Hi, everyone. Thanks for joining me today, and thanks to Product School for setting up this webinar. We are going to talk about my experience and share what I believe are good tips to break into product management. My name is Pavneet Alwalia. I'm a Senior Product Manager at Azure. Thanks everyone for joining. So let me start by giving a quick introduction of myself. Like I said, I'm Pavneet Singh Alwalia. I'm from India, New Delhi. Originally, I live here today in Seattle. I work at Microsoft as a senior PM for Azure Kubernetes Service, which is Azure's managed Kubernetes service, one of the largest services in Azure today. I have roughly three years of cloud product management experience. Prior to Microsoft, I worked at AWS for two years in containers, spaced with products like ECS and Fargate. Prior to that, I did my MBA from Michigan School of Business, Ross School of Business at Michigan University. By education, I'm a chemical engineer. Actually, that's what my undergrad was in. Then I did data science for a couple of years in a startup based out of India, followed that by working at Google and as a digital marketing product specialist with the sales orgs, post which I decided to pursue my MBA, which allowed me to transition into product management. That's my LinkedIn profile QR code. Feel free to scan it. Feel free to hit me up on LinkedIn if you want to follow up with anything post this webinar. So what do we expect from this session today? I like tackling problems and I like tackling big things into breaking it up into questions. So let's try to solve and find answers to these five questions through the session today. What is product management? What do they do? What does the life for product manager look like? Second, I want to get into some myth busting like, Hey, do I need a computer science degree to do product management in tech? Or do I need an MBA? Stuff like that common misconceptions that I want to dive deep into and answer those questions. Third, how do how to get product management interviews? Hey, I work in a very unrelated field or a very unrelated role. How do I even begin to get interviews so that I can crack product management? Right? That's the first step. That's probably the biggest hurdle. Next is how now that I have interviews, how do I prepare for them? What can I do to make sure that I'm putting my best foot forward and give myself the best chance of getting selected into a product role in any of the big tech companies? And then finally, hey, I've got multiple offers. Which one should I pick? Which product should I go for? Which team should I go for? We'll talk about a little bit about that and how I made those decisions in the past. So let's dive into it. First up, I think the biggest question some of you might have or probably already answered for yourself is what do product managers do? I like this comic that I found yesterday while making this presentation. Product managers spend a lot of time trying to figure out, hey, what to build? How do I build? What's the priority? And then somebody comes in tells us, somebody up top comes and tells us, we need to build that because XYZ customer said so. I think that happens sometimes, but that's not a true representation. So I want to clarify some of that here. I think somebody once said to me that product managers are CEOs without any authority. And I think that's a very good representation of the role. Why? Because everything that is wrong with the product, every problem, whether that's pricing, whether that's go to market strategy, whether that's hey, customers don't like the experience or engineering is struggling to figure out what to build next. All of those are your problems, just like a CEO would for a company. But you don't have the organizational authority to go tell sales to do this or go tell marketing to go do that. They look towards you for guidance. They look towards you to set the path, but you don't really have any direct organizational authority over them. So I think that's a good quote that sums it up. The way I think about it, about what my role as product manager is, I'll break it into these five steps, right? You're the customer advocate in all internal meetings. When the engineers are trying to decide, how do I build this feature? What does the UX look like? What does the backend design look like? It's your job to be the customer representative and fight for what's right for the customer. You're the product evangelist in the customer meetings. It's your job to sell it. If you're in a B2B product management role like me in the cloud space, you get on calls with a lot of customers, some of them large organizations, and it's your job to sell the product to them to help them understand how does this product solve their problems. You're the business leader in engineering meetings. It's your job to prioritize features. It's your job to help engineers understand why are we building this? How will this help the product? How will this help the customer? You're the engineering leader in business meetings, which means when the VP of your organization says, hey, we need to build this because XYZ customer told us to. It's your job to represent the engineers and set the pros and cons and set the trade offs in front of the leaders so that they can help you make the right decisions. It's your job to set the product strategy, the roadmap, the product positioning, the pricing. Pricing is not always a PM role, but in some companies it is, and the GTM and technical support. That's all everything that I do on a day-to-day basis, both in my previous role at AWS and now today at Microsoft Azure. If I had to sum it up at the end of the day, your job is to make a lot of decisions. And as you move up the chain, as you grow in, you know, as you get promoted and move up, you will have to make less and less decisions, but you'll have to make sure that they're of higher and higher quality. This is an oblique quote reference to something that Jeff Bezos said, but his job is, which is to make a lot of high quality decisions. So that brings me back to the fact that I would say a CEO, a product manager is a CEO of the product without any of the organizational authority. So let's get into the myth busting that I talked about earlier, right? Do I need to have a computer science engineering undergrad or post-grad degree to be a product manager in tech? The answer is no. I'm a life proof of that. I'm a chemical engineer by education and I've never been a software engineer in my whole life, but I was able to break into product management and I feel I do a pretty good job at it. So no, you don't need to be a computer science degree holder. It will help. It will certainly help if you get into some of the more technical products on the cloud side or on AI ML, but it's not a prerequisite. Do you need to have an MBA to be a product manager? Again, the answer is no. I chose that path because I was from India. I wanted to move to US and I wanted to work for the big tech companies and there was a glass ceiling that I needed to break through, which an MBA helped me with, but that's not the only way to go about it. Proof of that is several companies like Facebook, Microsoft, LinkedIn, Google have APM, which is associate product manager or entry level PM roles, which allow you to become PM early in your careers and then learn the basic skills on the job. Right. But I would say that if you're looking for something like growth PM role, where your job is to drive adoption or to drive GTM and marketing initiatives, an MBA will help. A formal education in those fields will help. Do I need to have a prior project management or program management experience? Again, no, but the ability to juggle multiple balls that are up in the air is a prerequisite, I think. So if you can show that they I'm good at, you know, executing, I'm good at holding two deadlines, I'm good at organizing multiple people and multiple initiatives together. That's what you need to show rather than on your resume, have project project management there. So what do you need to get into product management? I think it's important to focus on the skills rather than titles. I think these six plus one skills fairly represent what I do day to day in my job and what I've seen others do, depending on the company, depending on the role you might over index on one over the other, but broadly speaking, these are skills that are pretty ubiquitous across all product management roles in tech. First up is problem solving. PMs are at the end of the day problem solvers. The job is to understand customer problems and then find the best way to solve them. You need to define the problems crisply so that all your other teams understand what it is. You need to structure it because sometimes it's not one feature, but 10 different features that meet that can solve a customer problem, right? Sometimes it's not even a feature. Sometimes it's the right documentation, right? So you need to be able to structure and define it very crisply and then research and investigation, whether that is researching different ways to solve it, whether that is research and customer through customer research, through interviews, through UX, bug bashes, you need to be able to dive deep into the problem and structure it so that others can understand it and help you solve it. Second big skill is data skills. I put SQL and Python there. They're not precise. I think SQL is pretty much prerequisite. I think in any tech role, I think today you need to know SQL. Python is a big plus. You can learn it on the job. It's not too difficult. I still struggle with it sometimes to be honest, but it's great if you know it, right? You need to know basic steps. You need to know the difference between need and median and standard deviations and person tiles so that when data is presented to you, you can understand it because how else are you to understand the market and customer trends? How do you understand the product performance, feature adoption, customer behavior? You need those data skills to marry with the qualitative research that you will be doing and it's key to your decision-making skill, which is, I think, central to everything you do as a product manager. Third, I would say, is ability to learn quickly. Like I said, I came from a non-computer science, non-technical background, right? But I was able to learn everything I need to know to be in a very technical cloud product on the job. Yes, I struggled for the first six months because I felt, hey, I didn't know enough. I had imposter syndrome, but if you have that ability to learn quickly, you can overcome any deficiency that you might have coming into the role, right? For example, how do APIs work? How, what is load balancer? What are the basic principles of front end UI design? How do I price a product? All those things you may not know going in, but if you have the ability to learn quickly on the job and to be comfortable with not knowing, those are important skills to have, right? Customer empathy, I think enough people have talked about this over the last years. Amazon is a pioneer in customer empathy, so is Microsoft, so is Google when it comes to consumer tech. If you can't understand the customer by putting yourself in their shoes, then how can you solve their unmet needs, whether they know it about it or not? I think Apple is a great example for it. Steve Jobs is famous for saying, it's your job to solve the problems that customers don't even know that they have, and if you don't have customer empathy, you won't, you won't succeed at that. I think next on the list is influence without authority. Like I said, you don't actually have any organizational authority as a product manager. Engineers report to engineering manager, finance reports to somebody else, marketing reports to somebody else, sales is its own org, so you need to be able to convince them of the strategy that you want the product to go in of the right prioritizing decisions. You need to have empathy to understand why are they pushing back when they push back and not become a bully in the org. Nobody likes that. I think, especially in tech companies, that culture is corrosive, right? And then you need to be able to adapt to working with different people, with different skill set, different mindsets, and different goals, and be able to adapt your message so that they align behind it, and also learn from them as part of the consensus building and influencing part. I think that is a core skill that any product manager needs to have. That is going to be, again, ubiquitous across any PM role that you come across. Last but not least is business strategy. I worked on a product in AWS, which was a market leader for many years, but then got disrupted by open-source technology. How do you respond to that? How do you pivot your product strategy? How do you find a niche, or how do you change your product strategy to be able to still grow in over against overwhelming market odds, right? Or do you actually say, no, this is a waste of resource.  You need to have a good sense of business strategy, product strategy, understanding the competitive landscape, and monetizing. At the end of the day, the goal is to make money, right? So, as you grow as a product manager, more and more responsibility of the product strategy lands on you, and that's a core skill that you need to have to succeed as a product manager. Finally, I would say decision-making is pervasive through everything. You will need to make a lot of decisions on a day-to-day basis. You need to be comfortable with making high pressure, high impact decisions, sometimes without the right amount of data. So, you need to be comfortable with ambiguity. And you need to build your resume by highlighting all these skills, right?  Highlight those things. Show experiences where you might have influenced somebody, even if it was not product-related. Where you should come customer empathy, where you showed your data skills. If your resume represents these six skills throughout, you know, the many bullets that you're going to put there, you have a good chance of being noticed, if you, you know, and that's what you should be focusing on rather than titles. So, next up, how do you get product management interviews? So, somewhere, sometime during my MBA, I built this mental model, which I can try to put in, in graphics here, which I believe has never failed me and I don't think will ever fail you if you diligently follow it. Now, what is this model? I call it the seven habits of highly successful job hunters. Think of it as a marketing fund. At the top of it is, is awareness, right, where it's your job to reach out to as many people in the relevant companies and the relevant roles. And, and even if it's a cold email, even if it's a LinkedIn email, reach out to them, tell your story, show your passion for why you want to do product management or why do you want to work on those companies. And some of them will respond, some of them will not respond. That's okay. You only need one solid lead, right, but you have to reach broadly to be able to get what that one solid lead, that one person who's your advocate and who will vouch for you and who will fight for you, right. So top of the funnel is I think LinkedIn, cold emails, cold reaching out and just being persistent at it. Next up is, is coffee chats or informational interviews, as most MBA calls it, call it. That's about building relationships. You can get a cold referral by saying hey, hey, I want to apply to your team. I want to apply to this role as much as you may. Can you give me a referral? Most people will because they get referral bonus. They lose nothing by giving you a referral, but that's not enough. They're going to do it for hundreds of people, right. So you want to build relationships.  And the way to go about it is, when you've reached out on LinkedIn and somebody's responded, you ask for 20 minutes call. You ask for a coffee chat if you can meet in person or do a video call and tell your story, understand their experience, learn from them what, you know, that role looks like in a company and then tailor your resume and tailor your story so that you have the maximum chance of convincing that person to fight for you. And then yes, at the end of the day it comes down to referrals, but warm referrals, not cold referrals. You can follow seven steps to execute this, this framework. Make a list of companies that you want to apply to. I built, I built Excel trackers both during my MBA job recruiting and then later when I was thinking of leaving Amazon. And they helped. Here are the two 10 companies I want to apply to. Here are the 30 people I've reached out to in them. These are the people who responded. This is what the conversation was about. What is the next step? Do I need to follow up? Do I need to send them anything? Be ruthless about that tracking and staying on top of your networking, right? And Excel is a great tool for that. Reach out to PMs and adjacent roles in those companies via LinkedIn or your personal network. Once you know which companies you want to apply to, find people who are your second degree connections or third degree connections on LinkedIn and reach out to them, tell them your story, share them why you want to apply and then ask for their time. Ask for 10 minutes, 15 minutes, 20 minutes to have a genuine interaction with them which is non-transactional. Do coffee chats, do informational interviews to understand the role the company and the teams that you are applying to. You can learn a lot. Half your interview prep can be done right here if you do this right. Builders you may that marries your experience to the research and feedback that those people have told you. For example, Google puts a lot of emphasis on working with people on being entrepreneurial and being impact-driven. I like those things right whereas Amazon is more driven towards the 14 leadership principles like bias for action and other things. I like that if that's where you're applying. Build relationships, follow up, find out how you can help them. For example, you applied somewhere you didn't get through but now your friend is looking for a role in the same company. Therefore that person to your connections. Build a long-term relationship with those people you never know when and how that might help you. I did an internship in Amazon when I was in MBA and my manager became my mentor and then stayed my mentor for many years and even today if I need to make a big career decision I go back to that person. So don't treat these conversations as transactional. Cultivate advocates if you don't have relevant experience impress them through the right attitude and commitment and your passion for the product roles and product management and their company. And finally, yes, please get warm referrals. Don't do portal resume dumps. So now you've got multiple interviews. If you did the previous seven steps right I can guarantee you you will get multiple interviews. Now how do you prepare for them? I'm not going to cover frameworks and specific questions because I think there are a lot of good resources and books out there who talk to it and I collated that into a LinkedIn post a few months ago and the link to that is on the slide. Feel free to refer to that link look through all those resources. I think it's pretty exhaustive list there. But I want to broadly speak about what are the big buckets of things that you can expect in an interview in a product management interview. First up is product questions. What do they look like? They look like product design questions. For example, design a disaster recovery app for the government of the United States. They could be product strategy questions which is hey I'm thinking of launching Amazon Fresh in China. Should we or should we not? Last are technical interviews which could be something as simple as what happens when you type www.linkedin.com in your browser to super complex design questions or system design questions depending on the role that you're applying to. My tip here is have frameworks for each of them. There are books that give you brilliant frameworks strive to build your own because I think interviewers kind of already know what frames are frameworks are out there so if you can come with some come with something in genuine that's bonus points but you must have frameworks to tackle these type of problems so that you can structure your answers and you can cover all the main key points that you should be covering. Next up is behavioral stories. These are the kind of questions like tell me about about the time where you did X, Y, Z. These are very common in companies like Microsoft in Amazon and some of the startups as well you'll see these kind of questions a lot. My tip here is think and prepare in advance. Think about the 1012 most high probability questions that you're likely to get like examples of where you work with engineering where you dealt with ambiguity where you were building something from scratch right and write down your stories beforehand so that you're not forced to think on the spot last minute that's not the way to go about it don't take behavioral lightly they are probably as important if not more as the technical portion of your interviews. A good format that I use for behavioral stories is edge cars sorry it's not catchy but it's a good framework edge stands for headline start with the headline here I'm going to tell you about a time where I did this C is for context set the business context set the challenge what was the challenge that you face right give them the context they need to empathize with your story third is action what did you do why did you do it right result what was the outcome and then S stands for so what which is what did you learn right what was the insight that you gained from this experience that you will bring to our company don't forget that part now the last is understanding the company culture and research I think this is understated people don't spend enough time doing this because they feel hey it's a tech company it's a product question it's all I'm going to be saying I don't think so it's very important to understand what does the company mission stand for what does the CEO's personal work ethic is what does the product role specifically in that company look like how does product manager work with engineers how do product manager work with other teams is it a more collaboration defined company or is it more you know top-down goal defined company is it entrepreneurial or is it more strict you know strict rules and and path given company you by the time you actually reached the interview you should know enough about the company as the person interviewing you you need to immerse yourself in the company culture to be able to feel comfortable enough and ensure your passion and show the why you want to join this company right now how do you go about it some tips is study their career pages most companies give away the answers to most questions on their career pages like the amazon leadership principle and the amazon flywheel if you don't understand it don't go for an interview with amazon googliness you've probably heard this now if you don't understand that go don't go for an interview with google you're missing out on the key culture read their 10 case which is their annual reports and then the commentary that goes with it they most companies will tell their business strategy the risks and their threats in that commentary that goes with the annual reports please read them understand them watch youtube videos of the CEOs if you're applying to microsoft watch satya nadella talk about microsoft and azure and the company strategy and what he believes in and leading with empathy he's giving you the answers to most interview questions right there look at their conferences right try to attend them if you can if you have that much time one last thing that i would leave you with couple of things i would leave you with on this slide is do some mental exercises throughout your interview prep if you're applying to a company pick a product think through hey why is this product built this way what is its monetizing strategy what are its biggest threats what would you change about this product from marketing or from a feature perspective and lastly read read read read tech crunch read verge articles about the companies that you're applying to a lot of these articles do very good critical commentary on the companies think about it think about do you agree do you not agree and that will give you the confidence and the know-how about the company to go and interview with with confidence so the most important thing though about interview prep is mock interviews practice practice practice record yourself in your mock interviews go watch those recordings because nobody knows you better than you so when you watch your behavioral answers which are recorded you will definitely find problems you will find better ways to represent your stories once you see yourself deliver them that's hard to do unless you record and see yourself because you can't answer and have mental awareness of what you're answering at the same time that becomes too tricky so please do mock interviews record them watch them and learn from them lastly you got a few interviews you got a few offers you are feeling happy now you have the big decision of where to go there's a good video on youtube called price of admission which I really like you should check it out it's not geared towards career advice but I think that advice that that video is giving is pretty valid for career as well it's called price of admission please check it out now I've categorized some big questions that you need to answer to be able to pick which product you want to join first up is consumer versus B2B tech think about your natural skill sets are you good at UX design then maybe you should do consumer tech are you good at driving marketing and product adoption then maybe growth PM roles are better fit for you are you passionate about solving deep technical problems and enabling enterprises then maybe cloud PM is a good role for you so think about your skill set and how that applies to the role options that you've got next up is how important is the product to the company's success I think that is very important you want to be in the high growth part of the company where it's called leadership focus that will make it easier for you to win internal prioritization battles when you know it's the same engineering team that needs to either work for your product or somebody else's product if we know that the CEO's top down mandate is to grow your product it's going to be easier and it'll also accelerate your growth the first rule of battle is pick where you fight this talks to that how is the leadership of the org what is the culture like what is the VP believe in how is the manager do they incentivize try and error do they how do they make promotion decisions right those are important questions because a good manager will make or break your career and that's probably true for VPs as well right you can use blind as a common tool where people look at feedback but I think it's a little bias towards the negative so I would say go back to the people you spoke to during your informational interviews and coffee chats tell them here I got an offer in this team what do you suggest do you know anybody in that team what is your opinion either from the inside or the outside share your options with them get their feedback use that to make this decision as well how do you fit the company's mission and culture I think this is pretty self-evident by the question itself one example I can give you is I will never work for Meta or Facebook because I disagree with the company's values and don't have a passion for it so find what are you passionate about find what are you or your values that'll help you rule out some companies straight away what skills do you want to build I again give an example from my story which is when I was at when I was at MBA and I had multiple options between product roles I picked AWS because it was going to be a highly technical role it was going to be very challenging and I didn't have the technical skills so I struggled for six months for sure but two years down the road now I feel I have the technical principles and the foundation built to go do any product role in any field going forward so it was a little bit of pain for the first year or so but because I knew that was my weakness and it was something that was going to become a hindrance in my long-term career I went and tackled that hit up then lastly large organization versus startups well as you move from large companies like Google Microsoft to start-ups the level of ambiguity increases and your scope of work also increases so figure out what you want to do do you want to start or do you want to do a highly ambiguity high ambiguity role where you won't have mandates from top down where you won't have a narrow or well-defined scope of work then yeah maybe startups have a good place to go right so that's everything I wanted to talk about feel free to hit me up on LinkedIn if you have any follow-up questions I think product management is a great place to be I personally have loved the transition into product management having done various roles before that Microsoft is hiring so if you're looking for jobs once again hit me up on LinkedIn thank you and thanks product school for setting up this webinar I appreciate it


Hey there friends thanks for checking in today we have another is this pistol still relevant video this series has been a lot of fun and I'm super excited to share with you what I have to show today asking the question is this pistol still relevant the last time we did this I featured the Kimber EVO SP striker pistol now this was the pistol that replaced from Kimber the solo and that was known to be unreliable and Kimber said we have it right with the EVO SP this is the one that is replacing the solo and you should check it out because it's way better and it can feed fire and eject all types of ammo the problem was that it was very expensive and that's always an issue when shooters think that they're overpaying for a handgun they tend to drift away from it they said I don't want anything to do with it there are other choices out there and essentially that's the feedback that I received they said nice looking gun single stack seven round mags 3.1 inch barrel I get it you know aluminum frame it seems to have what many shooters think is nice for the features but for 650 bucks way too many choices out there to worry about that handgun like it's not even significant at that price and we know Kimbers are very expensive and they always been very expensive they make beautiful guns but they cost way too much today we're going in the opposite direction with a cheap little handgun that has a very rich history began in 1970 and it is Raven Arms I'm pretty sure most of you have checked one of these out perhaps you still own one you've at least shot your buddies this is chambered in 25 it's called the Raven Arms MP 25 but not this one see Raven Arms was developed in 1970 and it was a very cheap semi auto six round magazine chambered in 25 ACP it was a pocket carry gun with a two and a half inch barrel and it was somewhat reliable people will argue that point is that even reliable it's not reliable it's not significant in my eyes but if people would pocket carry these left and right you could pick it up at the local hardware store for 40 bucks and many people had several of them now you know this as the Raven Arms MP 25 with the blue slide wood grips and that was the pretty much the signature series for many years and then what happened was in 1990 there was a fire at the Raven factory and they sold off the design and the patent to Phoenix Arms and that's what this is and they came out with the stainless slide and frame and these fake plastic ivory grips kept the six round 25 ACP magazine and it's called Phoenix Arms and it's this one was produced out of California has a little thumb safety right there you have to click it up there and then sweep it down very much a pocket gun it has fixed sights it worked okay it was inconsistent throughout the years people would say you know I love it I remember a while back I said that gun is not very significant I don't even consider it part of my collection and people said what are you talking about you're nuts it has a very rich history and it's a centerfire gun compared to the rimfire 22s and it's an arguable point what is more effective and I would argue the 22 is but you're dealing with rimfires versus centerfires anyways the Phoenix Arms or the Raven MP 25 it would be considered a little pocket gun maybe a under the table in a poker game kind of gun it is not expensive many replaceable parts out there and shooters would say there are replaceable parts left and right because that's what you needed to do it is very breakable made out of a zinc alloy not the toughest thing in the world but very small would arguably get the job done depending on what you were doing but back then many people they they just dropped the gun in the pocket well they still do that but the 25 with fewer people armed back then at least carrying we think would would be effective so is the Raven Arms MP 25 or this right here the Phoenix Arms Raven is it significant in today's world or has it lost its value this would be considered the high point of its time very inexpensive people would own several of them it known to be just thrown away and pick up another one because is cheap ammo today is very expensive 25 acp you never hear any manufacturer creating much in 25 acp in fact you're hearing manufacturers discontinue handguns in 25 acp but the Raven Arms have you shot it have you checked it out do you own one and if you do is this pistol still relevant yeah if you like videos like this please subscribe and share i always appreciate thumbs up button thanks for watching and you guys be safe


Hi and welcome to the session. Today we will learn about equivalent fractions. Equivalent fractions are those fractions which represent the same part of a hole. Also, in proper fractions, many equivalent fractions to find an equivalent fraction of a given fraction, we may multiply or divide both the numerator and the denominator of the given fraction by the same number. For example, let us find out the equivalent fractions of the fraction 3 by 5. So now to find out the equivalent fraction of 3 by 5, we will multiply the numerator and denominator of the fraction 3 by 5 by the number 2 and we will get 6 by 10. So here 6 by 10 is the equivalent fraction of 3 by 5, that is 3 by 5 is equal to 6 by 10. Now let us find out one more equivalent fraction of 3 by 5. So here we will multiply the numerator and denominator by the number 3 and we will get 9 by 15. So 9 by 15 is an equivalent fraction of 3 by 5, thus we have 3 by 5 is equal to 6 by 10 is equal to 9 by 15. There is an interesting fact regarding equivalent fractions.  So from this we can say that a into t will be equal to b into c and these both are called the cross products of this pair. So that means we can say that the cross products of this pair will be equal. Now let us move on to our next topic, simplest form of a fraction. To be in the simplest if its numerator denominator has no common other than 1. Now let us see the shortest way find the equivalent fraction in the simplest form. First of all find the xc numerator denominator and then divide the numerator and denominator by the xcf. The simplest of the fraction 8 upon 14. So first of all let us find out the xcf of numerator and denominator. So we have xcf of 8 and 14 is equal to 2. So let us divide the numerator and denominator by the xcf that is we get 4 upon 7. So 4 upon 7 is the simplest fraction 8 upon 14. Now let us see what are like fractions. Fractions are the fractions for example 2 by 9, 5 by 9, 7 by 9 are all like fractions. Next we have unlike fractions. Fractions are the fractions with different denominator. For example 2 by 13, 7 by 15 are all unlike fractions. With this we finished this session hope you must have understood all the concepts. Goodbye and take care and have a nice day.


Okay, so hello everyone and welcome to our already 37th web seminar of the series of these Latin American webinars on physics My name is Nicolás Bernal and I'm from the University of Antio Nariño in Bogota, Colombia And it would be your host today So our speaker today is Enrico Nardi, so we're super happy to have you Enrico from the ENFN Frascati in Italy And Enrico will talk about action physics. I please the window for preferred action action models Right, and so I remind that you guys can be part of discussion writing questions and comments using the YouTube live chat system via Twitter So now I can hand you over to Enrico Okay, so Nicolás, thanks Thanks for inviting me to give this seminar. It's nice nice experience. Hope everything will We work properly So just confirm to me that you see the mouse and you see the slide Yes, perfect So that's a brief outline of my talk. I will give a short review of what is called a strong CP problem Just I will browse through the various experimental searches They're going and the searches that are planned for the next of next years. I will describe main main types of action models There are Generally, they noted as a KS2Z or QCD or a dronic action models. This refers to some single type and a dyno fishlers red Nicky's it means ski the FSZ actions, I Will describe What type of dark matter can we get out from action? through the misalignment mechanism and Then I will move to the original part of the talk Which is a description of the window where experiments should look for for actions so the phenomenologically preferred action models and For the dronic action and also I will add something for the DFS as the action models Where should we look for for the FSZ action models? So the strong CP problem QCD is defined in terms of two dimension as parameter not one, but two. They are not predicted by the theory So measurements yield a number which is pretty reasonable for the strength of the strong interaction The measurement depends that the energy where it is performed But is a number of order one unit unity roughly for the second parameter Which instead gives the amount of CP violation in strong interaction We have only an upper limit, but the upper limit is so tight 10 to the minus 10 For a parameter, which you would also expect is order one That the situation is really uncomfortable and we would much prefer if for some reason this parameter Is in fact zero vanish So I say that this parameter theta bar described by the amount of CP violation In fact, we can write the two sources of CP violation in the QCD Lagrangian one Is given by complex masses for the quarks for simplicity. I take just one copy of left and right handed quarks and one Is a a topological term theta multiplied by This combination ggt that was on the proper coupling which under integration in the 4x Is is a number is a topological In variant of the gauge field configuration So in the action you should read the second term as n time theta now These are not two independent sources because You can perform a chiral rotation on the mass term put the mass to be real And since the transformation is anomalous and the anomaly has Precisely the the structure modular factor of two Then you will have a shift of this theta in theta plus two alpha If you kill with a alpha transformation this this phase The other option is that you make disappear this term by putting everything inside a complex mass the relevant Point is that just the difference between theta and theta q is the physical quantity So there is just one one physical parameter that violates cp formally You can obtain this term in a beautiful construction due to fujikawa in 79 Where you can study If the measure of the path integral is or is not invariant under The chiral transformation you find that it is not invariant and when you properly regularize with the gauge invariant procedure You get that the transformation induce precisely this term that is written there Just a side remark now Theta different from from zero implies among other things and not zero neutron electron dipole moment How how big should be this quantity it's basically The size of the neutron so something of the order One fermi times a loop factor And times the value of theta So it's very simple At least on the basis of dimensional analysis you you expect this value multiplied by theta bar. You have This limit so ten orders of money to lower than what you Would expect which forces you to set these limits or there should be a an absolute value, of course Noted that this problem. This is a small number problem Is qualitatively different from other problems that we have in the standard model For example, theta bar receives the first finite log correction at order alpha square. This means that if you put by hand theta To 10 to the minus 10 it remains stable. You don't have a natural problem. You don't have a technical problem with natural This is unlike a m square h Which is quadratically sensitive to a cutoff scale And it is a very small number if you consider it on the scale of the plank of the plank scale Unlike the yukawa couplings of the first generation, which are also small even not as small as theta, but Not certainly not a border one Theta bar it evades explanation based on environmental selection So you cannot appeal to the idea that Why why so small otherwise the universe would look so different from what we know And I mentioned this paper from lorenzo valdi where This argument was was explored in some depth So you see, uh, it makes sense to study the The issue about strong cp violation independently of other small number problems Solution basically they are classified in three types of solution One is a massless quark. This is the simplest solution If you have a one massless quark, then you have an exact chiral symmetry So a theory with any value of theta can be made equivalent to a theory with a theta equals zero The only candidate For massless quark was until maybe 10 years ago So they have quark, but nowadays we know that Emma is different from zero by more than 20 sigma. So this is no more possible solution Another class of solution they impose theta equals zero by imposing cp conservation Of course cp is violated in weak interaction So then you need to do something to generate the phase of the ckm matrix and also to generate other phases that Might be responsible for the baryon asymmetry of the universe We know that we need cp violation for the matter anti matter asymmetry So this type of solution typically have a high degree of high tuning and very elaborated construction because If you allow for violation of cp in one sector of the theory In some way this with we leak in all sector within all sector via Loop corrections and we have still to fight with this number 10 to the minus 10 Moreover These type of models don't have a single unambiguous experimental signature This is not a theoretical issue is an issue that makes more appealing a model where you can tell what you should see To prove that the model is correct The last class of solution rely on the so-called pichet queen mechanism where you assume a global U1 symmetry It must be Spontaneously broken It must be qcd anomalous If you satisfy these two requirements, this is a good symmetry to solve the c in the strong cp problem spontaneously broken u1 implies An unbuggle stomboson, but since anomalies In an instant on the ground break explicitly the symmetry This is not really a mass less bone stomboson, but is what is called the pseudo bone stomboson It requires a tiny mass This object is known as the axiom. The axiom The u1 symmetry is reflected On the axiom transformation properties as a shift symmetry is written here Eventually the axiom will couple to everything only derivatively as a good and non-bou custom boson, but non derivatively to the Anomalous term because this is the explicit breaking now When you do things properly and you work out the potential for this type of of Scalar scalar boson You find that is a equipped with a periodic potential which brings The axiom writes to the place where in the background So its vacuum expectation value must cancel exactly a theta bar In few words, so this is a generally say that described as the theta becomes a dynamic parameter with space time dependence and is a driver dynamically to zero. It's the minimum of the potential Axiom models So the first attempt was straightforward. Well, identify The axiom with the phase of the higgs in a two-higgs doublet model Two-higgs doublet model because that's the only way you can enforce a petrified symmetry with one one-higgs. You cannot However, in this case the vacuum expectation value is the electro weak Value is written here and this implies that The axiom interacts too strongly with Matter the standard model particle. So the solution was ruled out quickly after being proposed You need to require that the vacuum expectation value of the axiom field of the scalar Is much larger than the electro weak web. So much larger than the 100 gv scale something around 10 to the 9 10 to the 12 That's the the right scale Those models are all together they notice invisible axiom models because the axiom interacts so weakly so weakly That is very difficult to detect it And here we have two types two classes of models. One is as I mentioned at the beginning DSFZ axiom Where the standard model works and the higgs are charged under the petrified symmetry You need two higgs doublet and one scalar singlet This scalar singlet can get a large level as large as you like without affecting the phenomenology Of the w mass and z mass The standard model leptos can also be charged in some model in other models. They are not Another option is instead to leave all the standard model particle Chargeless under the petrified queen and introduce new Firmium Charged under qcd transforming under the the su3 color and Again a scalar with the petrified queen charger. So in this case the complete sector of the Petrified queen type of solution is Is made of new particles Regardless of the fact that these classes seem to be quite different And there are some crucial model independent features One is that the axiom mass Is always inversely proportional to the To the petrified queen breaking scale Keep in mind if you wanted these simple relation approximate relation Where m axiom is equal to the pion mass Multiplied by the ratio between f pi. So this is 93 m e v and f a which is Around 10 to the time g v and you can recast in this way. So the typical Mass expected for the accent is very small Is around a million electron world and even less All axiom couplings also go inversely proportional to the f parameter So it's very useful in experimental exclusion plot to betray f For the axiom mass. So you can get plots where you have axiom couplings And uh As a function of the axiom mass which are the relevant parameters for long-term energy field knowledge Here is a short description of the axiom landscape. So possibilities in the first upper line You you have the axiom mass And below you have f a this is a capital f, but it's the same F a normal f there So we have exclusions from axiom production in the sun from the supernova From cooling of our giants Here from from uh, uh, the serna action search telescope and basically below 10 to the 9 Or 10 to the 80 if you want to be conservative uh as a value for f or above 5 in 10 to the minus 2 electron volt for the axiom mass The action is excluded on the small side we have searches from A dmx a dmx is uh, um, I will describe later, but he's searching for a dark matter in the form of axioms And uh, uh, it ranges the limit range around these values 10 to the 11 or so Uh, a strong argument is that axioms contribute to the dark matter and you cannot over close the universe so for natural values of the Parameters this region above 10 to the 12 is excluded. There is a still some controversy because of these it depends on on how how the topological susceptibility of qcd Goes with temperature. It's a very delicate and complicated argument typically what you get is between 10 And 5 in 10 to the 11 and few in 10 to the 12 depending on on what is what is The detail of your simulation typically on the lattice So I mentioned that axiom can give dark matter In fact, they can can give dark matter in three different ways one is through Thermalization so axiom can be also produced the interaction Interaction some amount of axiom is always produced the interaction the heavier the axiom And the the the heavier the axiom the Larger it's coupling the more easily you produce a thermal component Uh, another way is uh from a decay of topological defects Axiom physics is plowed by uh topological strings and topological domain walls Which eventually have to decay and can contribute to some axiom population But the most beautiful mechanism is what is called misalignment Which I will describe so as long as The temperature is below the breaking of the pechecum symmetry and above qcd We have a spontaneously broken theory with some massless constant bosons and a flat direction which is The minimum of this potential is represented here The axiom equation of motion Is described here as I said it has a periodic term Without a mass you see that a is constant and the solution of this equation is for A dot equal zero and a equal constant As soon as you go down with the temperature and you approach a lambda qcd then the potential becomes sensitive To the explicit breaking explicit breaking gives an explicit mass and these terms start becoming important Once this term dominates this one Eventually you end up in in an undamped harmonic oscillator so Keep in mind that uh at the scale of lambda qcd the Hubble parameter is 10 to the minus nine electron So it's already very very small So as soon as the mass starts going up No, because of the qcd effect you immediately fulfill this equality And a second not a second or an instant after This mass dominates And because this goes down as a temperature to the second power while the mass goes up As temperature to the eight at least is in a in a diluted gas instant on gas computation The potential tilts in this way The flat direction is lifted and and the axiom start Oscillating assuming that it was not accidentally sitting really here in zero Any other place even the axiom was sitting it will start rolling down and up down and undamped You can show that the energy stored in this oscillation Scales with the scale factor of the universe as a to the third power So it behaves as called that matter. That's the crucial point. It doesn't Also, the axiom is so uh, so light It doesn't scale as a temperature to the fourth as radiation, but as temperature to cube Uh, I will skip this And go to search strategies and current limits So astrophysical bounds are typically very strong and they can constrain coupling of the axiom to The photon to the electrons in case your model Allows the axiom to coupling to leptons to couple to leptons and to the nuclear we always have this copy and you see that this is The master of the model and the The limit on the coupling from the supernova implies this scale. So typically people assumes between five in 10 to the eight And uh, and below the 12 as I mentioned before So laboratory search techniques, they are virtually all sensitive at least until today to the axiom photon coupling They are of three pipes Light shining to the world Helioscopes we see a bit in detail So axiom typically coupled to photon and you can imagine that you have a magnetic field and axiom coming It converts and a photon coming it converts into an axiom It goes to a wall Again, it converts into a photon. So you pay a axiom photon coupling here axiom photon coupling there The square to get the rate. So a factor of g to the four To the fourth power. So that's an epictorial image of you see You shine a laser in the magnetic field Something is going through and some of these axiom that are passing through are reconverted Helioscopes they are looking for the axiom in the form of a dark matter. So if we have axioms oscillating around With a magnetic field We can hope to convert the axiom into the photon. So not the photon into the axiom, but the axiom into the photon the typical power in a cavity Absorbed by this conversion goes as the volume as the square of the magnetic field as a number of in the local patch of the galaxy and Multiplied by a coefficient, which is a quality factor You need to tune the cavity to meet the resonance condition. So just to tune you search for a specific mass of the axiom at each round of your experiment and then you tune you change the volume So you you change and modify a bit the resonance condition or you put gas you modify the apparatus Helioscopes The axiom that met our experiment at the university of washington is presently the most sensitive type of experiment of this This technique Helioscopes axiom are produced in the sun if they couple to photon and are emitted So the the sun is a potential source of a copious axiom flux You just need a magnetic field hoping that you can reconvert The axiom into a photon since the typical temperature in the sun are around Few kiwi what you get are photons in the x-ray band helioscope, there is The ongoing third generation experiment is cast ongoing and serma. It gave very good result and new results are expected for the summer and a project which hopefully will be founded but is still Going into an advanced state of rmd is is the axiom cast is using a superconducting magnet that was a prototype for lhc while For yakso that will be probably located in daisy Steel has to be decided the the magnet is is brand new And this is somewhere 20 meters object That has to follow the sun Now I go quick here just to show you some of the new proposals. So this is a princeton mit This is university of western australia This is in korea cool task in korea they even Founded an institute which is called for axiom and precision physics Mad Max Mad Max is mainly a german proposal Casper is in the united states. So this is very nice experiment, but I have no time to describe it This is an university of florida quax is is one of the i nfm proposals in lenaro in italy So you see with so many So many Proposal you have to tell possibly to the experimentalist where You should search for axiom where you expect to see the axiom Usually there was a window which is depicted here. Uh, that was in some way a bit arbitrary because It was centered on a reasonable value and The the width of the window was just taken from the literature from various models in the literature plotted here so The window from axiom models was plugged in some in some sense, but some arbitrariness in it's It's proper definition So now is our contribution in the last few minutes to To to few possibly So when we decide is okay take the draw the axiom model and they have a new quarks And they can see to these new quarks In representation of s u2 and u1 And see if they give problems. So what type of problems they can give I go quick here Basically if they would give a problem if they are stable we would have strong interacting Relics and strong interacting the relics are an issue in cosmology a serious issue Second if they sit in too large representation of s u2 Or or s u3 they can induce land out land out poles In in the running of the gauge couplings, which is a real unpleasant feature So we classified all the possible Cues that are allowed to decay into standard model particle fast enough That there is a limited number when you impose also The condition that there will be no land out poles in the gauge couplings below the plank scale You are left with 15 possibility So here also you have to go fast because I think I have half an hour Which is almost gone But uh The result is Okay, here are described a bit more cosmological constraint. You see what happens If the axiom if the q the exotic q decay before 10 to the minus two seconds No problem After 10 to the minus two seconds, they will start affecting big big bag of nuclear synthesis Longer After big bag of nuclear synthesis, they start leaving uh non-termal radiation that affects Recombination and leaves an imprint in cnb radiation After a combination if they decay they Contributed to the diffuse gamma ray backgrounds that has been constrained by Fermi If Eventually you say they have a lifetime longer than the lifetime of the universe So they do not affect all this type of phenomenological Events in the history of the universe Well, in generally they Contribute too much To the energy density of the universe. Uh, as we say they over close the universe So the limit is here 10 to the minus two seconds. They Are Forbidden not really rigourously forbidden, but let's say it would be unpleasant to have around particles that live longer than that Strongly interactive part here. There is a detail of the contribution To the dark matter. So this is a longer 10 omega H square omega of this heavy quark h square This is the limit which is the dark matter as measured cosmologically You see that If the annihilation of the quark is a free annihilation Basically, they cannot be heavier than maybe for tv Otherwise you enter in the over closure region This little corner might be well Excluded soon by lhc sooner or later. Maybe in the high There are other mechanisms to annihilate the qs bound states.  So the truth is in the middle But we have reason to think Motivated reason to think that the answer the real answer is much closer to the free Annihilation lines than to the bounded annihilation line. Yeah, there was a scheme of how Annihilation the bound state could could could proceed so That's the first election criteria. It forces us to assume that they decay through uh operator of dimension five or at the three level dimension six was already given to long lifetime and then the second criterion is that the The beta function should not reach the The explore should not drive the coupling to explode below a scale. We take it 10 to 18 gv just to avoid comments or maybe objection because it's known that the quantum gravity contributions tend to delay The occurrence of land outposts the sign of the contribution is known But at 10 to 18 gv you can expect that those contributions are still negligible So That's a list of the model where here you have Of the possibilities not more than the possibilities. So here you have The representation triplet of colors sextet of colors eight of colors 15 of colors This is su2. So we have doublet triplets Doublet's uh, and then this is a hyper charge Um, so these models are phenomenologically free of the two types of problem. I have described For this type of models you can compute the Axiom photon photon coupling, which is parameterizing in terms of this Or these numbers these numbers are related to the anomalies electromagnetic and color anomalies of these uh heavy quarks So you see the possibilities are restricted When you plot, uh, uh the possibilities you have The one with the weaker coupling and the one with the stronger coupling to the photon And you plot these on um on your mass Axiom photon coupling diagram And you see that you have a window which is now phenomenological motivated, which as a good overlapping with What was assumed before And if you want luckily it it drifted bit towards larger couplings Of course, you are also allowed to take more than one representation together Here we take only one if you take more representations You have more freedom, but you cannot take as many as you want because more representation You hit the land out pole condition at some point So we have computed the maximum allowed value of the axiom photon coupling Allowing as many representation you like subject to the condition that you have no land out pole We get a larger number which is here this described. I say the axiom photon coupling And uh, uh the window is here With two representation You can even also have uh if you want unfortunately Complete axiom photon decoupling at least within experimental errors so now you have to think that all this bench should be considered as a A phenomenologically allowed bend if you system only one type of quartz You are fixed in this stripe If you allow for two or three type of quartz then all this corner from here to there Is where your axiom model can sit I go quick to the conclusion Of course one say well, what about this the dfs at the axioms? Well for generic models which are natural which are reasonable You can show that you fall Always within the same band So this band eventually describes All natural axiom models that you can think of Um There are possibilities to get a larger axiom photon couplings and for this type of of models through a mechanism which Is a recent invention, which is called the clockwork mechanism but Which means that you besides the The scalax that coupled to uh to fermions you will introduce a Is a large amount of other singlets that do not couple to Directly to fermions just to boost up the the peche queen charges Okay, I will not go in detail because honestly, I don't like very much but You can add a scalar doubles up to 50 without violating The the condition of lambda poles So with 50 scalar doubles and each step each scalax connects to another to another to another to another you can announce Exponentially the charges and get to factor of these Ration that describes the axiom to photon coupling as large as 2 to the n So this is what is called a geometry It's called the exponential, but in fact is a geometrical enhancing of the coupling. So I reached the conclusions now The axiom hypothesis provides a well motivated scenario beyond the standard mode is by far The preferred type of solution of the problem, which is a real is a real problem a real serious problem Axiom models. So this is this transit the problem They provide an excellent that are met a candidate or thought they have not been invented for that This was a consequence that was discovered later And the nice feature is that There is an ambiguous test, which is just detect the axiom the tech the axiom measure his coupling today to the photon and then once you do that you you are confident That the strong cp problem is solved via a pchq symmetry maker and pchq mechanism theoretical developments are still ongoing. So There are some uncertainty that will be hopefully reduced as far as practice on the lattice theoretical uncertainty is due to model building also should be reduced And the final point is where does the pchq symmetry come from it is a global symmetry But it's not even a symmetry because it is anomalous So there is no reason why it should be respected by gravity not only gravity My other physics beyond beyond the physics of the standard modeling of axiom I have to mention that we are concluding a paper writing. So Lorentz or lucca diluzio Where I think we have an interesting proposal on how to generate Occidentally a pchq symmetry and how to protect the symmetry to basically any desired So that's would be would be I guess a relevant contribution to To fix to fix a disemplaison point in In axiom physics the origin of the pchq symmetry There is an healthy and lively experimental program Experiments are entering now the preferred axiom window for the qcd and for the the fsz axioms so still These windows have been only scratched a bit in the next years the intense experimental program will explore Large portion of this window New new ideas I put put forth for example casper. I mentioned before it's interesting Experiment because it wants to measure the axiom coupling to nucleons Not to photon. So even in our regional parameter space where the axon decouples from photon casper Would be able to get a signal coaxa coaxa is measuring the axiom coupling to electrons so again We have an experiment that is sensitive to axiom couplings Even if the axiom is decoupled from photon So until until today all the experiments are only sensitive to the axiom photon couplings is very welcome That we have proposals that tended to to to go beyond this So I conclude here Resuming what is the regional contribution of this seminar and what we have done is uh Defining An axiom for a window for preferred axiom models on the basis of precise phenomenological requirements And I thank you for your attention Okay, thank you Can you hear me guys? Yeah, I can so thank you Enrico for this super interesting seminar and now we should pass to the question round So, please, uh, let me remember you guys that you can ask questions to Enrico via the google's qna system At the webinar web page and also via twitter using the hashtag la wop So So I don't know if you guys have some questions From the audience Yes, I have a question for for Enrico So Enrico first of all very nice your talk and I wanted to ask you In this peche queen mechanism. Is it possible also to couple two leptons? Exclusively this action, right? Yes, it's mainly You can't I mean in the sense it's only possible because there is this qcd anomaly that perturbate The the potential I mean No, the the western Can be this mechanism be applied in the lepton sector is crucially No, no, no, you need the qcd anomaly That's the point you need a qcd anomaly because You have to cancel a topological term which has the same structure Then than the anomaly that's that's the thing, you know the thing is to have a qcd anomaly And the axiom couples to the qcd anomaly to the gg dual not to the dual dual term But in dine free share red niki and zit nisky models The the hicks carry a peche queen charge now You have the option to decide that the hicks Doubles that couples two leptons is not the same Than the x doublets that couple to the up and down quarks in that case It is not needed to be but The cheque in charges to the leptons and the leptons are a separate sector But if you want to to follow a more economical Type of models where for example, they are down type hicks Doublet couples gives masses also to the leptons Then since the down type hicks Doublet carries peche queen charges also the leptons have to check carry peche queen charges In that case it is unavoidable that the axiom which is composed by the Orbital models of all the scholars will eventually couple to To two to leptons. So in that type of models having couples to the leptons is I would say a natural expectation Not a not a mandatory expectation, but a natural one. You cannot build up a model that Is axiom coupling only to the leptons because In that case, you don't solve You don't solve the stronger qcd problem, but you can write models of that type in that case You you call axiom like particle So it's not an axiom The mass of the pseudo number was composed on doesn't come from the qcd anomaly. It's typically Put by hand as a As an additional term and you get a coupling only to the leptons. These are axiom like particles that are My opinion are less motivated than Than the qcd axiom Mm-hmm. So I'm a little bit continue with this question also with the what you mentioned in the in the conclusion about this experiment looking the The interaction with leptons and quarks What is more or less the the scape of these couplings with these fermions? in the sense because for the Gamma gamma axiom is more is a value doesn't more or less motivated by if you want to couple tag matters or like this, but The natural escape for these other couplings should be more or less the same order of these Couplings the photons all the couplings are given in In units of gv minus one This is because they are No, normalizable couplings and The scale is fixed by the inverse Of the symmetry breaking way so one over f as I tried to to explain F should be rather larger Larger than five in ten to the eight gv and not too larger Because if it is too large, uh, you would produce too much dark matter in the form of axioms from the misalignment mechanism So it's believed that it should be below ten to the twelve gv. So that's the window between let's say ten to the nine ten to the twelve gv and all the coupling go inversely with f measured so you see in these, uh If I can as we turn again the presentations You see the range here is Typically from ten to the minus fifteen ten to the minus eleven gv minus one Is uh depending on the axiom mass so, uh That's why it has been called the visible axiom because Larger the scale the more easily you can hide Here you go towards large scale in this corner and That's that's part of the difficulty To explore the parameter space at small masses And which means also small couplings here at large masses and large coupling. We are already doing a good job here cast And uh, and the yakso In the future we will just cut some slides Here is working, uh, admx with the resonant cavity type of experiments okay, these are is also A bit model dependent because it assumes that all the local amount of the meta is made up of of axioms So under this assumption they get these limits, but if axiom are only a partial contribution the limits would change Yeah, of course Yeah, thank you. So Thank the other question I guess Thank you Thank you riko. Yes. So are there more questions? I think I saw a question Okay, please go ahead learning some No, no, I said that I saw one appearing. I also would have a question, but there was already one by paola. I think Is that the one? Yes, yes, so paola Arias is asking you riko In this new axiom bands hole should be the dark matter window be understood And hope that we find a new course in the near future. So Uh, it's not Uh, it's not depicted here.  Yes. Yes So the region of uh, uh, where axiom could be A good cold dark matter candidate is around here Let's say I could tell you between a few in 10 to the minus six up maybe To five eight and 10 to the minus four That's that's a a good window if you go To larger mass and that is also to larger cap and you see this line Here you eat A limit where the axiom interact sufficiently strong That they get thermalized. So in that case axiom could be hot dark matter But uh, uh, in some way these Will be Sooner or later this part here would be will be excluded. I think In any case that that's nothing to do with the misaligned mechanism. So the the the window is around the axiom masses of 10 to the minus Five 10 to the minus four few in 10 to the minus six of few 10 to the minus four around here if you go to lower masses then Under some condition which I can mention and maybe if you want I can explain Um The axiom would be too abundant And they will over close the universe The reason is the following If you the axiom starts oscillating with an amplitude which is Typically a border f So the energy stored as is proportional to some power of f If f is too big, of course, you get too much contribution. So f big is in this corner Now there are possibilities to evade that One possibility is No, there is basically one possibility Which is imagine that accidentally the axiom Starts oscillating very close to its minimum. So you fine tune the initial condition You say the the the the axiom field was not distant something of border f from the minimum But in fact, it was very very close To the to the minimum by some some accident now This works only if the Pecèque symmetry is broken before inflation Because if it is broken before inflation, then a small patch which a single value of f gets inflated and All all the universe of the visible universe will have Basically one single value of the f of the axiom. So that's a new parameter in that case. This is really a parameter you have You have to measure You cannot play this fine tuning on the initial condition game in in post inflationary scenarios where the axiom Well, the the Pecèque symmetry is broken after inflation And and is not restored during reheating because in that case different patches of our visible universe and they have the size of Few few parses because the relevant scale is the the scale of 100 mev the qcd scale where the axiom start Oscillating around its value So in that case to get the amount of their matter is is correct to make an average over an angular variable and the average gives a value which is Square root of pi divided by three so the typical value of the amplitude of axiom oscillation is f square root of pi divided by three Which is a number of order one Or pi no pi divided by the square root of three, which is still a number of orders So in that case and no in post inflationary scenarios the limit 10 to the 12 gv is strict if you go to larger scales the axioms Axiom that matter from the misalignment mechanism of wood over close the universe so that can be safely ruled out Is a basically model independent way of ruling out those values under those conditions Okay, okay. Yes So polar you have a second question So she's wondering Suppose you have a discovery of an axiom like particle in an experiment that exploits Exploit the copy into photons and Supposed to have Okay, suppose you have a discovery of an axiom like particle in any experiment that exploit the copy to photons Yes, and hits into the region of these new action bands. So what information could you get from the new heavy quarks? well, and You see the the new heavy quarks are Heavy, but they don't have a bare masses The requirement for everything to work is that the new quarks get their masses from the wave of the axiom field So what you get? when you measure Presumably an axiom coupling and an axiom mass if you discover the axiom you will have a measurement of those two quantities then this would give you a value Of the vacuum expectation value of of the wave that breaks the pachet queen symmetry. So a value for f for f The masses of these heavy quarks are proportional to f modulo and yukawa coupling, which is unknown So under the reasonable assumption reasonable, I say also we see that Masses of the electron up and down are no way of the order of the electron we could have but With the theoretical preconcept that the dimensionless coupling should be of order one you would get an information on the On the mass scale of the heavy q. So this is what What you can get as an information? In another way you will measure also the value of f from the mass and directly the coupling The proportional the term of proportionality between the axiom photon coupling And one over f is given by the ratio of the electromagnetic and Qcd anomalies Which in turn depend on specific specific representations? So I would say that another information you can get from that measurement is What type of representation for the heavy q are ruled out and what types are are allowed If you have a very very precise measurement You would even be able to To pin down in which representation of the standard model group This heavy vector like q quark are sitting and this will be would be of course A great a great success just get into that point Okay So are there more questions? Lorenzo, maybe I didn't find how to end with the microphone. Yeah, I saw other questions. So that's why I was waiting Yes, a quick question So if I look at the plot that you're showing right now and rico on the It's interesting actually this is at least the second time that I kind of hear this story I mean not in your specific model But in general that it is easy to you know to build models that go in the you know lower right corner of your plot But it's incredibly hard to go the other direction Which would be the most interesting because it's where the experiments, you know could go Do you have an intuitive reason why also in your model like when you take this number of representations larger than one Can you explain intuitively why it's so easy to move all the way to cover the whole lower right corner of the plot? Yes, so uh, first of all It's not one model. It's the classification of All possible models that satisfy some phenomenological requirements So, uh, look, uh, just let me This precision look at this a combo shaped lines here Right one of these lines and there are more here that we did the knock plot Each one of these lines is a model So this gives you an idea of the model density in this density of models within within the band this band now if you go in this direction what There is a simple. Let me call it a theorem a simple theorem that tells you that If all the representation have a petri queen charge of the same sign then The maximum value Is the one the strongest coupling is the one you obtain with only a single representation So that's a simple theorem you say If all the petri queen Charges of the epic works are of the same sign. This is the upper bound You cannot as many more as you want. You cannot go But you have the option to put some with one sign positive and some with another sign, which is negative So why this option works? Well, it works because You see if I have here a different sign I can make this denominator very very small This is some type of effective coupling. So very small. It means this becomes big While you cannot go as much as you like to large couplings Well, because uh, this is a discrete set of numbers and you cannot get a sufficiently good cancellation And you cannot add More than free representation We have proved that with more than free representation of the one that we have classified You typically hit a land out pole. So you violate one of the conditions, no, you cannot add a 25 representation of strong interacting Quarks because you hit immediately land out poles in the hypercharging as you do in the color So that that's the reason why With these are within this approach, you cannot you cannot go More than that in that direction if you don't care about land out poles if you say that's Not something that I am scared about then You cannot many representation and you can you can go in that direction but we think that We are not saying Because if I All the models which are viable. We are more modest. We say the preferable Phenomenologically preferable access models. So models that are are viable without making Assumptions, no assumption like the access that the land out pole will take care about themselves about The coupling so the other region that's simply an accident. No, we We get that this combination or representation So you have a triplet of color a triplet of s u2 a cypher charge minus one third And also you have a sextet of color singlet of s u3 of s u2 with hypercharge minus one third If you compute e over n for this combination you get 23 divided 12 If you compute 23 divided 12 you get 1.92 Now you see that g a gamma gamma is e divided nc minus 1.92 with an error, which is four So we think this error These two representation give a complete and exact cancellation And this coupling is is consistent with zero We have found the three different Combination of a presentation that we think these errors are compatible with completely One gives a 1.1 1.92 1.94 another one and 1.95 another one note that There is no fine tuning. So once you choose the representation E over n is fixed. It's not that you are canceling by a fine tuning You can question if It is a kind of immoral To decide that you choose Precisely these two type of quarks and I would say yes, it's immoral But not fine tune. That's that's the relevant point. It's not an adjustment These are given by anomalies which are fixed by the representation. Yeah, very interesting And you get these already came with two quarks in two representation if you have a three and so on You get more cases, of course, right and these also You can have the similar situation also in the f s z models There are also the examples where you can get without fine tuning just with the choice of representation You can get Within experimental error. No, it's not experimental. This is a theoretical next to leading order chiral perturbation theory computation So it's not precisely It's not exactly an experimental error But within this error, let's say you get complete axiom photo decoupling And this remark is just to support the efforts of experiments that try to measure Axiom nuclear coupling or axiom electron coupling Because if by accident we sit on top of one of those Unlucky models, we will never detect the axiom photo Conversion Okay, thanks a lot. Are there more questions for the audience? Okay, there's one from Diego Restrepo Oh, they're concerning this Yes Say hi about the smash Hi, Diego from Enrico Uh, I'm concerning the smash model. So his question is Um Okay, concerning the question about the lepton sector in the smash models the scale of pechequeen pechequeen is defined with the scale Is identified with the scale of the siso A coupling between the peachy queen scalar and trinus is allowed You don't think you can comment on that? Which is a Mesh melon So repeat the quest, please So he's a concerning the question about the lepton sector in the smash model Oops, wait At the the smash model of ringvalde Exactly. Exactly. Yes The scale of the pechequeen is identified with the scale of the siso Such that the coupling between the pechequeen scalar and trinus is allowed So Could you please comment on that this question? And I No, I've not Not much to say. I'm not expert of that construction, but I wouldn't think there is a Nothing strange, you know, you couple The scale seems to be a good scale because 10 to the 10 is good for the siso and is good for for the art thing And uh, the The pechequeen breaking Scalar that can well couple to to the leptons like the trinus So, yeah, I believe that the construction is is fine It's fine. Of course, I'm trying to do one thing Two things with only one ingredient It's always I would say a good strategy because you can You can test or constrain the model from different approaches But uh, we didn't we didn't go in any Detail of that specific model. So my my answer is only a partial one just common sense Thanks Enrico. So are there more questions for the audience? So I guess that's okay. There's more questions. So Let me thank Enrico and all our viewers for this super interesting seminar Guys that in next week. So it will be april the fifth will have Marola Becky And well, I think yes, sorry talking about AMS the AMS experiment So we hope you have you guys next week As well. So thank you very much Enrico And thanks to all of you for for your attention and for following the seminar Okay, thanks a lot. Bye. Have a nice day. Ciao.