Welcome everyone to this new webinar, this time we will have Pablo from Simbestat. Pablo is his PhD in Valencia and then he moved for post-op position in Barcelona, then he went back to Mexico and he did a short post-doc in Unam. Now he is a researcher in Simbestat that is also in Mexico City. During the webinar you can make questions in the Google Hangouts or through our hashtag LaUkoP. Okay, then we'll have some people here in the room that will be asking questions after the talk. Please go ahead. Thank you very much Hermann for hosting this webinar. Also thanks to all the Latin American WayNars team. Now I will put my file on the screen. You should be seeing it now, is that right? Yes, now it's going well. Okay, good. So I'll be talking about Leptone Flavor Violation in a specific model that is called Simplest Little Fix Model. This work is based on a couple of papers in collaboration with my former PhD advisor for Porto Les and with Andrea Alami who obtained his PhD with advice by both of us. The first paper deals with Leptone Flavor Violating semi-leptonic tau decays. This is this one here. And the second one with Leptone Flavor Violating six decays. So for the second one you can just look anything in the reference. But for the first one we made an improved updated analysis taking advantage of these proceedings that correspond more to the things I'll be showing here for this tau Leptone Flavor Violating part. So having said that, I move to some delay. So I move to the motivation. Of course after the discovery of Nautilation, only this Flavor Violation is not measured yet in charged Leptone sector. In the minimally extended standard model with 100 neutrinos, signal is non-vanishing. You can see branching ratio at the level of 10 to the minus 54, but clearly unmeasurable. So anything you measure is clearly a signal of new physics in this type of process like new to gamma for instance. Experimental effort is ready to be admired. The upper limit is at the level of 10 to the minus 13 with very recent improvement. Here in this particular specific channel, of course, searches do not restrict to this particular decay channel and the hunt of new physics in Leptone Flavor Violation is a global effort in the collaborations and also in the decay channels involved. So in addition to this new to gamma, also new to three electrons, that is electron and electron-positron pair, is searched for also of great interest processes of new to electron conversion in nuclei. And even in heavy meson decays, one can search for these processes like at LHCV for instance. And here I'll be mostly concerned, as I told you, in semi-Leptonic Leptone Flavor Violating Tau Decays that should be at reach at bell 2 particularly. And also this Higgs Leptone Flavor Violating Decays that have attracted a lot of attention recently and there are Atlas and CMS are the ones trying to see this signal or at least to improve the bounds on that. So that's as far as the motivation for Leptone Flavor Violation then I go to the motivation for this particular new physics model that is simply the Higgs model. This is just recalling the old idea of composite Higgs models that dates back more than 30 years as you can see here. And the general idea is to understand the Higgs lightness as a result of it being a kind of pseudo-goldstone boson like a kind of pion in this sector. That's the main idea. So then in this class of models there is a scale of compositeness that is called F. There is hopefully a strong hierarchy between the electroweak and this compositeness scale so that the ratio of B over F is small enough and a perturbative expansion converges quite fast. And then Higgs potential is entirely partly radiative generated. These are general characteristics of these little Higgs models. Then in particular case Higgs masses look level generated and then one has specific signatures of the model as they are the appearance of little particles with masses of order of this compositeness scale for F so then it should be a few TVs for them. And everything is arranged in such a way that the quadratic the virgin contributions to the Higgs mass are cancelled in the way that the model is devised. That's the idea. Then of course the ultraviolet completion of the model is expected at some scale that we can roughly estimate at 4 pi times F. So this should be at least some 10 TV and it can be a bit higher. You expect some new particles at few TVs and then a more general theory at maybe 10, 20 TVs or a bit higher. Then there are two types of little Higgs models. There are product group models where you have the electroweak gauge group and you have N copies of that. In this case you need tiparity to really solve the little hierarchy problem on the Higgs mass. In our case on the contrary this is the simplest among the simple group models that are SUN times U1. So in our case we just have SU3, the simplest solution. This is the simplest little Higgs model and in this case you don't need to restore to any ad hoc symmetry like it is for instance tipart. In this case you can get this kind of solution to a little hierarchy problem without any additional synth. So that's the motivation for simple little Higgs model. And then if I go a bit more into the detail I told you that here we don't need any kind of additional symmetry. That's in principle nice. And since it is the simplest option so the electroweak group arises from the breakdown of just SU3 times U1. In this way we need to enlarge the SU2L doublets to SU3L triplets and corresponding RC-inglets. These new particles are highlighted with these red boxes that you can see here. So as you can see we need this kind of heavy neutrinos. This engage there here. And these are very important because these are the ones that in fact drive the electron player violation. This engage here, this heavy neutrinos. This is the corresponding singlet. And as you can see the issue here is not to explain neutrinomasis so for instance no refunded neutrinos is added. Then for the cores there is some freedom and one can choose an embedding that is anomaly free already or instead one can delay the anomaly cancellation to the more UV-complete theory. In our case we follow this anomaly free embedding but that's just a choice. And in this case the additional cores that are here are this capital D, capital S, capital D that you can see here for the left-handed components of triplet and the corresponding right-handed partners. Then you can search for variations from standard model induced by this simplest little Higgs model. For instance you can compare the rates of H to CC star to the standard model expectation and this is what you have in these plots here. So you see the one that is this line here and then you see the spread of the points in this kind of models. On the upper part these are little Higgs on the down part these are simplest little Higgs so you can see that. Generally there is more spread in simplest little Higgs models so larger deviations could be expected. In addition to this the data points are seen also here. This is Atlas, this is CMS for this particular ratio that I'm speaking about you see that they are well compatible with one and with still large errors and of course a big portion of the parameter space of the model is in agreement with these results. There are more comparisons in my additional material and you can look there for instance for H to gamma gamma compared to the standard model result and all these kind of things but in general I mean the model is naturally in good agreement with the current measurements on Higgs physics. Then I'll go to explain a little bit more in detail how the model works so we need two complex scalar fridges there are triplets under SU3 these are these phi1 and phi2 here and then you need these two because you need to have two breakings of the symmetry you need to have a global breaking and also a breaking of a local gauge symmetry this is why you need at least these two complex scalar fields so the basic mechanism of the symmetry breaking is summarized here so you have two copies of the group and then only the diagonal part is gauge so there is the breaking of the global symmetry on the one hand and as a result of this you get the Higgs the well-known Higgs degrees of freedom and in addition this a singlet this hitter could play some role in for instance in that matter and this is discussed in these references here and then of course at a lower scale this undergoes electro-higgs symmetry breaking and is the well-known standard model so this as far as the global symmetry is concerned then in addition you have the breaking of the local gauge symmetry and as a result of this breaking then you get you're breaking five generators so you get five additional massive gauge bosons heavy copies of the W and C bosons that are in red here and then this additional boson that doesn't play any role in our study so the most important things here are these heavy gauge bosons W prime, Z prime and also it is of overall importance this heavy neutrality here because with this we have the left and right relating effects we are discussing so I think that's enough for the introduction of the model then I go to discuss the phenomenology so in the first part I'll be talking about this semi-leptonic lepton-flavor-relating tau decays and as I said the analysis in the paper is updated in these procedures of the tau 16 conference so again I'd like to stress how impressive the experimental effort has been in the last year so from Clio to the B factories we have had an improvement of some two orders of magnitudes in the main decay mode so lepton into another lepton and photon lepton into another lepton and a pseudo-scalar or instead of the pseudo-scalar a scalar, a vector and we have also the strategies of a lepton into three leptons and you can see the different points depending on the mode generally two orders of magnitudes of improvements in Clio to Bobar and Bell now we will have up to two orders of magnitudes further improvement from Bell to right as it starts acquiring data so up to 10 to the minus 10 if we are lucky enough it can be probed with this with this facility then it's exciting times there is no lepton flow violation there then we notice that there's been some with amount of activity in lepton to a lepton and a photon or lepton to a lepton and a lepton-anti-lepton pair from the virtual photon so there has been some activity but on the contrary for this semi-leptonic decays where you have an addition for instance a pseudo-scalar vectors then there's quite much less activity and we could find only the basically these references here so then some analysis in supersymmetry in little fix model with parity recently and 3-1 models effective theory but in this sense we wanted to fill the gap in other little fix models for this analysis that was also our motivation then I'll be a bit quick the calculation of the details of the model here I'm including the one loop diagrams so these are photons C or C prime the 80 diagrams I'm always omitting the adornization of this this photon C to C prime or C prime going to QQ bar then this adornize and give you the the mesons that you have in final state but I am omitting just for space to see here QQ bar and then adornizing right so here here everywhere we have employed unitary tickets and then in this way you only have physical particles appearing everywhere also the cancellation of divergence a bit more involved but on the other hand this is good because then you have let's say more more strict check of the calculations so these are the diagrams mediated by the photon and as you can see in all of them the important thing is to have this sum that is driving the electron flow violation in this tau to mu transition and then you have the couplings with the W with the W primes and also self energy type of diagrams yeah another thing that is important to note is that I'm always including muon but nothing changes if I place the muon by an electron there is electron universality in all the couplings here so for definiteness I'm presenting to muon but it's the same for electron and also the kinematics is it's almost the same so no difference for me so that's for photomediated diagrams then here on this part of this slide I'm including the set and C prime mediated diagrams you see there is a bit more richness here in the diagrams and that's because of the different diagrams that you can have with one light neutrino or without light neutrinos essentially in this kind of diagrams these are the C and C prime mediated contributions then in addition to this you have box type of contributions as you can see here then you have W or W primes here and then you have these scores here are included because otherwise it's confusing the diagram as opposed to all the other diagrams and not including the QQ bar that later adornizes to give you the the mesons in the final state and here one particular thing about the unitary gauge, I'm sorry, one particular thing about the unitary gauge is that the cancellation of divergences is a bit subtle because as opposed to the top prime engage here the divergences cancel between the sum of all penguin self energy type diagrams with the divergences coming from the box diagram, so the cancellation is not independent but still, as I said this is a nice check of everything I guess so these are the diagrams that we are considering then ok, there's some delay ok now, so I already said about this cancellation of divergences then as I mentioned at the beginning we hope that the ratio between the electroweak and composite scale is small enough so that the perturbative expansion converges quickly and in this scenario you can organize the perturbative expansion in this way so first contribution is of order to the matrix element is of order b squared over f squared which are corrections of the next order but these are clearly smaller than these ones so we can throw them away safely then another approximation in the propagators we can span because the scale of external momenta is at most given by the tau mass and the tau mass is much smaller than the heavy particles in the loop like the w, the w prime we can make this expansion and again throw terms that are suppressed by these by these external momentum scales over heavy particle scales in the loop in addition to these of course we can put light neutrino masses to zero also muon, even more electron and light pore masses to zero and as I said once we have made this expansion we can throw consistently away all these ratios that are small okay and yeah I also mentioned that external momenta can be set to zero in the computation of boxes based on the same argument I have been discussing so these are the approximations for our computation and then we get the results for the amplitudes for instance this is for the photomediated amplitude and then we have a couple of four factors in each of the structures right so this is the dipole like there this is the one going with the charge and then you have left and right four factors in each of them right I note that we organize the computation in such a way that we have explicit factor of e squared here and then we make also explicit the expansions that's the leading term that the only one we are keeping that is of order e squared over f squared as I mentioned also we have the separation of the four factors because of heavy particle masses four half of them then only the other half are important and in them we have made explicit again the other separation that is given by this alpha week as the ratio of alpha over the sine squared of the week angle right and then where else remains so the dependencies are given in terms of this kij that you can see here kij being the ratio between heavy neutrino mass j over w prime mass everything squared ok so these are two of the little particles so these are in principle of order of the same order for the TV then this ratio of order one ok for the counting and then the only other important thing that remains is this delta new here delta new here is basically the inverse of f tangent beta ok and this is giving you the mixing in the in the neutrino sector between light and heavy neutrino and as you see it depends on f tangent beta this means that in fact these two quantities f and tangent beta are not independent in the model so there's a strong correlation between them that's important ok so that was the photon for the other contribution I won't be giving that much details ok so the basic things you can see already in the photon contribution so some four factors vanish because they are suppressed by heavy particle masses in the loop and for the others we may explicit the separation in the expansion in ratio of the electro week scale over the composite scale and then there are also the electro week separation factors here clearly noted and then the other important things in the model are this ratio between little particle masses ok so heavy neutrinos driving the electron formulation and the W prime in this case and this delta new that is inversely proportional to f tangent ok so now I go to the other contribution with much less details then again for the CNC prime we may explicit some of the of the suppressions in this here and then we have again four factors ok so once more this one with the sub index are here and here are suppressed at least as m tau square over m c square so we can say if we neglect them and for the other two you have the expressions in the additional material and again the expansion is of the same kind I discuss already for the for the photon contribution I note here in this set and C prime contribution the appearance of this coefficient zl zr z prime l z prime r so that again include high let's say some separation in in electro week in electro week factor ok and in addition to this you can have the dependence on the on the week angle and on the charges of the of the external quarks involved ok the electric charge but these are quite straightforward to obtain this ok then it remains only the box contributions and we write these contributions in this way you can see here so again explicit the separation in a week and then there are times that go with the log of this quantity j that I told you is order one and then others that are going as log delta where delta is again another one quantity is is the ratio between one of these new heavy quarks and w prime masses square and then we have a part that is log independent ok this this one here you can find this presence for all of them in the additional material the expansion is made in the in the same way as as before ok again I know this correlation between F and tangent beta you can see here that's important and one thing I'd like to mention is that the box contribution turn out to be relevant ok you may guess that in in channels with only one scale armation because in this case because of c party the photon contributions are forbidden then you may guess ok so in the case with way as once a scalar box contribution may be important but even in the case with two pseudo scalars or what is equivalent with a vector this turn out to be important that's a particular feature that is relevant and that I like to highlight in this simple logic model ok then I move to the adrenization so as I told you for instance if I if I come back here we have some quad bilinear here that needs to be adrenized right so this is I mean this is for the box contribution but it's basically the same also for the photon c and c prime mediated contribution then how do we do the adrenization how do we connect this at the quark level at the quark level with the with the with the mesons that we have in the experiment so this adrenization is driven by low by low energy qcd properties so in this sense we write this in terms of the flavor currents and then we proceed to the adrenization respecting the known limits of low energy qcd so chiral symmetry then dispersion relations allow you to automatically excuse me to automatically include a general axiomatic field theory properties like unitarity and eliticity gross symmetry then in addition you make sure that the right qcd asymptotic behavior is fulfilled namely behavior for all factors and even more I mean apart from all these theoretical machinery it's good that for the four factors of interest so for instance biomes vector currents we have very accurate data so then we can use them to refine the theoretical approach and particularly to fix the attraction constants of the dispersion relations in this way we have a very controlled framework to adrenize the quark bilinears into the mesons and vectors that we are measuring then for the case with just one scalar sold out to a muon or an electron and then a pseudo scalar that is a pi zero eta or eta prime meson then you make the algebra and it's very easy everything depends on the pseudo scalar decay constant and then in addition to these at most in the eta prime mixing angle that you can see here that's quite easy and then you have for instance the box functions here and trivial factors of the weak angle in this way and you can treat all of them in the same footing and then I move to the dedication to pseudo scalars then the adronization of the quark bilinear current is straightforward and apart from the from the Lorentz structure it gives you the well-known two meson vector for factor and as I said for this we have very accurate data it's been widely studied so it's very very well under control you can see the expression so again additional material of the talk and I emphasize we are including all these known theoretical tools and getting advantage of the very accurate data in these decay modes then it's not that clear how to proceed in the case where you are talking about how to amuse an abector namely a row or a phi in this case you need to specify what do you understand as an abector and then what is close to the experimental situation and also it's reasonable from the theoretical point of view it's consistent is to say that a row is in fact a pi plus pi minus around the pole mass and width values of the row and this is what you can see in these expressions here so it's peak at the row mass and then it takes into account the width and this is a row and you can vary a bit the definition here but basically if it's all do not change much and even more in the case of the phi because the phi is quite narrow ok so you do it including the different kind of contribution and that's how you make contact between the theoretical computations and the experimental measures so then we can go to the predictions we also benefit from previous work done on leptompholar violation in the simplest little pitch model this is done in this reference in blue here the LaGlaiana Jenkins and they studied thoroughly new to the gamma new to three electrons and new to the electron conversion in nuclei ok so this analysis they get abound on as I told you F tangent beta that's correlated so it should be at least 3.5 dB let's say and then again delta new is not independent you can look here and they made a very complete study of the allowed heavy neutrino mass hierarchies ok in this paper they took the simplified case were only two heavy neutrinos matter ok so that's kind of gym like so for instance you can understand that the mixing matrix for this heavy neutrinos is almost unitary in the two times two sectors so the third one is almost a couple in practice that's what they look at and the reasonable bounds on the model parameters that they took were F between 2 and 10 dB tangent beta between 1 and 10 and this this relation for the heavy quarts involved also making contact with this delta new parameter here ok and these results in fact in small mixing for all these queues and that makes everything consistent in an easier way with all precision data in meson physics ok to make it short ok so we took advantage as I said of these studies and then we looked to the semi-electron electron flavor violating tau dk's that are written here and also I will tell you later about that and it's important to emphasize that every time we are taking all low energy constraints into account ok so if we throw a point if we scan in the parameter space and we get something that is consistent with one of the low energy constraints then we throw this point out ok so then I go to the plots here you can see in this part these are the different tau lepton flavor violating processes considered experimental bounds for the case with a muon in this column and for the case with an electron in this column and these are in units of 10 to the minus 8 at 90% confidence level as it's written here ok and then you can see in this plot we are scattering the model the model parameter values for professional values of them and you see that in general you may be in conflict with some of the low energy constraints so here in the x-axis we have tau to mu gamma in the y-axis we have mu to mu gamma and we see that some portion of the plots go outside of the experimental upper bounds that are represented by these red lines that you can see so these red lines correspond to the upper limit that you can read in this table here so you see that it's important to take into account the low energy constraints because otherwise you can get in conflict with them here I am taking to begin with the simplified scenario with only two effective heavy neutrinos now I am plotting branching ratio of tau to mu and a pair of pions with this upper limit 2.1 times to the minus 8 versus the branching ratio for mu to gamma then the x-axis is cut here at the upper limit of mu to gamma so all the points to the right of the plot are cut then all plots here are consistent with mu to gamma and we see that being consistent with mu to gamma automatically brings consistency with the upper limit in tau to mu to mu and a pair of pions because the upper limit would be 10 to the minus 8 and you can hardly get points 10 to the minus 13 you can see here in these two heavy neutrinos now the same for tau to mu pi 0 versus mu to gamma so if you are not violating the mu to gamma constraint then automatically again you are in agreement with the upper bound tau to mu and pi 0 for these two heavy neutrinos now I go to examine the correlation between tau to mu and pi 0 and tau to mu pi plus pi minus you see that the correlation is striking and even more if you remember that the main production mechanism is different in both cases because in this one here tau to mu pi plus pi minus this here is dominated by the photon contribution while here in mu to pi 0 this is forbidden by symmetries by the box then in principle it is difficult to see to guess at first sight this correlation but it is a result of the adornization mechanism and this is explained in the paper so in the end this correlation is understood but it is not a violent at first sight now in the next plot now I am going to the three heavy neutrinos scenario of course here you have more freedom we have restricted it a bit because we neglected the phase that could be here and just to have one less free parameter but you can of course do that and then you can have a bit larger branching ratios for instance using this parameter but in this scenario now we see that contrary to the previous one we can be in agreement with mu to i gamma all these points are in agreement with mu to i gamma and sometimes it is a bit hard but you can still violate the upper bound on tau to mu and upper of pi so in this case this can happen it is this does not appear to be the case for mu to and pi not because here if you are in a chord with the upper limit in mu to i gamma then you still are so some 2 to 3 orders of magnitude below the upper bound on tau to mu pi so in the model even in the three heavy neutrinos scenario it is hard to get sizeable signals from mu to pi not but not on tau to mu and upper of pi so here it is more promising for detection in this sense now I go to plot the branching ratios as function of the model parameters and now before in the previous plots I was including here branching ratios on the axis directly branching ratios now it is not the case to the upper limit so here that is some point in the parameter space that happen to be very low so you see it is much below the upper limit and here you see that green line is a contribution blue line is a prime contribution this is logarithmic scale so c and c prime contributions are negligible so everything in tau to mu pi comes from the box contribution I told you that a photon contribution is forbidden so here everything is box now for tau to mu and pair of pions again c and c prime contributions are negligible as you can see here and now there is some strong interference between photon and box contributions so these are the pair of lines here in green and red colors and using as a result of this interference you are in practice losing a factor of let's say 5 some 5 in the overall result so this interference brings results down now I am including for some specific point in the model parameter space I am comparing the branching ratios that you can get for the different modes and confirming earlier expectations we see that those that get the higher rates pair of pions and the closely related mu to rho so these are the two that we can see here and these are always at least an order of magnitude larger that mu to pi not for instance and also even more larger than the others so most promising for detection are mu to pi plus pi minus and mu to rho of course apart from mu to gamma and tau to mu gamma and mu to be conversion in nuclei but these were stuck from the semi-leptonic the most promising ones are mu to pair of pions and mu to rho then I was plotting previously always the branch F of the composite in a scale now I am plotting them against tangent vita and here the behavior for large tangent vita is quite monotonous on the contrary at low values of tangent vita there is some mark deep around 2 remember this scale is logarithmic so you can lose here more than an order of magnitude from varying tangent vita factor of 2 not here so if tangent vita happens to be around here then it's even more difficult to see any signal within this model now these are again branching ratios plotted as a function of the mixing angle between the two heavy neutrinos that's this theta here where I recall you in this simplified two heavy neutrinos scenario so everything is given in this sector only in terms of this angle and of course it couldn't be the other way the behavior is quite monotonous there's just a consistency let's say so I go for the next plot and now I'm representing the branching ratios with respect to the upper limits I recall versus the mass of the lightest of these heavy neutrinos and here there are two different scenarios ok there is a case where these two heavy neutrinos N1 and N2 are almost degenerate and in this case the gene-like mechanism of cancellation acts more efficiently so then the branching ratios are lower and then if there is quite some hierarchy between these two like heavy neutrinos this N1 and N2 then this cancellation mechanism acts less effectively so then now first this is large splitting case the branching ratios are larger than in the case with small splitting cases you can see so two orders of magnitude are lost from here to here because of this cancellation mechanism that acts more effectively in the case where there is small splitting between N1 and N2 but this is in agreement with expectations that is just another consistency observation ok now we go to 3D plots so here you can for instance compare the behavior in F and the behavior in tangent beta and in this plot you can see again this correlation in these two so you cannot have simultaneously F and tangent beta large so that's why you are having these extreme colors here and here and this is large but this we already knew from the dependence on delta nu now this is more monotonous on F and sine 2 theta so branching ratios are large when sine 2 theta is large and on F only there is this deep around 2TB but for the rest it's quite smooth in this region here and again we don't learn basically anything else new from these plots in F and the mass of the lightest among the heavy neutrinos if we remember what we have learned about this cancellation mechanism so no further information is got from these plots here if provided this seems like cancellation mechanism is understood ok so with this I would go to lepton flare violating his decays and I'll be a bit shorter on this part so quite a long time ago some 25 years his 2TB nu was proposed as a promising channel to discover flavor violation of char leptons and even in some cases it was proposed as one of the first decay channels of the heat that could be detected and the interest on this decay mode has been kept very intense over the years it was even renewed further increased with improved limits on these lepton flare violating decays obtained by the refactories but above all the really good trigger for renewing this interest was the 2015 CMS hint so as you know they came up with this number so 0.84 with an error of basically 0.4% so which represented an upper bound of 1.5% at 95% confidence level so it was a bit above 2 signal so this increased a lot the activity in this area people were very excited but just a bit later on Atlas didn't confirm this apparent hint from CMS and their upper limit was basically in agreement with this one from CMS and sadly let me say CMS updated the result and now it appeared that what happened was a downward fluctuation you see here the central negative value with an error of course consistent with 0 but all in all now the gain for a signal has gone below 2 signals and we wait for the update for Atlas but it may be that it goes even even further down but for the moment let us consider the Higgs to tau mu maybe not at 1% but still at a size measurable level at the LH that's the motivation to keep doing these studies so within this simply little fix model these are the one loop diagrams you see WNW can mediate the diagrams again the heavy neutrino is driving the left arm failure violation as you can see here or here this diagram you can also have it with this WW prime self penalty type of contribution in this leg but since you will have if you have the tau the tau mass is not that small but if you have mu and electron this type of contribution will be suppressed by the mu and electron mass so you can forget about this contribution and we have also this kind of contribution with heavy and light neutrinos as you can see here now the appearance of the Higgs mass brings you a hr scale so we can have scales of order 1 as I did before and these are the ratio between the heavy neutrino I'm sorry between the heavy neutrino masses and W prime square as you can see here but also between W and Higgs mass this is also of the same order of these ones these are the order 1 scales and the problem and now the small scales and the problem before as omega so the ratio between W and W prime mass square and now we can form some ratios that are also of this order of this order omega that is order mu square over s square that is much smaller than 1 as you can see here okay so that's the way we organize the computation and we have also considered it both in the 2 heavy in the 2 effective heavy neutrino scenario and also in the general 3 heavy neutrino case in the same way I explained before okay so then we organize the amplitudes in this way we have the overall dependence on the town neutrino mass and this immediately tells you that if you are considering Higgs to mu an electron the suppression is quite strong so in principle you expect a measurable signal if any only in Higgs to tau mu or Higgs to tau electron but not in Higgs to mu electron very very suppressed and then we have again contributions that go that are of log type and non log type here so again we have the dependence on this delta nu that is inversely correlated to F tangent beta as they call and then we have this dependence on the ratio that is order 1 kij here and then also on tangent beta on the remixing angle basically as before okay so then with this again I recall the way we are introducing the 3 heavy neutrino scenario without any phase here and in Cp violating phase here just for simplicity and in the amplitude it is very easy to go from the 2 heavy neutrino to the 3 heavy neutrino case because in the 2 heavy neutrino as I told you everything is multiplied by this mixing angle in the heavy neutrino sector and then you have this ratio only of log type 1 over type 2 and then non logarithmic pieces depending on type 1 and type 2 but then this just changes from this dependence here to the general dependence on the on the mixing matrix coefficients that are multiplied here and then you also have also gain this dependence on omega omega I recall this in small scale so in principle you notice that you can have larger signals for the 3 heavy neutrino scenario 1 because you have more parameters this gives you more freedom and also because you can have you can gain a moderately larger log here because this is order 1 and this is small scale so these are the 2 facts that contribute to have larger branching ratios in the 3 heavy neutrino scenario that's the important thing then I go to the plots so always in this part of the talk I'm showing on the left-hand side the results obtained in the effective 2 heavy neutrino scenario on the right-hand side I'm presenting the results in the more general 3 heavy neutrino case and as I read some before you observe this enhancement in the general case so you see that some 5 to 6 order of minus are gain in going from the left to the right that's what you expect still the branching ratio are given in the percents here and the red line represents the upper limit obtained by CMS so then if you compare it you are well well below no charge for detection so at least 7 orders of magnitude even in this case here now that was the dependence of the branching ratios connect that is quite monotonous now that's the dependence on the lightest among the heavy neutrino masses it's quite smooth and once more you get very small and measurable branching ratios at the late C so this is a characteristic of the little Higgs models I will make this point stronger later on now the dependence is on tangent V, again you seem to observe some kind of deep here but you seem to observe it but still you are very very low compared to the current experimental bound and even to the observability region at LHG that should be here so you can't observe Higgs left on flare biolating decays according to the simplest little Higgs model and finally here branching ratios are plotted versus the only angle given in the mixing in the 2 heavy neutrino scenario and versus the maximum of the mixing that you can get in the 3 heavy neutrino scenario the conclusions are in agreement with the previously shown plots finally here I am comparing the branching ratio of mu to gamma versus the branching ratio of Higgs to 2,000 mu again this is the upper limit obtained by CMS at 95% confidence level and once more this axis is cut here at the upper limit of mu to gamma so if you are in the plot you are in agreement with mu to gamma and usually that provided this agreement happens there is no way to be close to the CMS upper limit so even in the 3 heavy neutrino scenario when we are getting larger rates we are at least 4 orders 4 to 5 orders of magnitude below the upper limit ok and this is to be a general characteristic of little Higgs model because in a recent study of little Higgs model with the parity that I am quoting here again this observation is confirmed so if you are in agreement with the low energy limits then you cannot explain within this class of models left on floor violating Higgs decays at a rate close to 1% it should be much less or at most 10 to the minus 6 here ok then sadly an observable at the LHC ok so with this I go to the conclusions so theoretically little Higgs models particularly simple little Higgs models that is the one I have been talking about seem to be elegant candidates to understand why the Higgs is so light and they respect all experimental bounds I showed you Higgs to say C-C prime but also Higgs to a couple of photons another Higgs observables are in agreement with a very very good portion of this little Higgs model parameter space so that's one thing then we have explored that and we see that the left on floor violating signals predicted by this class of models are very very small in the case of semi-leptonic tau decays and even more in the case of left on player violating Higgs decays so according to this model there is no hope to observe left on player violating Higgs decays at LHC on the contrary if these models happen to be right then left on player violating detection is not impossible it would be easier in the decays mu to gamma tau to mu gamma left on to three left ons mu on to electron conversion in nuclei and then among the processes we are discussing here it could be detected in tau to mu on or electron in a pair of pions or tau to mu on an electron in a row so that's the change from this style and I emphasize the easier it would be the closer we are to the effective to the three heavy neutrino scenario so if there is some kind of gym-like cancellation then it would be even harder to detect these models so again within little Higgs models it's very very hard to understand any measurable signal at LHC but on the contrary in tau to mu gamma mu to gamma left on to three left ons mu on to electron conversion in nuclei and also and this was discussed at length in this talk also in tau to mu on or electron in a pair of pions and in tau to mu on an electron in a row you can have easier detection if three heavy neutrinos are active within the model and I think that's all for the moment from my side and thanks for your attention Thank you very much Pablo for this very nice talk I shall confess that it is completely new for me I didn't knew too much about this little Higgs model okay I have an eco I don't know if it is only me but well now we are going to the questions I don't know if any in the room has a question for Pablo I can I can you can take the voice any question hello hello, did you hear me? okay okay somebody else can go ahead no, you go okay okay thank you so I saw very nice talk by the way it was very detailed so I saw in one of your initial plots that you gave the branching ratio for tau mu gamma and there was a line around the 10 to the minus 12 exactly right there so I mean it is bound on the branching ratio I think it is of the order of 10 to the minus 8 is it so is this what Bell expects to improve to go down to 10 to the minus 12 yeah in fact yeah okay I didn't explain these lines correctly so you are right this red line here this corresponds to the upper limit of mu to gamma okay this one the current upper limit to mu to gamma then my general practice is to be cutting the plots here in mu to gamma at the current upper limit that was what I am basically doing and here I didn't do this I could have cut this one here that should be here for instance and I am showing this value that is even a bit lower than 10 to the minus 12 that could be maybe the most optimistic scenario for Bell to I mean with the complete statistics and even use systematic effects in the detection yeah but you are right that this is present and this should be future projections here you are not getting out for this point the points out will be here yeah yes but so we can go down to 10 to the minus 12 I'm quite surprised I expect 10 to the minus 9 or so but okay it's I mean from the statistics it should be it's a factor of 50 with Babar and Bell combined with the complete Bell to statistics so it's two orders of magnitude with Bell for instance and then if you further improve on the systematic depending on the detection mode you can get a bit more you can gain a bit more then you can go below 10 to the minus 10 for sure I think maybe maybe it would be more realistic to make it up one order of magnitude I see that's probably too optimistic okay fantastic so there's another question so you are considering most of your heavy neutrinos are I mean are very heavy right of the order of the TV but every now and then you consider I've seen some plots that you were putting heavy neutrinos of the order of a couple hundred a GV so have you seen I mean the possibility of directly producing them at collider experiments in that case and see if there's any correlation between that yeah in fact okay so first thing is that if you are very aggressive you can take the PDG bound that comes from the absence of their observation in set decays so then you can go down exactly to this point here if you do that that's very aggressive in principle the realistic region doesn't start here should start here so for the too heavy neutrinos scenario we took a reference I mean the authors where I'm sure they pitch and I think I don't remember their authors but they consider signals of this kind of heavy neutrinos in the two heavy neutrinos case so in the two heavy neutrinos case we took into account their constraints in the three heavy neutrinos case we couldn't find a reference that made this study and we didn't do it that's too bad we weren't pushing that much there to be sure that we were within the limits okay okay cool thank you any other question comments complaints about the presentations I have a question because of before just how El was giving the answer so regarding to this heavy neutrinos Pablo is it possible to make it to work with neutrino masses to participate in the mechanism for neutrino masses in this scenario okay so yeah if you are thinking whatever yeah I get the question so yeah one thing is that it is not one of the concerns of the model to explain neutrino masses so from the beginning they were worried about the hierarchy problem on the heat masses and then the phenomenology has been explored but the answer was the heat mass value then you can do easy things like having neutrino for instance and then you get some mass but again you have the fine tuning problem with the specific value of the power you could maybe do other things but I mean one one thing is that these heavy neutrinos are not that heavy they could be as light as maybe 100 WB at most one TV or a bit more so then it's very difficult to make I think I'm not completely sure of that but I think it's very difficult to make them part of an explanation of the light neutrino masses because they are very light compared to digital explanations so I mean if you try this probably the fine tuning reappears and it's not less than the original one so then I don't think that it's very attractive from the view but I I must admit I have understood that yeah I understand they are too light to be the 0.106 of type one yeah so another question I was wondering and because when you have this type of model and with this z prime and w prime you have any correction for instance to the g-2 of neon ah yeah yeah extra phenomenon this question I've got almost every time I'm spoken about this yeah it's very natural because I mean there is one of the few places where there seems to be still a deviation between theory and experiment yeah so we haven't done this but we suspect that a general trend of this kind of model is that they use naturally small effects in a sense they were built to explain the lightness of the heat and on the other hand to give very small effects everywhere so for instance in the g-2 we have left and right at both ends of the diagram and then you can have a contribution to the g-2 but I'm sure it's a fresh because it is the general trend of the model to give you very small very small things so summarizing we haven't done it but we are sure that the effect will be negligible compared to the to the difference between theory and experiment and to the errors on both of them so in the sense that the source of the deviation couldn't be related to this should be in a bigger with a larger part of the counter if you if you do not violate low energy constraints then it's the same we have of service analogous to what we have in fixed left and right you don't have enough freedom to meet the effect of the same idea yeah so I don't know I had all the questions but thought I want to leave space for the rest okay actually I have a question because well well you're saying that what your conclusion is that there is a possibility to detect this kind of models in leptom flavor violation but I'm not sure well if we detect something can be sure that then the Higgs is a composite state of particles or there is other models that will predict the same I mean what will be the signature that you expect to and yeah I mean so I mean I would look to many different things for instance as you said here in this plot it's not impossible that I mean if simply little Higgs model is right that's speculative but this happened to be right then we could measure according to this plot for instance we could measure mu to gamma or tau to mu pi plus pi minus I mean this could be or not a signal of this little Higgs models then something that is quite specific from these models is this correlation so if I can find if I measure one then the other one is basically predicted there is not that much freedom especially in the higher end of this plot so here correlation is very very strict so then if I expect to see something tau to mu plus pi minus and then not to see something very soon in tau to mu pi not because this is typically a bit surprised with respect to the other so then with more data I would see tau to mu pi not that's something but then that's not enough so I would need to look at the beginning I would need to look closely to the deviations in Higgs physics then this should be there are some signatures of these deviations in the little Higgs models in Higgs to CC prime also in Higgs to a couple of photons there are specific models related to the scalar that one has here so if you don't discover this scalar then a particle is missing in the model so if you look for it I mean if you fix things from other observables and you conclude that this should be I mean I don't know at 30 GB and you don't discover it then you falsify the model so I would need to put all the pieces together in a sense. Okay thank you very much Roberto have a question Rodino go ahead Roberto please okay I mean the question is from Abelino he's asking to you and your setup is very similar to the variant in 331 model which the third component of the electronic SU-3 left is neutral therefore do you expect do your results also apply to the so I think I didn't get the question so Abelino sorry he said basically that your model is very similar to this 331 model in which you have two SU-3 two times times one you want so he's asking if he could apply your results in this framework okay so I am not at all an expert in 331 models but my doubt is I mean in these models because of this assume Higgs compositeness you have all observables expressed as ratios of this no of the electroweak and the compositeness case and then this converges quickly I'm not sure about this expansion parameter or similar expansion parameter in analogous way in the 31 models so if that is the case yes I would expect that because of the symmetries in the group I am not sure about this so maybe results are further suppressed here because of the hierarchies that happened here so here I mean this is related also to the corrections to the Higgs muscle I mean F need to be probably three and I mean that also relates to Higgs physics and I don't know in 331 models if you have a similar restriction also here you have this particular correlation between F and tangent beta and I doubt if this happens in 331 models so I again I am not at all an expert in 31 models but I will have my doubts because of these two things I am mentioning I don't know if this specific dependence is here and here and this correlation here are also shared by the 31 models so I don't know if Fabelino can shed more light on this yeah okay I guess meanwhile we can wait if Fabelino want to make a reply to your answer in the cat but anyway I have a question from my side because I was I guess I heard some but I don't know if it is possible in the simplest little Higgs model but usually also it's a source of possible dark matter candidate but yeah when you put the part I don't know in this framework you can also have some stable or long-linked particles that could take the role of dark matter yeah yeah there is one higher state composite yeah you are absolutely right there is one so let me find this slide where this is commented so it should be here okay so from the breaking you get the Higgs degrees of freedom and in addition this scalar this eta here this eta could be a candidate for stable dark matter and this is exploring in these references here I mean it's not there is not any very recent reference so I don't know to which extent this is updated at least that I know of very recent references but at this time this was examined in this program is the state that appeared here oh and this is the simplest little Higgs model so one can explore a pair of hittas or a set and an eta so yeah these are very interesting signatures and as you said then in the little Higgs model you have a parity that is analogous to the super symmetry and can explain why the lightness of your particles under the sim can be absolutely so and I was wondering which is the future for the experiment after the AC and what is expected to be experiment to search for this kind of left and right variation processes okay so I don't know if the linear collider also gonna be looking for that but yeah I don't know all the prospects for the linear collider I know that at the LHC they will keep having activity on here I mean that's a central part of the program for sure for the years to come in which they will be studio operating and of course for bell 2 there will be a lot of years and I mean as far as I know there will be great advances in mu2 to 3 leptons mu2 electron conversion in nuclei so I I mean of course besides this that was more related to my talk but in mu2 to 3 leptons I mean sorry I mean mu2 electron conversion in nuclei I think that they will be improving the limits a lot so that could be the frontier for killing models and for maybe finding something hopefully you know that Romino just replied to your reply and your answer I mean and he's saying I would say not sure that at least qualitatively it should be similar one has the same vertices with the prime and W prime of course there might be quantitative differences due to the specific model relation yeah maybe this one for instance but yeah in general I agree I think I would say he's right okay do we have more questions yes I have one okay go ahead Nicolas thank you actually I had two and since you were talking about this eta field and the right hand and the heavy neutrinos how do these fields get mass how are the mechanisms in which they get masses okay yeah okay so I mean for the standard model particles it is breaking of the symmetry that gives them mass and then as a result of the breaking of this local part of the sequence you want then this 5 gauge boson gets mass for us only W prime and Z prime are of importance but this is what gives mass to them okay but how is configured the interactions in which the in which the eta is present I mean for instance is it present are there any interactions in between the massive eta and the neutrinos I mean the standard model neutrinos and the heavy neutrinos okay I must have something in my back up about this okay so not here okay you see this I already said but you see here explicitly okay corrections to the standard model relations that are given in powers of this square over square that's a general term of the model okay then here here you can see the mass of these of these heavy neutrinos how it arrives so it's proportional again to F they are little particles then it has this dependence one from side beta and this this lambda I that is free in the model so you can okay sort of the symmetry these particles that's mass and also here you see explicitly I was talking about this delta new the mixing between the light and heavy neutrinos and you can see this here okay so the eta field has no water I mean I didn't get it whether it was a scalar or so the scalar but in the case it is a scalar let's say does it have a pseudo scalar companion no no it doesn't okay okay no the point was trying to patch a neutrino mass mechanism for instance if you would have been nice whether this field had a new a pseudo scalar companion in order to mix them up and give rise to a scotogenic kind mechanism yeah I see here yes exactly you need another additional degree of freedom in order to have a neutrino mass relatively generated yeah that possibility could be the estimate I see thank you so much okay is any other question for Pablo okay I see no okay well thank you very much Pablo for this very nice talk it was very very interesting about this model and the experimental signature and well we will see all together in two weeks well and for the next webinar I think this is the last webinar of the year and well thank you very much for being here to you all next episode I would just like to say again thank you to you Herman for the American Webinar team and it's a very very nice initiative and I encourage you to go on because it's not great so congratulations okay thank you very much okay good bye bye bye


Happy Chinese New Year! This is Belle, and currently, I'm teaching English to ESL students in the training school, aiming at teaching them test preparations and speaking as well. I feel so lucky that I took the 120-hour TESOL course several months ago, and I completed it with flying colors and got a certificate right now. Well, I have to say that the course is a very good fit. Not only did I learn the ESL methodologies and the techniques of all kinds, but I also learned how to have a smart classroom management, which is a very helpful part in teaching. And the best part I like the course is the video part. I can see several times whenever I can, so that I can learn something from the experienced teacher. I really like the course and I'm considering to do another course in the near future. Hope to see you soon!


CHAPTERS 22 THROUGH 28 Again Jesus spoke to them in figurative language. The kingdom of the heavens, he said, may be compared to a king who celebrated the marriage of his son, and sent his servants to call the invited guests to the wedding, but they were unwilling to come. Again he sent other servants with a message to those who were invited. My breakfast is now ready, he said, my bollocks and fat cattle are killed, and every preparation is made. Come to the wedding! They however gave no heed, but went one to his home in the country, another to his business, and the rest seized the king's servants, maltreated them, and murdered them. So the king's anger was stirred, and he sent his troops and destroyed those murderers and burnt their city. Then he said to his servants, the wedding banquet is ready, but those who were invited were unworthy of it. Go out, therefore, to the crossroads, and everybody you meet, invite to the wedding. So they went out into the roads, and gathered together all they could find, both good and bad, and the banqueting hall was filled with guests. Now the king came in to see the guests, and among them he discovered one who was not wearing a wedding robe. My friend, he said, how is it that you came in here without a wedding robe? The man stood speechless, then the king said to the servants, bind him hand and foot, and fling him into the darkness outside, there will be the weeping aloud and the gnashing of teeth, for there are many called, but few chosen.  Give us your judgment, therefore. Is it allowable for us to pay a toll tax to Caesar, or not? During their wickedness, Jesus replied, Why are you hypocrites trying to ensnare me? Show me the tribute coin. And they brought him a shilling. Whose likeness and inscription, he asked, is this? Caesar's, they replied. Pay therefore, he rejoined, what his Caesar's to Caesar and what his God's to God. They heard this and were astonished, then left him and went their way. On the same day a party of Sadducees came to him, contending that there is no resurrection, and they put this case to him. Teacher, they said, Moses enjoined, If a man died childless, his brother shall marry his widow and raise up a family for him. Now we had among us seven brothers, the eldest of them married but died childless, leaving his wife to his brother. So also did the second and the third down to the seventh, till the woman also died, after surviving them all. At the resurrection, therefore, whose wife of the seven will she be? For they all married her. The reply of Jesus was, You are in error through ignorance of the Scriptures and of the power of God. For in the resurrection men neither marry nor are women given in marriage, but they are like angels in heaven. But as to the resurrection of the dead, have you never read what God says to you? I am the God of Abraham, the God of Isaac, and the God of Jacob. He is not the God of dead, but of living men. All the crowd heard this, and were filled with amazement at his teaching. Now the Pharisees came up when they heard that he had silenced the Sadducees, and one of them, an expounder of the law, asked him as a test question, Teacher, which is the greatest commandment in the law? Thou shalt love the Lord thy God, he answered, with thy whole heart, thy whole soul, thy whole mind. This is the greatest and foremost commandment, and the second is similar to it. Thou shalt love thy fellow man as much as thyself. The whole of the law and the prophets is summed up in these two commandments. While the Pharisees were still assembled there, Jesus put a question to them. What think you about the Christ, he said, whose son is he? David's, they replied. How then, he asked, does David, taught by the Spirit, call him Lord when he says, The Lord said to my Lord, sit at my right hand until I have put thy foes beneath thy feet? If therefore David calls him Lord, how can he be his son? No one could say a word in reply, nor from that day did anyone venture again to put a question to him. CHAPTER XXIII Then Jesus addressed the crowds and his disciples. The scribes, he said, and the Pharisees sit in the chair of Moses, therefore do and observe everything that they command you, but do not imitate their lives, for though they tell others what to do, they do not do it themselves. Only in cumbress burdens they bind together and load men's shoulders with them, while as for themselves, not with one finger do they choose to lift them, and everything they do, they do with a view to being observed by men, for they widen their phylacteries and make the tassels large and love the best seats at a dinner party or in the synagogues, and like to be bowed to in places of public resort, and to be addressed by men as, Rabbi! As for you, do not accept the title of Rabbi, for one alone is your teacher, and you are all brothers, and call no one on earth your father, for one alone is your father, the heavenly father, and do not accept the name of leader, for your leader is one alone, the Christ.  Blind fools, why, which is greater, the gold or the sanctuary which has made the gold holy, and you say whoever swears by the altar, it is nothing, but whoever swears by the offering lying on it is bound by the oath, you are blind, why, which is greater, the offering or the altar which makes the offering holy, he who swears by the altar swears both by it and by everything on it, he who swears by the sanctuary swears both by it and by him who dwells in it, and he who swears by heaven swears both by the throne of God and by him who sits upon it, alas for you scribes and Pharisees, hypocrites, for you pay the tithe on mint, dill, and cumin, while you have neglected the weightier requirements of the law, just judgment, mercy, and faithful dealing, these things you ought to have done, and yet you ought not to have left the others undone, you blind guides, straining out the nat, while you gulp down the camel, alas for you scribes and Pharisees, hypocrites, for you wash clean the outside of the copper dish, while within they are full of greed and self indulgence, blind Pharisee first wash clean the inside of the copper dish, and then the outside will be clean also, alas for you scribes and Pharisees, hypocrites, for you are just like whitewashed sepulchres, the outside of which pleases the eye, though inside they are full of dead men's bones and of all that is unclean, the same is true of you.  Oh, serpents, oh, vipers brood, how are you to escape condemnation to Gehenna? For this reason, I am sending to you prophets and wise men and scribes, some of them you will put to death, nay, crucify, some of them you will flog in your synagogues and chase from town to town, that all the innocent blood shed upon earth may come on you, from the blood of righteous Abel to the blood of Zechariah, the son of Barakiah, whom you murdered between the sanctuary and the altar. I tell you in solemn truth that all these things will come upon the present generation.  See, your house will now be left to you desolate, for I tell you that you will never see me again until you say, blessed be he who comes in the name of the Lord. Chapter twenty-four. Jesus had left the temple and was going on his way when his disciples came and called his attention to the temple buildings. You see all these, he replied, in solemn truth I tell you that there will not be left here one stone upon another that will not be pulled down. Afterwards he was on the Mount of Olives and was seated there when the disciples came to him, apart from the others, and said, tell us when this will be, and what will be the sign of your coming and of the close of the age?  Do not be alarmed, for such things must be, but the end is not yet. For nation will rise in arms against nation, kingdom against kingdom, and there will be famines at earthquakes in various places, but all these miseries are but like the early pains of childbirth.  Then will many stumble and fall, and they will betray one another and hate one another. Many false prophets will rise up and lead multitudes astray, and because of the prevalent disregard of God's law, the love of the great majority will grow cold. But those who stand firm to the end shall be saved, and this good news of the kingdom shall be proclaimed throughout the whole world to set the evidence before all the Gentiles, and then the end will come. When you have seen, to use the language of the prophet Daniel, the abomination of desolation standing in the holy place, let the reader observe these words, then let those who are in Judea escape to the hills. Let him who is on the roof not go down to fetch what is in his house, nor let him who is outside the city stay to pick up his outer garment, and alas for the women who at that time are with child or have infants, but pray that your flight may not be in winter nor on the Sabbath, for it will be a time of great suffering, such as never has been from the beginning of the world till now, and assuredly never will be again. And if those days had not been cut short, no one would escape, but for the sake of God's own people those days will be cut short. If at that time anyone should say to you, See, here is the Christ, or here, give no credence to it, for there will rise up false Christs and false prophets, displaying wonderful signs and prodigies, so as to deceive were it possible, even God's own people. Remember, I have forewarned you. If therefore they should say to you, See, he is in the desert, do not go out there, or See, he is indoors in the room, do not believe it, for just as the lightning flashes in the east and is seen to the very west, so will be the coming of the Son of Man, wherever the dead body is, there will the vultures flock together. But immediately after those times of distress, the sun will be darkened, the moon will not shed her light, the stars will fall from the firmament, and the forces which control the heavens will be disordered and disturbed, then will appear the sign of the Son of Man in the sky, and then will all the nations of the earth lament when they see the Son of Man coming on the clouds of the sky with great power and glory, and he will send out his angels with a loud trumpet blast, and they will bring together his own people to him from north, southeast, and west, from one extremity of the world to the other. Now learn from the fig tree the lesson it teaches, as soon as its branches have now become soft, and it is bursting into leaf, you all know that summer is near, so you also when you see all these signs, may be sure that he is near, at your very door. I tell you in solemn truth, that the present generation will certainly not pass away without all these things having first taken place. Earth and sky will pass away, but it is certain that my words will not pass away. But as to that day, and the exact time no one knows, not even the angels of heaven, nor the Son, but the Father alone. For as it was in the time of Noah, so it will be at the coming of the Son of Man. At that time, before the Deluge, men were busy eating and drinking, taking lives or giving them, up to the very day when Noah entered the ark, nor did they realize any danger till the Deluge came and swept them all away. So will it be at the coming of the Son of Man. Then will two men be in the open country, one will be taken away, and one left behind. Two women will be grinding at the mill, one will be taken away, and one left behind. Be on the alert, therefore, for you do not know the day on which your Lord is coming, but of this be assured, that if the Master of the house had known the hour at which the robber was coming, he would have kept awake and not have allowed his house to be broken into, therefore you also must be ready, for it is at a time when you do not expect him that the Son of Man will come. Who, therefore, is the loyal and intelligent servant, to whom his Master has entrusted the control of his household, to give them their rations at the appointed time? Blessed is that servant whom his Master, when he comes, shall find so doing. In solemn truth I tell you, that he will give him the management of all his wealth. But if the man, being a bad servant, should say in his heart, my Master is a long time in coming, and should begin to beat his fellow-servants, while he eats and drinks with drunkards, the Master of that servant will arrive on a day when he is not expecting him, and at an hour of which he has not been informed. He will treat him with the utmost severity, and assign him a place among the hypocrites. There will be the weeping, and the gnashing of teeth. Chapter 25 Then will the kingdom of the heavens be found to be like ten bridesmaids who took their torches and went out to meet the bridegroom. Five of them were foolish, and five were wise. For the foolish, when they took their torches, did not provide themselves with oil, but the wise, besides their torches, took oil in their flasks. The bridegroom was a long time in coming, so that meanwhile they all became drowsy and fell asleep. But at midnight there is a loud cry, the bridegroom, go out and meet him! Then all those bridesmaids roused themselves and trimmed their torches. Give us some of your oil, said the foolish ones to the wise, for our torches are going out. But perhaps, replied the wise, there will not be enough for all of us. Go to the shops, rather, and buy some for yourselves. So they went to buy. But meanwhile the bridegroom came. Those bridesmaids who were ready went in with him to the wedding banquet, and the door was shut. Afterwards the other bridesmaids came and cried, Sir, Sir, open the door to us! In solemn truth I tell you, he replied, I do not know you. Keep awake, therefore, for you know neither the day nor the hour. Why, it is like a man who, when going on his travels, called his bond-servants and entrusted his property to their care. To one he gave five talents, to another two, to another one, to each according to his individual capacity, and then started from home. Without delay the one who had received the five talents went and employed them in business and gained five more. In the same way he who had the two gained two more. But the man who had received the one went and dug a hole and buried his master's money. After a long lapse of time the master of those servants returned and had a reckoning with them. The one who had received the five talents came and brought five more, and said, Sir, it was five talents that you entrusted to me. See, I have gained five more. You have done well, good and trustworthy servant, replied his master. You have been trustworthy in the management of a little. I will put you in charge of much. Share your master's joy. The second, who had received the two talents, came and said, Sir, it was two talents you entrusted to me. See, I have gained two more. Good and trustworthy servant, you have done well, his master replied. You have been trustworthy in the management of a little. I will put you in charge of much. Share your master's joy. But next the man who had the one talent in his keeping came and said, Sir, I knew you to be a severe man, reaping where you had not sown and garnering what you had not winnowed. So being afraid, I went and buried your talent in the ground. There you have what belongs to you. You wicked and slothful servant replied his master, did you know that I reap where I have not sown and garner what I have not winnowed? Your duty then was to deposit my money in some bank and so when I came I should have got back my property with interest. So take away the talent from him and give it to the man who has the ten for to everyone who has more shall be given and he shall have abundance but from him who has nothing even what he has shall be taken away. But as for this worthless servant put him out into the darkness outside there will be the weeping and the gnashing of teeth. When the son of man comes in his glory and all the angels with him then will he sit upon his glorious throne and all the nations will be gathered into his presence and he will separate them from one another just as a shepherd separates the sheep from the goats and will make the sheep stand at his right hand and the goats at his left. Then the king will say to those at his right, come my father's blessed ones receive your inheritance of the kingdom which has been divinely intended for you ever since the creation of the world for when I was hungry you gave me food when I was thirsty you gave me drink when I was homeless you gave me a welcome when I was ill clad you clothed me when I was sick you visited me when I was in prison you came to see me when Lord the righteous will reply did we see the hungry and feed the or thirsty and give the drink when did we see the homeless and give the a welcome or ill clad and cloth the when did we see the sick or in prison and come to see the but the king will answer them in solemn truth I tell you that in so far as you rendered such services to one of the humblest of these my brethren you rendered them to myself then he will say to those at his left be gone from me with a curse resting upon you into the fire of the ages which has been prepared for the devil and his angels for when I was hungry you gave me nothing to eat when thirsty you gave me nothing to drink when homeless you gave me no welcome ill clad you clothed me not sick or in prison you visited me not then will they also answer Lord when did we see the hungry or thirsty or homeless or ill clad or sick or in prison and not come to serve thee but he will reply in solemn truth I tell you that in so far as you withheld such services from one of the humblest of these you withheld them from me and these shall go away into the punishment of the ages but the righteous into the life of the ages chapter 26 when Jesus had ended all these discourses he said to his disciples you know that in two days time the Passover comes and the son of man will be delivered up to be crucified then the high priests and elders of the people assembled in the court of the palace of the high priest Caiaphas and consulted how to get Jesus into their power by stratagem and put him to death but they said not during the festival lest there be a riot among the people now in Jesus was come to Bethany and was at the house of Simon the lever a woman came to him with a jar of very costly sweet scented ointment which she poured over his head as he reclined at table why such waste indignantly exclaimed the disciples for this might have been sold for a considerable sum and the money given to the poor but Jesus heard it and said to them why are you vexing her for she has done a most gracious act towards me the poor you always have with you but me you have not always in pouring this ointment over me her object was to prepare me for burial in solemn truth i tell you that wherever in the whole world this good news shall be proclaimed this deed of hers shall be spoken of in memory of her at that time one of the twelve the one called Judas Iscariot went to the high priests and said what are you willing to give me if I betray him to you so they weighed out to him thirty shekels and from that moment he was on the lookout for an opportunity to betray him on the first day of the unleavened bread the disciples came to Jesus with the question where shall we make preparations for you to eat the Passover go into the city he replied to a certain man and tell him the teacher says my time is close at hand it is at your house that i shall keep the Passover with my disciples the disciples did as Jesus directed them and got the Passover ready when evening came he was at table with the twelve disciples and the meal was proceeding when Jesus said in solemn truth i tell you that one of you will betray me intensely grieved they began one after another to ask him can it be i master the one who has dipped his fingers in the bowl with me he answered is the man who will betray me the son of man is indeed going as is written concerning him but alas for that man by whom the son of man is betrayed it had been a happy thing for that man if he had never been born then Judas the disciple who was betraying him asked can it be i rabbi it is you he replied during the meal Jesus took a Passover biscuit blessed it and broke it he then gave it to the disciples saying take this and eat it it is my body and he took the cup and gave thanks and gave it to them saying drink from it all of you for this is my blood which is to be poured out for many for the remission of sins the blood which ratifies the covenant i tell you that i will never again take the produce of the wine till that day when i shall drink the new wine with you in my father's kingdom so they sang the hymn and went out to the mount of allans then said Jesus this night all of you will stumble and fail in your fidelity to me for it is written i will strike the shepherd and the sheep of the flock will be scattered in all directions but after i have risen to life again i will go before you into Galilee all may stumble and fail said Peter but i never will in solemn truth i tell you replied Jesus that this very night before the cock crows you will three times disown me even if i must die with you declared peter i will never disown you in like manner protested all the disciples then jesus came with them to a place called Gethsemane and he said to the disciples sit down here whilst i go yonder and there pray and he took with him Peter and the two sons of Zabdai then he began to be full of anguish and distress and he said to them my soul is crushed with anguish to the very point of death wait here and keep awake with me going forward a short distance he fell on his face and prayed my father he said if it is possible let this cup pass away from me nevertheless not as i will but as thou willest then he came to the disciples and found them asleep and he said to peter alas none of you could keep awake with me for even a single hour keep awake and pray that you may not enter into temptation the spirit is right willing but the body is frail again a second time he went away and prayed saying my father if it is impossible for this cup to pass without my drinking it thy will be done he came and again found them asleep for they were very tired so he left them and went away once more and prayed a third time again using the same words then he came to the disciples and said sleep on and rest see the moment is close at hand when the son of man is to be betrayed into the hands of sinful men rouse yourselves let us be going my betrayer is close at hand he had scarcely finished speaking when judas came one of the twelve accompanied by a great crowd of men armed with swords and bludgeons sent by the high priests and elders of the people now the betrayer had agreed upon a sign with them to direct them he had said the one whom i kiss is the man lay hold of him so he went straight to jesus and said peace to you rabbi and he kissed him eagerly friend said jesus carry out your intention then they came and laid their hands on jesus and seized him firmly but one of those with jesus drew his sword and struck the high priest's servant cutting off his ear put back your sword again said jesus for all who draw the sword shall perish by the sword or do you suppose i cannot entreat my father and he would instantly send to my help more than 12 legions of angels in that case how are the scriptures to be fulfilled which declared that thus it must be then said jesus to the crowds have you come out as if to fight with a robber with swords and bludgeons to apprehend me day after day i have been sitting teaching in the temple and you did not arrest me but all this has taken place in order that the writings of the prophets may be fulfilled at this point the disciples all left him and fled but the officers who had laid hold of jesus led him away to kaiathus the high priest at whose house the scribes and the elders had assembled and peter kept following him at a distance till he came even to the court of the high priest's palace where he entered and sat down among the officers to see the issue meanwhile the high priest and the whole sanhedrin were seeking false testimony against jesus in order to put him to death but they could find none although many false witnesses came forward at length there came two who testified this man said i am able to pull down the sanctuary of god and three days afterwards to build a new one then the high priest stood up and asked him have you no answer to make what is it these men are saying in evidence against you jesus however remained silent again the high priest addressed him in the name of the ever-living god he said i now put you on your oath tell us whether you are the christ the son of god i am he replied jesus but i tell you that later on you will see the son of man sitting at the right hand of omnipotence and coming on the clouds of the sky then the high priest tore his robes and exclaimed impious language what further need have we of witnesses see you have now heard the impiety what is your verdict he deserves to die they replied then they spat in his face and struck him some with the fist some with the open hand while they taunted him saying christ prove yourself a prophet by telling us who it was that struck you peter meanwhile was sitting outside in the court of the palace when one of the maid servants came over to him and said you two were with jesus the Galilean he denied it before them all saying i do not know what you mean soon afterwards he went out and stood in the gateway when another girl saw him and said addressing the people there this man was with jesus the nazarene again he denied it with an oath i do not know the man he said a short time afterwards the people standing there came and said to peter certainly you too are one of them for your brogue shows it then with curses and oaths he declared i do not know the man immediately a cock crowed and peter recollected the words of jesus how he had said before the cock crows you will three times disown me and he went out and wept aloud bitterly chapter 27 when morning came all the high priests and the elders of the people consulted together against jesus to put him to death and binding him they led him away and handed him over to pilot the governor then when judas who had betrayed him saw that he was condemned smitten with remorse he brought back the 30 shekels to the high priests and elders and said i have sinned in betraying to death one who is innocent what does that matter to us they replied it is your business flinging the shekels into the sanctuary he left the place and went and hanged himself when the high priests had gathered up the money they said it is illegal to put it into the treasury because it is the price of blood so after consulting together they spent the money in the purchase of the potters field as a burial place for people not belonging to the city for which reason that piece of ground received the name which it still bears of the field of blood then were fulfilled the words spoken by the prophet Jeremiah and i took the 30 shekels the price of the prized one on whom israelites had set a price and gave them for the potters field as the lord directed me meanwhile jesus was brought before the governor and the latter put the question are you the king of the jews i am their king he answered when however the high priests and the elders kept bringing their charges against him he said not a word in reply do you not hear asked pilot what a massive evidence they are bringing against you but he made no reply to a single accusation so that the governor was greatly astonished now it was the governor's custom at the festival to release some one prisoner whom so ever the populace desired and at this time they had a notorious prisoner called barabas so when they were now assembled pilot appealed to them whom shall i release to you he said barabas or jesus the so-called christ for he knew that it was from envious hatred that jesus had been brought before him while he was sitting on the tribunal a message came to him from his wife have nothing to do with that innocent man she said for during the night i have suffered terribly in a dream through him the high priests however and the elders urged the crowd to ask for barabas and to demand the death of jesus so when the governor a second time asked them which of the two shall i release to you they cried barabas what then said pilot shall i do with jesus the so-called christ with one voice they shouted let him be crucified why what crime has he committed asked pilot but they kept on furiously shouting let him be crucified so when he saw that he could gain nothing but that on the contrary there was a riot threatening he called for water and washed his hands incited them all saying i am not responsible for this murder you must answer for it his blood replied all the people be on us and on our children then he released barabas to them but jesus he ordered to be scourged and gave him up to be crucified then the governor soldiers took jesus into the praetorium and called together the whole battalion to make sport of him stripping off his garments they put on him a general's short crimson cloak they twisted a wreath of thorny twigs and put it on his head and they put a scepter of cane in his right hand and kneeling to him they shouted in mockery long live the king of the jews then they spat upon him and taking the cane they repeatedly struck him on the head with it at last having finished their sport they took off the cloak clothed him again in his own garments and led him away for crucifixion going out they met a sirenian named simon whom they compelled to carry his cross and so they came to a place called gogatha which means skull ground here they gave him a mixture of wine and gall to drink but having tasted it he refused to drink it after crucifying him they divided his garments among them by lot and sat down there on guard over his head they placed a written statement of the charge against him this is jesus the king of the jews at the same time two robbers were crucified with him one at his right hand and the other at his left and the passersby reviled him they shook their heads at him and said you who would pull down the sanctuary and build a new one with him three days save yourself if you are god's son come down from the cross in like manner the high priests also together with the scribes and the elders taunted him he saved others they said himself he cannot save he is the king of israel let him now come down from the cross and we will believe in him his trust is in god let god deliver him now if he will have him for he said i am god's son insults of the same kind were heaped on him even by the robbers who were being crucified with him now from noon until three o'clock in the afternoon there was darkness over the whole land but about three o'clock jesus cried out in a loud voice Eli lamas up back tonight that is to say my god my god why has thou forsaken me the man is calling for Elijah said some of the bystanders one of them ran forthwith and filling a sponge with sour wine put it on the end of a cane and offered it him to drink while the rest said let us see whether Elijah is coming to deliver him but jesus uttered another loud cry and then yielded up his spirit immediately the curtain of the sanctuary was torn in two from top to bottom the earth quaked the rocks split the tombs opened and many of god's people who were asleep in death awoke and coming out of their tombs after christ's resurrection they entered the holy city and showed themselves to many as for the captain and the soldiers who were with him keeping guard over Jesus when they witnessed the earthquake in the other occurrences they were filled with terror and exclaimed assuredly he was god's son and there were a number of women they're looking on from a distance who had followed jesus from Galilee ministering to his necessities among them being Mary of Magdala Mary the mother of James and Josie's and the mother of the sons of Zabdi towards sunset there came a wealthy inhabitant of Arimathea named Joseph who himself also had become a disciple of Jesus he went to Pilate and begged to have the body of Jesus and Pilate ordered it to be given to him so joseph took the body and wrapped it in a clean sheet of fine linen he then laid it in his own new tomb which he had hewn in the solid rock and after rolling a great stone against the door of the tomb he went home Mary of Magdala and the other Mary were both present there sitting opposite to the sepulcher on the next day the day after the preparation the high priests and the Pharisees came in a body to Pilate sir they said we recollect that during his lifetime that impostor pretended that after two days he was to rise to life again so give orders for the sepulcher to be securely guarded till the third day for fear his disciples should come by night and steal the body and then tell the people that he has come back to life and so the last impostor will be more serious than the first you can have a guard said Pilate go and make all safe as best you can so they went and made the sepulcher secure sealing the stone besides setting the guard chapter 28 after the Sabbath in the early dawn of the first day of the week Mary of Magdala and the other Mary came to see the sepulcher but to their amazement there had been a great earthquake for an angel of the Lord had descended from heaven and had come and rolled back the stone and was sitting upon it his appearance was like lightning and his raiment white as snow for fear of him the guards trembled violently and became like dead men but the angel said to the women as for you dismiss your fears I know that it is Jesus that you are looking for the crucified one he is not here he has come back to life as he foretold come and see the place where he lay and go quickly and tell his disciples that he has risen from the dead and is going before you into Galilee there you shall see him remember I have told you they quickly left the tomb and ran still terrified but full of unspeakable joy to carry the news to his disciples and then suddenly they saw Jesus coming to meet them peace be to you he said and they came and clasped his feet bowing to the ground before him then he said dismiss all fear go and take word to my brethren to go into Galilee and there they shall see me while they went on this errand some of the guards came into the city and reported to the high priests every detail of what had happened so the latter held a conference with the elders and after consultation with them they heavily bribed the soldiers telling them to say his disciples came during the night and stole his body while we were asleep and if this they added is reported to the governor we will satisfy him and screen you from punishment so they took the money and did as they were instructed and this story was noised about among the Jews and is current to this day as for the 11 disciples they proceeded into Galilee to the hill where Jesus had arranged to meet them there they saw him and prostrated themselves before him yet some doubted Jesus however came near and said to them all power in heaven and over the earth has been given to me go therefore and make disciples of all the nations baptize them into the name of the father and of the son and of the holy spirit and teach them to obey every command which I have given you and remember I am with you always day by day until the close of the age Amen the end of chapters 22 through 28 and the end of the gospel according to Matthew from the Weymouth New Testament in modern speech translated by Richard Francis Weymouth recording by Mark Penfold