is game seven. We want to close it out. Here we go. We need something big. We need something huge. How about Rainbow Dragon? Come on Rainbow Dragon. We want to show up. You've shown up for us once. Can you do it again? That would be insane. Chrysalis Pantel. Here we go. Chrysalis Larva. Snake Lizzle. Chrysalis Mole. Symbols of Duty. Footlock. Footlock. It's okay. It's okay. It's okay. We got two more packs. We got two more chances. Light of Destruction has been our best pack so far. We're going to go with Phantom Darkness. We're going to leave Light of Destruction for the end to close out to win us the game. Win us the series. Gladiator Beast Areas. We need the like button for luck, guys. If we're not at like 2,000 likes by now, you guys should be slamming the like button. That's all I'm saying. Double tag team. Here we go. Black Velocity Company. Gigapoint. All right. Here's the moment of truth. Gigapoint's actually decent, I think. Cybernetic Hidden Technology. Okay. Line of Pipement. Okay, that's fine. That's fine. We believe that Light of Destruction will carry us. We'll pull us something huge. I'm thinking Judgment Dragon. I'm thinking Honest Ghost Rare. What do you guys think? Ultimate Rare, maybe? I don't even know what the Ultimates are besides the Arcana card. We already pulled it. But something good. Probably something Light's for. Demise of the Land. There's a good one. That was like five, like eight bucks for a while, actually. Limit Reverse. Okay, here we go. Arcana Force 18, the Moon. Cup of Ace. We need some luck here. Froggy Force Field. Okay. Let's do this, guys. Believe. All right. Okay, no Force One. Wetlands. All right. All right. That's fine. That's fine. That's fine. We're still going to win, I believe. So let's go over what we did get. All right. So we got the 10 Honest, but for the purposes of the battle, we both got those, so we're not going to show those. So it doesn't really, you know, they don't, they offset. Then we get, for our Commons, we got Goggle Golem, the Lady and White. Demise of the Land. That's a nice one. Ojama Knight. Two Summon Limit. Gift Card. That's for our Commons. We did pretty good there. We got a Giga Plant Rare. Super Poly. Great. Two Snake Rains. That's awesome. For our Supers, we got Double Light of Redemption. I don't think that's very good. Aalias Wolf. Lightsworn Beast. Doomsday Horror. And then for Ultras, we got Arcana Forest 21. One day one. We got Elementor of the Dark Bright. Dark Horus. And for our Secret Rares, we got an Honest Secret Rare and a Belial. Belial. Marquis of Darkness. So we did pretty good overall, I think. But Yugimo definitely has a chance, so make sure you guys go check out his video in the description below. Let him know that we won. Unless he won, then I guess you guys can say he won. But that's it for today. Hope you guys did enjoy this battle. And I'll see you guys later. Peace. The Metal Hero. Dark Bright. Boom. Oh my goodness. There's so much trash. It's like Yugimo.  Oh yeah.  Just wait. We will beat him good. I can't wait to win this battle. Yugimo. You are sucky. Alright. Just wait. We will beat him good. I can't wait to win this battle. Yugimo, you are sucky.


فشرف بالشتغالي بالعلم ولا تبغي به ما عشت يا بدا بدا وياله من شراف عظيمي سين دلالله مين by this الشرك شرك are you with me brothers so when you understanding the Quran أهل السنة والجماعة telling you to understand the Quran based on what ما أراد الله that which Allah intended by it and that which the messenger intended by it not what you intended by it or what you understood from the Quran and now Allah the Quran doesn't need no reform it does not need it the Quran does not need you to come and tamper with it and reinterpret it it does not need that from you the Quran has been set it's rules and regulations are put in place are you following the rules for it like it that's the problem and the second way that you're going to understand the Quran and the sunnah the أهل السنة tell you is ما قاله الصحابة what did the companion say about this verse what did the Sahabah say about this what did the students of the Sahabahs say about this why why pay attention because لأن الرسولة لما خاطبهم الكتاب والصدع عرفهم ما أراد بتلك الألفاض they understood what the Prophet meant by those words that was their language they were the Arabs the language that was being spoken they understood it what helped them that Sahabahs as well was the fact that the revelation was coming down in a circumstances which they could relate to are you with me it came down in their environment in their land they knew the temperature that day and the heat the way it was they know how the environment felt that day they know how the faces of the companions looked that day they know the Prophet ﷺ when he said that verse was he smiling was he angry they know every detail regarding it which supports the understanding of the verse صح they saw the Prophet ﷺ in a crime scene whose statement does a police officer take the eyewitness the police officer will take the statement of the eyewitnesses those who were there when the incident happened not those who came months weeks later the Sahabahs are the eyewitnesses they saw the incident happen and that which took place so we need to know and we want to understand get every sorry narrations of how they understood this particular verse and how they understood this particular حريث also the Sahabahs didn't have this hidden agenda they didn't have it like it creeped into the later generation they had the greatest form of piety and Taqwa so when they understood the verse it was stripped from desires there was no desires involved other people are taking the verse in accordance to their desires صحابة رسول الله they did not have that the language of the Arabic didn't dilute it didn't wear out that it changed as time went by that here we are with one word it has six different meanings because as time came by it started to change they have it in the purest essence of that word and what it used to be at the time of the Prophet عليه الصلاة والسلام رضي الله تعالى عنهم the biggest the biggest way to tackle these extremist ideologies are by those who are taking those points because those called those خوارج the خوارج are not they are not اهل العراء they are not opinionated in a sense where they are not اهل الرأي they are not people of opinion they were always people who would bring اديلا نقول at the evidences that was misunderstood evidences that were corrupted evidences in which they were corrupted in this understanding meaning the خوارج were not like when I say اهل الرأي I mean by they were not like the جهمية الذين يقدمون العقل على النقل that were given presidents to touch logic and rationality over texture evidence خوارج one like that خوارج one like that خوارج one say قال الله قال الله قال الله قال الله قال الله so the person who wants to tackle their ideology has to be a person who gives importance to the Quran and the Sunnah not a group of people who they themselves don't respect the Quran and the Sunnah so Sufi can't argue and debate and confront these extremists no canadio banli no can a liberal quillian foundation do that the only people who can are the Salafis اهل السنة والجماعة are the only people because what they're going to do is every verse that they break the خوارج don't have any source from the حديث of the prophet صلى الله عليه وسلم they break their backs with the حديث of the prophet صلى الله عليه وسلم are you with me brothers like you look at the government what do they do they shut down the Salafis to counter these individuals when in reality the ones who can deal with them are them rather than the only ones who ever dealt with them from the time of the companions who are the people who are dealing with it the people who are from the Sunnah عبد الله من عباس was the one who was dealing with it قرن بعد the current generation after the generation the people who dealt with the خوارج are who يا اخوة هو ذي look at the books of the Sunnah look at the books of the Prophet Muhammad رحمة رحمة والله the books of Imam البلبهاري أبو بكر الإسماعيلي قوام السنة أبو قاسم التيمي and others they all dealt with the خوارج in their books and refuted the ideologies of the خوارج until محمد مع عبد الله came and he refuted them and he blasted them عليه رحمة الله ولي ذلك there is a a kitab I advise you guys to read with him بأبو صلاح الافغاني شيخ أبو صلاح الافغاني اسكو التقرات عامة الدعوة النجنية in refuting the خوارج and their methodology he wrote his this is his PhD I think it's got the تقديم of the Mufti عبد عزيز آل الشيخ on it what he does is that he brings all of the كلام of the آئمة الدعوة النجنية proving that they refuted and they blasted the خوارج and they have nothing to do with them عشيخ صلاح الافغاني when he did this thesis when he wrote it the Mufti was was part of the committee of نقاش he was legend of the نقاش the Mufti was there sitting listening to his thesis and commented on it and the audio is on YouTube and the book is published القاعدة الثالثة والعشرون the thirtieth قاعدة the 23rd قاعدة أنهم يحثون على دراسة السنة النبوية والعمل بها ويحذرون من هجرها from the قاعدة بها للسنة والجماعة is what they urge the people to study the سنة of the prophet عليه الصلاة والسلام they urge the people to what to study the what the sunnah of the messenger عليه الصلاة والسلام the sunnah of the prophet عليه الصلاة والعمل به and to implement it where you حذرون من هجرها and they warn the people from what boycotting the sunnah of the prophet عليه الصلاة والسلام the sunnah of the prophet عليه الصلاة is divided into two علم الحديث and the sunnah of the prophet عليه الصلاة is what رواية and the second one is دراية علم الحديث رواية right رواية means narration wise the first one is called علم الحديث رواية رواية means here narration and there are three things that fall under that one the first one علم الحديث رواية and three things fall under it مصطلح الحديث اما قواعد الحديث same thing مصطلح الحديث which is the signs of حديث are you with me brother and sisters مصطلح الحديث which is what falls under is called مصطلح الحديث and we recently took الكتاب نخبة الفكرة written by في مصطلح أهل الأثر written by who حافظ إبنو حجر العسق العاني رحمه الله we study that book so we said the sunnah of the prophet عليه الصلاة حديث of the prophet عليه الصلاة is divided into how much two the first one is called علم الحديث رواية علم الحديث in terms of what دراية and we said that's divided into how much it is divided into 2 I said 3 it's divided into 2 the first one is مصطلح الحديث the first one is called مصطلح الحديث and the first one whoever authored in this science مصطلح الحديث is أبو محمد الرامهر مزيو الرامهر مزيو his name is أبو محمد الرامهر مزيو he authored a book which he called it المحدث الفاصل المحدث المحدث الفاصل he's the first person who wrote in it he wrote with me brothers and sisters and then after him الكيب الامام أبو عبد الله حاكب النسابوري رحمه الله he authored his كتاب الكفاية في علم الرواية and then after him الكيب الامام أبو نعين الأصبهاني رحمه الله he wrote his كتاب المستخرج and then after him came الامام خطيب البغدادي and he wrote and then after him came الامام ومخطيب البغدادي حافظ المحدث he spoke about these three dimensions the first one being أبو محمد الرامهر مزيو إنه كتاب المحدث الفاصل أن الكتاب رتبه الامام وخطيب البغدادي and also الكتاب بيخطيب البغدادي is called الجامع لأخلاق الراوي وعدام السابع and the second one was who the third one sorry is الامام أبو نعين الأصبهاني رحمه الله الكتاب is مستخرج are you with me brothers مستخرج these three sorry three sorry I mentioned four الفاصل is أبو محمد الرامهر مزيو the second one is أبو عبدلا حاكم إنه سابوريو and the third one was أبو نعين الأصبهانيو أبو نعين is مستخرج is basically taken from the أبو عبدلا حاكم إنه سابوريو حافظ من حجر سن about أبو حاكم أبو محمد الرامهر مزيو since he was the first one who authored it he didn't really put the signs in in proper order and then أبو حاكم إنه سابوريو he's one's also good but he said the sequence and the way he structured it wasn't good as for what do you call it أبو حاكم أبو نعين الأصبهانيو he's مستخرج حافظ من حجر سن he left room for somebody to come and add on to it but the one he prays highly is the one written by أبو باكر خطيب البقداديو رحمه الله أبو باكر خطيب البقداديو his kitab is جامع لأخلاق الراوي وأداب السامع this kitab he said as he brought from أبو باكر من نقطة أبو باكر من نقطة said everybody who came and spoke about signs of hadith after خطيب البقداديو was in need of the works of أبو خطيب البقداديو because he wrote in every signs he spoke every particular issue of مصطلحة الحديث the signs of hadith he wrote about it he wrote a particular book regarding it and then after that came none other than the great noble Imam ابن صلاح wrote his مقدمة is known as علوم الحديث when he wrote it then every single body came and took it from that and Imam حافظ زيلادين العراقي came and what did he do حافظ زيلادين العراقي who is the sheikh of حافظ ابن حجر he done a he done a what he done poetry on the كتاب written by written by ابن صلاح before زيلادين العراقي was who before زيلادين العراقي was ابنه كثير ابنه كثير then اختصار علوم الحديث اختصار علوم الحديث is a summary of علوم الحديث written by ابن صلاح also بلقينة رحمه الله he did the صلاح جديد بلقينة نعم بلقينة بلقينة however you want to say it and others and then came the book that we studied which is نخبة الفكر which حافظ ابن حجر wrote which is then the book that everybody gave acceptance to so that's the first of the two in علم الرواية the second one is علجرحو التعديل علجرحو والتعديل علجرحو التعديل is criticism and praise of the narrators and scholars they authored that in three ways علجرحو التعديل as was written in three ways are you with me brothers books that talked about اثيقات the reliable narrators and the second one is the praised narrators which sorry the reliable and the praised ones are the first one and the second one is the criticized narrators اضععفاء the weak narrators and the third one is اضععفاء والثقات the criticized and the praised are all in there and each and every one of them many come out of it العلم الجرحو التعديل can be categorized into two a type which is نظري which is more theoretical which is that فلاني زب وضع he places narrations كذاب فاسق لا يؤخذ بحديثي ليس بشيء لا بأس به ذلك جرحو التعديل ثم افرقات which is basically علل that way you have now studied مصطلحو الحديث and then the person has studied what then the person has studied جرحو التعديل the criticism the praise and the best book written in علل by the consensus of the علماء it is the best nothing has been seen the likes of it is the the kitab written by علماء الدارة قطنية رحمه الله which is called العلل الواليدة that book is the best لا مثيلة له and wallahi is amazing because that kitab is is over 10 volumes and علماء الدارة قطنية you wrote it from his memory they wrote it all from his memory all of it came from his head he criticizes he questions he speaks about narrations and all of it was written from the top of علماء الدارة قطنية his head عليه رحمة الله he was something else عليه رحمة الله something else something else رحمه الله رحمة واسعة واسعة and also what the practical side is as you see today manifested many books علم التخرج the تخرج of our hadiths many books have been written in that one of the books that are great in تخرج if you want to see تخرج means when you read a book placing bring تخرج is different from تحقيق by the way many people confused the two تخرج doesn't mean that the person gives you the rule of the hadith it just means that he brings all of the narrations in that particular حديث for you every different روايات and different narrations regarding that hadith there are many books that are written in that in that regard from the books that are written in it is البدر المنير written by ابن ملقن he is the sheikh of حافظ المحجر he with me ابن ملقن wrote a book بدر المنير and بدر المنير is basically في تخرج حديث شرح الكبير written by ابن ملقن ابن ملقن summarized his own book and also the same book حافظ المحجر also worked on it which is a nice كتب تخرج book it's called تلخيص الحبيب في تخرج حديث حديث الرافعي الكبير is also by him it's the same book he done تخرج of the حديث of شرح الكبير by الرافعي he came and he put تخرج on it from the books because I mentioned it fast is نصب الراية by الامام وزيل عرحمه الله which is تخرج on كتاب حداية written by المرغييناني which is حنف بكتاب الامام وزيل عرحمه الله he has done تخرج on that book also from that is ألباني رحمه الله محمد ناصر لدينا ألباني رحمه الله is كتاب and he done تخرج all the أحاليث which they use one of the books I forgot also is that great amazing كتاب التنقيح والتحقيق في أحاليث التعليق by حافظ ابن عبدالهادي رحمه الله حافظ ابن عبدالهادي he does تخرج on the أحاليث الأحكام that was gathered by ابن الجوز رحمه الله he does تحقيق of it it's an amazing by them anyways أهل السنة والجماعة and the other one is علم الحديثي ديراية علم الحديثي ديراية means understanding الأحاليث فق الأحاليث so they tell the people to go to what books like بلوغ المرأ have you studied بلوغ المرأ they go through عمدة الحكام have you now studied عمدة الحكام now go for the كتب that are written like المحرر المنتقى يدين أبو البركات of course you go for the different explanations of these books for example المنتقى you go to say كتاب نيل الأوطار by رحمه الله بلوغ المرأ you go for the different شروح and the different explanations there are the earliest of it being سبل السلام written by أمير السنعاني رحمه الله and those who came after him who then took from him and you go for the books of أحديث الحكام after that such as the كتاب سنان أبي داود أمام أبي داود كتاب سنان is from أحديث الحكام أحديث الحكام are basically what أحديث which are just about jurisprudent rulings so you take the فقيات from it and the سنة والجماعة push the people to study those books and they say you study those books عليه الصلاة والسلام and they warn the people from staying away from the حديث of the prophet عليه الصلاة والسلام then you go for the other books of أحديث one of the biggest books in كتاب أحديث الحكام if not the biggest is سنة الكبرى by بي حقي it's the biggest that is the biggest أحديث الحكام is written by who yeah so I would urge every one of you if you could go and buy that book the كتاب سنة الكبرى by بي حقي رحمة الله so what was this قاعدة again أهل السنة والجماعة they urge the people and they push the people to study the حديث of the prophet عليه الصلاة والسلام and the سنة of the prophet والعمل so if you study something and you learn it what are you going to do you're going to implement it where you حد رونة من حجرها and they warn the people from boycotting the حديث of the prophet عليه الصلاة والسلام now you find a war against the prophet سنة you find a person he's studying فق he's never ever studied a book of حديث on فق he's never studied بلو المرام مثلا or he hasn't studied any books of حديث الحكام all day he's doing he's saying he said this مالك said this but he doesn't have any narration of what the prophet did and this is what we will الله he brothers is deficiency and it's weakness you have to give importance to the دراسة to the سنة النبوية studying the prophet عليه الصلاة والسلام السنة الإمام البخاري رحمه الله he chapted a bab in his صحيح write this down very important الإمام البخاري رحمه الله he chapted how will knowledge be taken and I want you to understand this الإمام البخاري he chapted in his صحيح he chapted and he wrote there كيف يقبض العلم how will knowledge be taken وكتب عمار ابن عبد العزيز إلى أبي and then this is what he brings الإمام البخاري رحمه الله brings this وكتب عمار ابن عبد العزيز إلى أبي بكر ابن حزمن عمار ابن عبد العزيز he wrote to this noble إمام ابو بكر ابن حزمن الإمام عمر ابن عبد العزيز the great noble تابعي what did he do he wrote towards to who ابو بكر ابن حزمن and look what he said to him he said امضر ما كان من حديث رسول الله فاكتبه عمر ابن عبد العزيز wrote to him and said to him look that which the prophet عليه وسلم his hadith and write it look and basically research the hadith of the prophet عليه وسلم and write them فإني خفتو دروس العلم ودهاب العلم for I am scared that knowledge will wear out and the scholars will go ولا تقبل إلا حديث النبي صلى الله عليه وسلم and it will not be accepted and it will not be accepted from us except the hadith عليه سلم so what he said was امضر look at ما كان من حديث رسول الله look at the hadith of the prophet عليه وسلم فاكتبه and write it research and look for the hadith of the prophet عليه وسلم and write it فإني خفتو I am scared دروس العلم that knowledge will go and the scholars are also going to go so what did he consider knowledge is going to go by the hadith of the prophet going if the hadith of the prophet عليه وسلم goes knowledge is going to go ألمام ابن القيم said ألمام ابن القيم said in his كتاب اجتباع الجيوش الإسلامية ابن القيم said فإن سنة حسن الله الحصين ابن القيم said that the sunnah is the fortress of Allah it's a fortress you know if you are in a fortress you are out of the outer harm the sunnah is a fortress من دخله anyone who enters into that fortress كان من الأمين that person is from the saved people they are going to be saved right so what is the sunnah is a fortress that protects the people once that fortress goes my beloved brothers and sisters once that fortress goes what's going to happen which is the sunnah then you are vulnerable anyone can attack you your religion can be attacked everything that's why it's powerful that the person studies the sunnah of the Prophet صلى الله عليه وسلم شيخ الإسلام ابن القيم said something very powerful he said ابن القيم says and this is the reason why innovation became clear and it became out and apparent in the umma sorry in every nation شيخ الإسلام ابن القيم says the reason why innovation became clear in every nation is because هو خفاء السنان المرسلين فيهم the sunnah of each prophet was hidden from the people it got hidden from the people وبذلك يقعوا الهلاك and because of that destruction occurs وليها ذا كانوا يقولون and because of that the salaf used to say الإعطصام بالسنة تنجات holding on to the sunnah is what successes why were every previous nation destroyed because they were the sunnah of the prophet their prophets was missing from them and when the sunnah of every prophet is absent from any nation their destruction is what comes to them next إن شاء الله تعالى we're going to take 15 minutes break and then we're going to go into the next إن شاء الله تعالى


Okay. So we're going to start the third lecture on dark matter. So take your seats, please. Can you hear me? So in the first lecture, we had a brief review of why we believe there is some abundance of dark matter in the universe today in our galaxy and even at larger scales. Two days ago in the second lecture, in the second lecture, we went back in time and we looked at possible ways, mostly one way. We looked at one way to produce dark matter in the early universe that was thermal freeze out. And we derived a relation between the abundance and the cross section and we saw that the relic abundance requirement in some sense give us an idea of how much dark matter should interact with us. So what we did the last time was exactly going back in time when the universe was very, very young and we studied the production of dark matter. What we do today, we come back to the present and we have an overview of experimental strategies to actually search for these particles. So we will talk about three main ways that you may have heard of before of detecting dark matter. There are direct detection, indirect detection and collider. And it's good to start this topic by drawing a diagram that you probably have seen before, but just... So this is just a more visual way of visualizing the annihilation process that we were discussing on Tuesday. You have two dark matter particles arriving, finding each other. They interact and they give rise to a final state made of some other particles. So I didn't emphasize that but in the previous lecture I was always assuming that the hour of the time was going from left to right in this diagram. So this is my initial state and this is my final state. And if this is the case, so if time goes from left to right this diagram describes an annihilation. And we saw on Tuesday that this is the process that sets the relative density. So the cross section for this process tells us how much dark matter should be around today. What we will see today, the same process that happened in the universe and the process that set the number density of dark matter can still happen today. For example, at the center of the Milky Way, our galaxy or in dwarf galaxies around us. And this process is how we do indirect detection. So for now I'm just giving you the name but then we will review experimentally how you look for these annihilation processes. Now the time can actually go in two other ways in this diagram. So if you consider time going from the bottom of the blackboard or the top, then you have an elastic collision. So you have a dark matter particle that collides with a thermal particle and in the final state you have the same two states. So it's just a collision where the initial state and the final states are the same. So this is the process that is probing direct detection experiments. So it's an elastic collision between dark matter and us, standard model. And I take advantage of this opportunity to mention something that was more appropriate to cover on Tuesday but there was no time. But this is also the process that set kinetic decoupling in the early universe. So we saw on Tuesday that when gamma for annihilation is equal to Hubble you get chemical fees out. So number changing interactions are not effective anymore and the number density is frozen. But these elastic processes can still take place and this is what allows dark matter particles and the thermal particles to keep the same temperature until lower scales, lower times when the universe is older. And this kinetic decoupling process is very important because it sets the scale of the smallest object we can have in the universe. So you can put a bound on this cross-section by looking at structure similar to what I was discussing when I said that dark matter has to be cold. So if you're interested to hear more about decoupling come talk to me later. But since this lecture is about searches today so we will focus on direct detection and the last option is to read this diagram from right to left so this describes a collision of two standard model particles producing a pair of dark matter particles so from right to left. So this is what happens, for example, what could happen at the LAC. You collide two protons, they collide and you end up producing two dark matter particles in the final state. So this is, here I wrote LAC but it fits within a broader category which is dark matter searches at colliders. So the plan for today is to describe without giving of course too many details because I'm interested more on giving you the idea and how the experiment works and what is the output of the experiment so when you look at the plot if you're sitting in a dark matter talk you understand where the plot comes from and what it means. And I will follow this order direct detection first, indirect and collider. There is no reason to prefer one with respect to the other it's just a choice. OK, so direct detection. So direct detection, the idea of direct detection was suggested in the 80s by Goodman and Whitten and the idea is just to look for events of this kind so the idea is to look for elastic collisions between a dark matter particle and some target. Here I call the target N so this will belong to the experiment and it is typically a nucleus. We will see later that if it's large it's good so typical targets are large nuclei like Xenon or Xenon and Germanium are probably the most diffuse in these experiments. OK, so before we get to the actual experiment let's get an idea why we expect this event to happen in the first place. OK, so what we can do is to take a nucleus of course we don't take a single one, we take many but we put the nucleus in the lab here we wait and then if we see that these things move it means that it was kicked by something by something invisible that we cannot see and so by... Oh, let me close. So if you sit and wait and you see some recoil momentum and recoil energy without seeing anything else so that means that there was something invisible because the momentum is conserved so something invisible kicked it and the hope is to detect an event where something invisible was this dark matter particle. OK, so how common are these events? What is the typical rate for these events? Let's see, in order to give an estimate of the rate we need to know how much flux we have here on Earth, OK? So if I... Let's see, if I consider one centimeter square, OK? One centimeter square and I consider one second so one centimeter square is this big, OK? Here on my front how many dark matter particles passes my head one centimeter square of my head in one second? Do you have any idea? Ten, five, thousand So it depends, it depends because what we know is the mass density not the number density, OK? So the flux is number density times the velocity, OK? And the velocity we know that around the solar system and in general in our galaxy is ten to the minus three times the speed of light, OK? So they are very relativistic today, this particle in our galaxy, but the number density of course is the ratio between the mass density and the mass of a single particle that's how many particles we have. So this is the number I give you, OK? So we know everything because we know how fast dark matter particles move around our galaxy today, yes? So the velocity is just hydrostatic equilibrium so there is gravitational there is gravity that wants dark matter to collapse at the center of the galaxy and then there is velocity dispersion that acts like a pressure even though it's not correct to speak about pressure but so it's a competition between the dispersional velocity and gravity and once you impose the static equilibrium you see that you need this velocity in order for the system to be in equilibrium so the halo around our galaxy for example, OK? So we know the velocity we know a row, so for each mass we can estimate the flux and know how many particles hit my head in one second. So let's put one number which is 100 GV this 100 GV is as we saw on Tuesday it's a very interesting mass range because there are motivated dark matter candidates from the hierarchy problem they get produced with the right density so this is a good target and we estimate the flux for this case and we get 10 to the 5 per unit surface per unit time, OK? So it's a big number it's a big number it's 100,000 dark matter particles hitting one centimeter on Earth per second it is really big now, it is big or not? Looks big, right? Now for comparison, think about the neutrinos coming from the Sun, OK? Neutrinos produce through nuclear reactions in the Sun we get the flux of those neutrinos which is if I remember the number correctly 65 billion, OK? So it's 10 to the 10 and detecting those neutrinos was a huge pain it was really, really difficult so we were not, probably none of us was born around some of us but so this is a success that we finally managed to so I wasn't around those days but I'm sure it was extremely difficult to detect these neutrinos from the Sun because it's true that the flux is a big number but the rate is flux times cross section and if something is weakly coupled you need really large flux to detect that, OK? So these numbers are just to say that direct detection is an extremely tricky business because we are really looking for something with a very small probability to happen, OK? Because the full rate is flux time cross section, interaction strength and it's just a very small number, OK? So that's why all the direct detection experiments they are never in this room or at the level of the Earth's surface they go deep underground like there is a lab here in Italy at Gran Sasso and there are many others in the world you have to go really deep inside the mountains where you reduce the background because of course if I put this bottle here and I look for this bottle to move there are not only dark matter particles making that move there are other things like cosmic rays and so on so we want to reduce the background as much as possible and that's why we need to go into some environment where there is no much dark matter around OK very good so this is one reason why it's difficult it's because it's something very rare there is another reason why it's difficult so it's difficult twice not only because the events are very rare but because each single event is very hard to detect, OK? The reason why the event is hard to detect is that of course we don't see the dark matter particle we don't see the effects of this dark matter we see these things, this bottle or this target moving so what we measure is the recoil energy of this object and so let's try to make an estimate of what the typical recoil energy is for this process, OK? so the kinematics is this so before with a given momentum which is the mass times the velocity I can use the non relativistic expression because V is small so P is just MV, OK? and you have a nuclear target here which is at rest, OK? so if this collision happens then you see the vector after the collision both chi and the nucleus are moving, OK? and of course we don't see chi moving chi is dark matter is invisible, it just escapes the detector what we see is this nucleon moving and so we can measure through some very sophisticated experimental setup it's not an easy thing to measure we can measure the recoil energy, OK? so direct detection experiments measure the recoil energy of the of the target nucleus so we can try to make an estimate of how big the typical recoil energy is for these processes and see that it's actually very small so not only you have very few events but each event is extremely difficult to to detect so let me use this so I will leave this, I will not erase this blackboard so we will always keep in mind that this is the topic for today but let's go through the kinematics, OK? so this is a very simple problem in classical mechanics it's a binary collision of two non relativistic objects it's something that you can use by imposing conservation of momentum and energy so let's without putting all the factor of two in the right place, let's just get a feeling of what is the typical order of magnitude so the momentum transfer which is just the final momentum of chi minus the initial momentum of chi is defined, I define it as q and the size of q, the typical size of q is let me make sure I yes, so it's this is just a straightforward kinematics so as you may remember there is the reduced mass of the two body system that enters the equation and the typical momentum transfer is the mass times the relative velocity, the relative velocity is V because the target is at rest at the beginning, OK? so the typical recoil energy for the nucleus is, well, it's M sorry, it's the momentum over twice the mass why? because the initial momentum of the nucleus was zero so all the momentum transfer went to the nucleus just by conservation and I know that in the non relativistic regime the energy is momentum square over twice the mass OK, so I substitute the first equation into the second equation so this is the typical size of the recoil energy, now keep in mind that V chi is ten to the minus three V chi square is ten to the minus six OK, so typically matter particle and the target have mass in between ten 100 gV so this factor within the parenthesis of the order of ten gV, ten 100 gV you multiply that by ten to the minus six so the typical recoil energy it depends of course on M chi and on M n but you can convince yourself that it's in this range here OK? and so these are very very small energies to detect and that's the second reason why direct detection is difficult so two reasons why it is difficult and when we see the experimental results we will be that it's amazing how much progress they made over the last 30 years and how much regional parameter space they were able to exclude so before I do that let me just give you an expression OK, so there is another important quantity that plays a role in the experimental setup which is the threshold recoil energy for each experiment so each experiment can measure a recoil energy up to some value, below that value it will be just too small, OK, so you lose the ability of reconstructing that recoil energy so I call this ET OK? T stands for threshold, it's a threshold below which my experiment doesn't work anymore so now you see that let me rewrite this very important equation so there is a minimum velocity that the dark matter particle needs to have in order to observe an event OK, if V gets too small then ER becomes too small and ER gets below this threshold value OK, so I say this because I gave you this 10 to the minus 3 number but actually dark matter particles in our galaxy they have a distribution, OK and this distribution is a Gaussian some actual, well to a very good approximation but there may be corrections but for now let's assume it's a Gaussian this V0 is precisely 10 to the minus 3 the speed of light OK, so once I compute the actual rate I have to take an average over all the possible incoming velocity of the dark matter and this distribution holds as long as the velocity is not big enough that the particle can escape from the galaxy, so the escape velocity is something you can estimate the same way you estimate the one for the earth OK, is there any question? Yeah, yes, yes this one this is 0, the first one is for non-activistic particle, yes, but I mean you should just think that this is not an equilibrium, not in the sense that you reach thermal equilibrium, just that you get a distribution in the velocity that it's a Gaussian distribution with a typical value V0, OK, other questions? OK, so I wanted to say that because let's compute the minimum velocity that you need in order to get a rate OK, so the minimum velocity I just solve this equation by imposing that the recoil energy is equal to the threshold energy OK, so it's 2 mn over mu square e threshold to the one-half OK, and now I want to write down this equation in two, for two different cases because here there is the reduced mass so if you have a two-body system where the mass are very different from each other the reduced mass is basically the mass of the lightest object OK, so let's take the case where the mass of chi is much, much less than the mass of the nucleon then this equation becomes 2 mn m chi square Et, sorry, and here instead you get 2 Et over mn OK, so square root, thank you, yes, yes, thank you, thank you OK, so let's just go through the logic again we see that if a dark matter particle arrives with a given V chi there is a typical recoil energy that is produced the smaller V chi the smaller ER will be and there is a point where we eat the threshold which is typical of the experiment, if V chi is too small then we don't produce much now the reason why I emphasize these two cases is you see that V min gets large for small m chi OK because you see that from the first equation when m chi is small the reduced mass is basically the same as m chi and then you pay a huge price and this is bad because the escape velocity for our galaxy is more or less 600 kilometers per second but we made that the same way you do for the escape velocity if I throw this shock on the air to just escape the gravitational field of the earth so this means that our experiment will be effective to test dark matter particle up to some mass below which we lose sensitivity because the velocity the minimum velocity I need for that specific mass is going to be either bigger on the escape or you start to pay this exponential suppression so you lose sensitivity very quickly so for small mx we see that we don't do very well what about large mx m chi so I call it chi, not x for large m chi so it's very useful to write an equation for the rate so now I will explain what I mean with this equation but let me just write that first so we saw yesterday that an interaction rate is typically n s v how many interactions per second so this is n, this is s and then I take an average over all the possible v with the distribution f that is here so this is just an average of n s v to give us the rate per unit recoil energy and of course I have to plug the cross section per unit energy now let me rewrite this equation a different way as we already said we don't know n but we know rho we know rho very well around the solar system which is where we perform the experiment so I replace n with rho over m and once I do that I see immediately that if m gets large then I get less events in other words I'm paying a price because a bigger mass corresponds to a smaller number density around the galaxy and so if the mass gets very large eventually I get no events so we see that we have two bounds on the mass below which the experiment doesn't have enough sensitivity because we require a minimum velocity that's too large and we also lose sensitivity at high masses because high masses correspond to low number density so we don't have particles coming here at any rate that would work so now let's go and see what is the typical output of a data detection experiment put that here, skipping many steps and a lot of experimental good work if you have a dark weather model where the relevant parameter space is the mass which I put on the horizontal axis and the cross section to scatter of some nucleon let me put also some scale here so these are the typical scales that these experiments probe for the mass so above the GV and by the time you get to 10 TV you see the limit gets very weak so let's stop there and actually I have a real plot here that was public only a few weeks ago and this is the current best limit data detection 45 ok so these are all small numbers and I emphasize that the dimension that they used to plot are cm2 so when you read this plot and you say 10 to the minus 46 that's 10 to the minus 46 cm2 for the cross section and if you look at the experimental bound that comes from an experiment that is called Xenon 1 ton so it's easy to remember because Xenon is the target material they use and 1 ton is how big the target is and this is an experimental Gran Sasso and if you look at the bound you see that something like this ok so this is the experimental bound whenever you see a line on a plot like this it means that you are not allowed to live on one side of the line and of course in this case means that whatever is here is excluded and that makes sense because you exclude cross section bigger than some given value you want the cross section to be small enough because they have observed no events that look like dark matter ok so few comments you see that the rise here is very sharp and you lose sensitivity very quickly because of this effect I was saying here so once we mean gets very very small then your experiment is not going to perform well for that mass range so when the mass gets around 1gV the details depend on the experiment the overall scale is always around 1gV ok so a 1gV you lose sensitivity and then your bound it goes almost along a vertical line ok below that mass you cannot say much so here it's also easy to understand why the bound gets worse because this corresponds to if you measure the slope of this line it's like 1 over m chi and this is the flux factor that I mentioned before here that you pay because if you consider larger particles masses then you have less number density so you have less incoming flux and your limit gets weaker ok ok yes yes so it is model dependent of course it is model dependent so it doesn't matter because it's a non relativistic cross section so Fermin or Boson it doesn't matter in this case but no but that's a good comment because of course if you have a model when you know the theory and you can compute cross sections as a theory you can actually give you can make a plot of this quantity ok you say ok I know the rho I know v more or less I compute the sigma dr with my Lagrangian and the tools I have and then I compare that with data now for this plot there is an assumption and the assumption is that sigma is the so-called spin independent ok so there are it means two things first the cross section is taken in the limit when q goes to 0 the momentum transfer and that is a constant that approach so it doesn't vanish in that limit and then there is the assumption that the dark matter particle interacts coherently with the nucleus and not just with a single nucleon and so the cross section scales so the cross section to scatter off the full nucleus is the one for a nucleon times the number of nucleon that are in the target squared because you have to square the amplitude so there are some assumptions but this plot is valid for this class of theories spin giving spin independent cross section there are other cases like spin dependent where the dark matter particle in that case is a fermion and interacts with the spin of the nucleon and that's another expression and the plot looks different so there are several cases but this is if you want the case where the cross section predicted is the largest possible one and so these are the best limits available so just some questions yes in that region I would say something at the end if there is time there are new ideas using different targets not nuclei but the experiments dark detection experiments the old way the ones suggested in the 80s they cannot say much now below the GV there has been some improvement there is this experiment called super CDMS that they can really get to a very small threshold pre-coil energy so their bound goes like this it gets worse but not too much but I think it's fair to say that it's a territory that is going to be explored in the next 5-10 years and there are many ideas to do that yeah okay so there are it's very easy if you play with these things for a while then you can always find way to hide so the most famous example is actually the a Majorana fermion interacting with the standard model Z boson so the process you have is this you have chi, chi then you have Z and then you have the nucleus here and if this is a Majorana fermion this vertex can only be the axial vector current because you apply the self-conjugation property of Majorana fields and you see that the vector current is too vanish and this cross section is spin dependent not independent so you don't gain the da2 factor here so you all interact with one nucleon not with the full nucleus and then the bound for that type of particle is quite weak there are other cases where sigma is proportional to V squared and we know that V is small so that's even more suppressed so it is a model dependent so there is a broad class of models where you this plot is valid but there are models where this is not okay wow it's already 240 okay so let's conclude this direction with this plot with two comments I'm sure you may have heard there is a neutrino floor which is something like this so there is a irreducible background to these experiments that I don't even know if it's correct to call background because it looks like a signal okay neutrinos coming from the sun, atmospheric neutrinos and other neutrinos they give an experimental signal identical to the one of a dark matter particle so by the time the bound will get here then we will see something but we don't have something it's standard model physics so when you see this plot there is also a shaded region here which is the neutrino background region but we are still ah they didn't put that here okay we are still few orders of mind to the way so there is reason to push this bound here and that's something that you will happen with conventional well conventional with the same techniques just increasing the amount of material in the target and increasing the exposure time and so this bound will be improved here when the same bound improved it means either we improve the bound or we see something and we discover something as was mentioned before there is all this region here GV below the GV and this is there is some bound there but there are more ideas than bound which is good because there are ideas for new experiments to be built that were put forward in the last five years so it's a very active field also with a substantial contribution from theories too not only experimentalist and there were a lot of ideas again something very recent and some of these experiments will be built and we will also explore this window with the same caveat in mind that in the sub MEV region it's tricky because we know BBN right so having something below the MEV scale that is interacting with us strongly enough to give us a signal to be in thermal equilibrium in the early years so we will spoil BBN and so let's say that I see two interesting region MEV to GV where there is really nothing to worry about there can be particles living there with a good cross section we see that sub MEV we need to be more creative with the models because there are these BBN bounds but there can still be models that will be tested so yes this is not the sigma it's just the bound on sigma so it's not a result from field theory that I do the calculation and I find that it goes like 1 over M I'm just saying that if you look at the plot and you want to find an equation for this line it's sigma is a constant over M because you lose the incoming flux by increasing the mass so I will what is the boss? I have to finish at 315 so let's do indirect detection then if there is time I'll say something about collider otherwise I'll just do that so before I start indirect detection if there is more question about direct detection think about that while I clean the blackboard ok so if there is no other question let's move let's look now at this diagram from left to right ok so we want to detect something like this kai kai finding each other in the universe today annihilating and giving rise to standard model final states so whatever I say in the last half an hour will be true for annihilations kai kai going to SMSM but it's actually true also for decay so if you have as we discussed I think already before dark matter particles do not have to be absolutely stable they can be metal stable they can be stable until today but with a long lifetime long enough to be around but also to give us some of these events here so what I say here is valid for both ok and how do we do that well we need to point our telescopes that can be either telescope on earth or on satellites spinning around the earth towards regions where there is a high density of dark matter ok because we want this process to happen so we need to look at places where there is dark matter and moreover this place this environment where there is a lot of matter they should not be too far away from us because if they are far away from us then we lose in terms of the flux because if they emit if this process happens and they emit isotropically around the environment then we lose one over our square one over the distance ok so they have to be rich of dark matter particles and not too far away so there are two main targets one is the one is the center of the Milky Way so it's very it's very close because we are in the Milky Way so we don't pay a huge price in terms of distance and we know there is dark matter there ok so that's a good one and the other one is to look at dwarf galaxies that are not too far away from our galaxy and these are good too because they are small but they are rich of dark matter and they don't have too much background as I will discuss in a second ok so these are the places where these reactions can happen but then what we detect is here on earth ok so what do we detect so what is SM in this case it cannot be something like a muon if you know what it is so a muon is a particle like the electron just heavier 200 times heavier than the electron with the same properties but it's unstable so even if the dark matter goes to mu plus mu minus then the muon eventually decays and it decays before you make it to the earth where we detect that so SM here really means stable standard matter particles so I gave the example of the muon but it's true for any other unstable somewhere so if you go to a couple of X bosons for example in this annihilation and then again the X boson is unstable so you get the decay products here ok so stable some other particles and there is not many of them ok there is not many why so we can make a list of the most popular targets so let's see neutral so we can look for something that carries electric charge like electrons positrons protons antiprotons we can look and detect these objects here but then we can also look at something neutral like photons or neutrinos ok and there is a why well it depends so there are advantages and disadvantages about both ok so if you look for something charged for example there is the advantage that E plus is antimatter the antiproton is of course antimatter and we know that there is there are no many well known mechanisms to produce antimatter in the universe at the very high energy so if you observe something which is positrons or antiprotons at very high energy it's something we don't know and it can be very likely to come from annihilation like this where the energy scale is set by the mass of these particles or by the decay ok so this is what is good about charged stuff the bad thing is that charged stuff not propagate straight because they get deflected in magnetic field of the galaxy so once we detect them here we don't know where they came from ok if you have an positron being created somewhere in the galaxy it moves as a consequence of the magnetic field and it hits our detector with a direction that in principle has nothing to do with the incoming direction and the other thing is that they lose energy so once they get here we don't know the energy they were produced with ok so there are good and bad things so today since I had to make a choice because the amount of time I have is finite I will discuss one specific final state which are photons ok so let's discuss photons in more details but I want you to emphasize that when people speak about indirect detection it doesn't mean only photons even though I'm going to discuss only photons today it means positrons it means antiprotons it means neutrinos and so if you want to know more about the others you can ask me of course ok photons so first of all dark matter we say that it doesn't interact too much with photons that's something we discussed in the first lecture and also in the second also in the Q&A session it was brought up this issue so how do we produce photons from dark matter annihilations ok there are several ways so let's make a distinction between primary and secondary photons so primary photons are photons produced by processes like this so the dark matter particle can go to two photons ok it may be small the rate but there could be a rate for example if you we know that the dark matter doesn't interact too strongly with the photon but the dark matter can interact with something that is charged and then you go to the next next to the leading order perturbation theory for example you compute one loop diagram if you know what it is you get two photons in the final state ok so this is definitely possible even if the dark matter doesn't have an electric charge that is big ok just perturbation theory you go to the next order then there is also the possibility of producing photons in this way you have I don't know what can we do W ok so this is one example the W the photon is the mediator of one of the mediators of weak interactions and so the dark matter can talk with the W with no problem it doesn't mean it's charged but then these W's are unstable they evolved they decay and you can get photons from final state radiation because it's true that the dark matter is not charged but if dark matter annihilation produce something charged then these final state particles they can radiate photons this is just Bremstra-Lungov of the W's that are produced with the very high energy ok moreover we know that the W also has Hadron decay modes so it can decay to stuff a nice color charge and in this chain you can produce neutral pions pi zeros and we know that the main decay mode of the pi zero is to gamma gamma ok so you see that there are multiple ways that from a process well you either go to two photons straight and that's very easy or even though you don't go to a photon pair you go to W plus W minus then you follow the evolution of these two and you get photons in the final state these are called primary photons because they are produced basically at the same location of dark matter annihilation ok now there are also what are called secondary photons so why secondary because there is nothing to do in principle with the production at the annihilation site ok but imagine that you have kai-kai annihilating to something and this something gives you electron or positrons ok then what happens is that these electron and positrons they travel through the galaxy and they can excite photons through inverse compton these can be CMB photons, photons from stars but if you produce electrons these are very energetic because the energy here is it could be hundreds of gv so these could be photons with a very big kinetic energy and they may hit CMB photons, photons from stars and then you get photons that are at the energy much higher than the corresponding energy before like CMB photons are 10 to the minus 4 electron volts ok and also there is synchrotron radiation because we know that there is a magnetic field in our galaxy so if the electron propagates in the magnetic field it radiates photons and if you plug the number both for the electron energy and the typical size of the magnetic field in our galaxy which I think is microgauss more or less you expect photons in the radio band of the electromagnetic spectrum ok so why I made this distinction I made this distinction because from a single particle kai let's say kai 100 gv we have ways to look at the sky and add photons in different range of the electromagnetic spectrum because primary photons are produced at energy very close to the mass but these secondary photons like either inverse, counter or synchrotron they correspond to lower energy ok and so we look at the sky with different experiments we look for photons and we can also try to correlate if we see a signal or not ok so it's clear the idea more or less ok so now let's do something analogous to what we did with direct detection let's see how we estimate the flux how we estimate the number of photons we expect to see on Earth and how we derive bounds the same way a plot similar to the one I drew before ok so how many photons do I expect so let's make the estimate for one specific case so we can give names to all the particles and we know what to call what ok so I have this example here so we have kai kai that goes to tau plus tau minus so tau is a lepton of the third family so it's a heavier causing of the electron it's 9gb it's heavy and other than the mass it's identical to the electron and our goal is to estimate this number so I have a model where my dark matter particle annihilates two tau's I want to estimate how many photons I produce for example if I look at some dwarf galaxy I look at the dwarf galaxy I want to know how many photons are supposed to come to Earth because of this interaction here the way it works is the following so we need to specify the cross-section ok so this process will have an associated cross-section which will tell us how big the interaction strength is giving rise to this annihilation and then I write down the equation then I will explain what I mean ok so let's go through this equation and this is a two so numerical factors are not important I just want to explain the different things ok so the flux of photons is given by and remember as I said before that charged stuff gets deflected but photons do not get deflected so when we see a photon coming from there we know it was produced there it was the guys produced and it traveled straight to us so we look at this dwarf galaxy and we integrate over the fraction of solid angle that we observe the galaxy and this is important because of course if this is me here ok and this is a dwarf galaxy so when I look at the dwarf galaxy with my eye I'm only observing a given fraction of the solid angle but photons get produced in all the directions in the dwarf galaxy so it's unavoidable that I pay a price which is the whole solid angle over 4 pi so that's easy to understand it just means that the galaxy emits photons isotropically we only detect the ones that are produced toward us ok this is also easy to understand because it's the integral along the line of sight this is the line of sight so I look toward the galaxy of what? n squared times sigma v why n squared? because they need two chi's to have an annihilation I need a chi here, a chi here and then they collide with probability given by the cross section so that's why there is this combination n chi squared sigma v and chi is the density, the number density as a comparison if instead of the annihilation I'm considering a decay so if I'm considering this process here so my dark matter is metastable and then decays to tau plus time minus then here instead of n chi sigma v the product of the first power of n chi times the decay width of chi gamma why? because I don't need two particles anymore to produce tau, I just need one and wait that it decays, that's gamma that means how many I have in a single volume and finally this is a product that tells us how many photons with the given energy I produce per single annihilation so imagine you have one single annihilation chi chi going to tau plus time minus and you want to know for that single given annihilation how many photons you produce with respect to the energy so differential in the energy and this is something by the way that you can compute by using well established techniques in particle physics because this is something you can test at colliders and all you have to do is to produce two tau's with an energy in the center of mass as given by twice the dark matter mass and follow the evolution so there is a very nice way to rewrite this equation I will rewrite in that way and then we will get to the experimental bounds ok so I didn't do much, all I did I took this equation and instead of n I replace n as I did all the time in the last week rho over m, number density is mass density over the mass. Once I do this then I collect this j factor that is defined here and I write the rate as a product of multiple factors this is a nice decomposition because let me write it here ok so 1 over 8 pi is just a number and there is not much to say ok, j, the j factor so the j factor is something that depends on the target only ok because you see by definition you are just integrating over the line of side on the solid angle of the square of the dark matter density so this quantity knows nothing about your dark matter model if it goes to tau or if it goes to W's it's just something that it depends on the target only if you look at the dwarf galaxy and you must know that there is an associated j factor with that target yes, the cross section is no it's not in the integral the cross section is, I'm taking it as a constant here yeah no, it's outside, it's outside so this is, you are just integrating over matter density along the line of side so the cross section is outside now the second piece is this and this is really where I have to specify what dark matter model I am considering so if I am writing a paper on a given dark matter model and I want to see what is the flux of photons in that model, well j I look for a reference and these things are known they've been observed and it's just something that doesn't know anything about my model but once I write down my model then sigma v and m chi these are parameters of my model I can compute sigma v, I can choose a mass so this is a model dependent quantity finally, so this is something that it doesn't depend on the target and it doesn't depend on the model this is something that is I would say this is standard model physics so it's something we know very well not only how to describe theoretically but we know it works because we tested this at collider for many many years and this is just a quantity that describes given the single annihilation into tau and given a dark matter mass which here enters just as the energy the ambient mass of the tau plus tau minus pair what is the spectrum of photons that I get after I let tau plus time minus evolve so that's why it's standard model physics because this is something that can happen in the vacuum it can happen at the LAC, it can happen I don't need the galaxy to describe this so this is standard model physics so this is a nice way to factorize the rate into three contributions very different nature and if you are an observational astronomer you care about the J factor and this is a very important job because there are still uncertainties on the J factor of dwarf galaxies and they can be improved if you are a dark matter model builder you specify sigma v and m chi and this is something that I think by now we can take from Monte Carlo codes that generate evolution of tau plus and minus pairs at the given center of mass energy and we can just use that with a lot of confidence ok ok so now let's look at the limits so now I have a plot from the where is the echo yes ok so this is a plot from the Fermi collaboration so the Fermi satellite is satellite that was launched I don't know more or less ten years ago so this result is the outcome of the observation of a set of dwarf galaxies for which the J factor was known they specified this annihilation channel that I mentioned before so this plot is valid for tau plus and minus and these were the two parameters that they use to bound the system because they say ok we predict how many photons we expect to see from this dwarf galaxies using this equation we count the number of photons we impose that the number we see cannot be accounted for so this is an upper limit on the cross section otherwise you would see more you would predict more than what you actually saw and then you put bounds on this parameter space so let's go through the details this is sigma v here this is m chi now sigma v they use these units centimeter cube over second so sigma is a cross section v is a velocity so the dimension looks right but if you remember yes two days ago the wind miracle let me call it thermal there was this cross section that was the magic number to get the rally density I express this in natural units but you can also explain that with these other units so the number we have to face once we look at the bound is this magic number this is the number of the wind miracle I just translated that from natural units to units where I restore the speed of light okay so NH bar so let's see the plot again what are the ranges of the mass so this is 10g let's just say mass in gv 10 100 so again we are exploring a range of mass very similar to the one from that actual experiment that we just discussed and on the vertical axis here we have what are the typical numbers the typical numbers are 10 to the minus 27 10 to the minus 26 25 24 so we can immediately identify on this plot the magic so this is the one so in some sense and I remind you this result was very independent on the dark matter mass we saw on Tuesday that regardless on the mass up to some very tiny logarithm dependence if the annihilation cross-section is equal to this value then you get a successful production in the early universe so this is an interesting benchmark for experimental observations because in some sense you expect this number to be the one of your model as I say there are caveats to this number as I discussed there is an assumption about knowing the history of the universe all the way to very high temperature so that doesn't have to be the case but it's an interesting benchmark so now let's go to the result and then I will stop 27 ok so this is the result from the Fermi collaboration ok and again as I said before this region is excluded so we see already something interesting here that if the dark matter mass is below more or less 100 gV thermal production seems to be excluded for this channel by the way Fermi collaboration in their paper released this plot for many other final states not just out plus time ions and they all look very similar ok there is not really a sharp difference there are there is some difference but more or less the messages is the same ok so it is very interesting that we managed to test the thermal up to masses of 100 gV of course this region is still viable and the fact that this region is excluded doesn't mean that these models cannot exist with a successful production rate because as I say this line is a big caveat it was derived under the assumption that Hubble is the one we extrapolate from the thing so this ends the review on the protection what I couldn't cover today was the collider researchers so you can ask me in private if you want I would be more than happy to say a few things about that and tomorrow in the last lecture we will discuss the QCD action that is a dark matter candidate that we never discussed until now thank you


Hi, this is Dr. Don and we're on part three of the Money Curl-O simulation series of videos. We're now going to move ahead. In part two, we talked about building randomized variables. And in this part, we're going to change two of the variables that were fixed in the basic model and make them randomized variables. We're changing the unit variable cost, UVC, and make it a normal distribution variable. And there you can see the random function, which is critical to the simulation. And then we've changed the demand. Also made it normal just for simplification here. There's the ran function. In this case, we're rounding because units, we don't want fraction of units. And down at the bottom of my assumptions table, you can see where I put that data, and that's the references here, C23 and D23, and C25 and D25 that populate those models. Okay, I built the start of a table off to the right here. When you do a simulation, you need to have not only the values that you're looking for, in this case, we want the delta, the difference in costs, and the decision, but we need to have all the variables that are changing. In some models that can make this a pretty big table, as you'll see when we look at multi-year forecasts. The reason for that, if you don't have the variable that contains the random function over here in your simulation, then it will not necessarily update every time you want the simulation to occur. So the only way to force it is to make sure that every variable that you want to randomize is included in this table. We start with getting our trials, and I know in the video I showed you, Excel's Fun Guy talks about calling up a special menu. The way I like to do it is just go to home, fill, series, select columns to make sure it goes down. I'm just going to do 100 here just to make this video go faster. And it's like, okay, that gives me my trials. Now I need to populate the table and we link back to the cells that include that random function. So this is my UVC, I'm going to link to that cell. My demand D, I'm going to link to that cell. My delta is one of my outputs that I want. So I'm going to link to delta and then I want my decision. Manufacturer, and what I like to do is copy that formatting right there. So it'll be replicated as it goes down. I think it replicates automatically. But there is the basic table now. I've got the two variables that we're randomizing. We've got the two outputs that we want to talk about. So if you remember, we need to select that row that's got the formulas. If you select the header, this won't work. And the reason we use the data table remember, if you've got 10,000 trials and you manually copy these formulas down, Excel can really, really, really slow down. It can actually stumble sometimes. It's better to use this data table trick. So we select that row that has the formulas and the trial number. And I like to use the control shift down error to automatically go down to the bottom of the data and select it. And to get back to where I want to actually do something, we go to control backspace and it brings us back up to the top. That's control down area, control backspace. That's your handy when you've got 10,000 rows. So next we go to data, what if analysis, data table. We don't put anything in the roll. Remember, we're tricking data table. And we don't want to actually relate to any of the formulas here. So make sure your cursor is in the column input cell. Pick a blank cell, a cell you know you're not going to later put something in. And then we click okay. Sometimes it takes a while. Okay, it populated there. One thing you need to remember, depending upon what you've got happening, you may want to set your calculation option so you can control it. Remember that formulas, calculation options, you can have it set for automatic except for data tables when you're doing the simulation sometimes. That's helpful or you can set it manually. Manually means you hit the F9 key. Automatic means if you make a change somewhere on the table, then it will update. But in this case, I forgot that it does not take the formatting. So you'll have to format these. You can see it didn't include the dollars here or there or my conditional formatting. So you'll have to copy those formats down. So, but anyway, I hope this helps you see about setting up the data table that you need for the Monte Carlo simulation.