 Thank you very much. Can you hear me or can you hear me in the back? So thank you Giovanni and the other organizers for the invitation. I have never been here and it promises to be a very interesting week for me. I would like to ask you, I feel completely sleepy and jet lagged so please if you have any questions interrupt me, yell at me, do something so that I notice you even if I'm looking at the blackboard and I really mean it, just shout at me and then one of us will get you a microphone or I will repeat your question but just don't let me go on if you have any questions because it will be better for all of us. So I wanted to start with a simple example which will illustrate a lot of the things that I want to subsequently explain and that's KK bi-mixing. So this is, if you don't know what the K-meson is, it's a neutral particle and I will get to there a little bit later. What I want to emphasize is that there is, so there are two particles, the mass difference is measured experimentally to be something like 3.4 times 10 to the minus 15 GeV and you might ask where on earth does 10 to the minus 15 GeV come from in a problem that somehow relates to weak interactions, the typical scale of weak interactions is 100 GeV, this is a particle whose mass is 500 MeV. So how do you get to 10 to the minus 15 out of, there is nothing apparent here which gives you such an incredibly small scale. So how does the standard model do this and how can new physics not violate such a constraint which looks like, you know, like 15 orders of magnitude smaller than the typical mass scale in this problem. And of course for those of you who have studied weak interactions, you know that in the standard model which I will just denote by SM, this is coming from what's called a box diagram. So this is an S-quark, these are W bosons and if you look at the standard model calculation of this quantity, so this is the experimental value, then you get some expression which goes like the weak coupling to the 4S power, because there are four vertices, there are some CKM elements which I will define you later, if you know what they are then you know what I'm talking about and if not then I'll explain it in probably 15 minutes. It's coming from a loop diagram so there is a 1 over 16 pi square. The other terms which are important, there is the charm-quark mass over MW to the 4S power and there is some other, yet other quantities which are denoted by the K on decay constant, some other letter which forget about back parameters, so there's the K on mass which enters and some other things which are whether one quantities and are completely unimportant for this discussion. So you see that the standard model gets to the 10 to the minus 15 by having 16 pi square which is a factor of 100, MW is for all practical purposes 10 to the 2G EV, so this is 10 to the 8, M charm is one over one and a half, the CKM elements give you some suppression, G2 to the 4 give you some suppression, the K on decay constant is something like 150 MEV and this is like half a GEV, so you get a lot of factors together, so there are loop effects, there are the CKM factors, sometimes people call this the gym mechanism, the glacial ileopolis-mayone mechanism which in many of these processes gives you some light-quark mass suppression and all the hadronic physics like how does this diagram, ultimately you're asking what is the matrix element of this guy between K mesons and all that hadronic physics comes into some matrix element which I can't calculate for you, let this QCD people can, but it is, again you know what is the characteristic scale of that and we are not going to worry about whether one factor is. Now what happens in new physics scenarios and we'll get back to this in the last lecture in some more details, so if you have some new physics let's just hypothetically assume that there is some particle which can have an S-quark and the D-quark coupling with some coupling strings G to some particle X and make, so from SD by make a DS by and if you work out what is you know X is presumably some very heavy particle G is some effective coupling which we'll talk about whether it's order one or rather 10 to the minus three so you work out what is delta MK in some random new physics model divided by the experimental value and you get again that so this G is a different G than the G2 so you get G-square from two couplings there is certainly a one over Mx quail because this is some heavy particle that propagates there again we have to calculate this matrix element which will go some hadronic physics scale lambda QCD to the cube times delta MK the experimental measured value and so point number one throughout my lectures lambda QCD will not necessarily mean the same quantity as in Michelangelo's lecture which is strictly the QCD scale at the in the better function for me lambda QCD is some typical hadronic interaction scale take half a GB where like the room as on mass which is 700 MBV some some typical QCD scale and not necessarily the the the the same symbol that people sometimes write in the better function and what this tells you is that if this new physics is not to violate this experimental bound then you find that Mx has to be greater than G times something like two times 10 to the 3 TV so you say okay what is happening this is really a huge scale and you see that if you abandon all these particular suppression mechanisms that exist in the standard model then you get some very large scale that has to suppress such a process and of course you may ask I don't know anything about physics at the 10 to the 3 TV scale maybe there is no such particle but in many of the common TV scale new physics models you can generate this coupling G at one loop so even in in in low energy supersymmetry you could imagine contributions that G is not order one but order one over 16 pi square and you see that even if you plug in G equals 10 to the minus 2 or 10 to the minus 3 then you are still probing physics at the TV scale and and and that's really sort of generic that these kind of couplings can occur in most beyond standard model scenarios at one loop level so so there are lots of things that this example illustrates and before I say that I I should say one more thing that that all of this has been known since the 70s actually since the 60s so for example for a new physics model building if some new physics scenario gave a large contribution to delta mk that violated the experimental measurement this measurement has an uncertainty of about one percent then then then those models were kind of dead on rival so then specific mechanisms were invented to yield some additional suppressions for a new physics not to violate this bound in fact what's equally interesting that there's a parameter called epsilon k which is CP violation in kk by mixing and we'll talk about later what that is the difference in the case of epsilon k is that the dominant contribution comes from terms that go like the top that goes with the top contribution so it goes like VTD VTS square so in some sense epsilon CP violation in the K on sector is even more suppressed than just delta mk and generically has sensitivity to higher mass scales and the point is not that we can necessarily precisely calculate delta mk in the standard model if you take the state of the art calculations from lattice QCD there is still a long-distance contribution here and all we know is that the standard model can account probably within a 30 40% uncertainty for this observed value of delta mk so we don't need to calculate be able to calculate this thing very precisely it can still give us extremely strong bounds on new physics and again that will be a general question just like you heard from Michelangelo that quite often the issue is what are the processes where adoronic physics is tractable where we can understand strong interaction physics so that we can learn about you know beyond standard model phenomena that we really want to discover and understand and study if it exists within the reach of future experiments then one of the key questions in flavor of physics will certainly be in which cases can we understand the strong interaction physics and in which cases does strong interaction physics give you some uncertainties which are insurmountable and and and and and and it for in some cases it does for a bit learning about beyond standard model phenomena so so there is CP violation which can sometimes be even more sensitive to higher scales and of course the ultimate example of whatever the standard model or what we call now sort of the minimal extension of the standard model consistent with neutrino masses is that if you look at flavor changing neutral currents so for example interactions like new to e gamma then since the discovery of neutrino masses and neutrino oscillations we know that whichever way you extend the standard model to accommodate neutrino masses there is contribution to this process coming from one loop diagrams which now so if you ask what is this then again in the minimal extensions of the standard model to accommodate neutrino masses this decay rate will have suppressions by neutrino mass square over Mw square factors which is kind of one extreme case of fermion masses suppressing some decay rates and in that case sort of the predictions beyond without assuming additional new physics is that this rate would be something like the 10 to the minus 50 level again because you get some huge suppression from some light fermion mass over the weak scale to some power and and and probably I will get back to charge left on flavor violation in some of the later lectures so any questions yes this will certainly keep me awake so you quoted a bound on this kind of gauge boson X that this G times 2 TV to intend a bit TV so that bound seems to depend quite strongly on the choice of lambda QCD and it was because the expression depends on lambda cube and you said that it can be chosen 300 MV or 700 MV so it actually very strongly depends on your choice of lambda QCD so I want to know what exactly dictates your choice of lambda QCD I mean because if I assume 300 MV for lambda QCD then the bound will come down to one order of magnitude maybe so yes or certainly I this argument is not precise at that level so probably I should remove these two and just put here some whether one number and if you change so what I meant here by lambda QCD is that when you evaluate this matrix element whatever I'll say this is not a big work so as by left then you get some hadronic physics parameters and the K on mass which has mass dimensions 3 and we don't know a priori what that value is so whether you put here 300 MV or 700 MV I completely agree with you it changes this answer by a factor of 2 or 3 and that's kind of beyond the accuracy that I care about for this argument here all I mean what I really cared about is the 10 to the 3 TV and even if G is 10 to the minus 2 at 10 to the minus 3 you are still probing TV scale physics that's what I want to know actually so can I put it there 300 MV for example so you are putting there 700 or 800 MV if I put say 300 MV then it is lambda Q it enhances by a factor of 7 by 3 whole cube right because it's MX quail I have taken one square root in between so this scale goes like the 3 halves power of what I put here okay yeah even if I put here a factor of 3 bigger a 3 smaller scale the answer will only change up way down by a factor of 4 and where the purpose is of this yeah so you can change this by an order of magnitude but not more okay thanks any other questions so so what do I want to do so I want to give you some examples and some some of the theoretical background to explain how flavor is sensitive to beyond standard model phenomena it certainly and then again there is no way to distinguish this from the fact of what it taught us about the standard model in the past so sort of there will be some historical some historical aspects of developments of the standard model in recent years there were example of sort of let's call them anomalies that show up in experimental data that could be beyond standard model physics and I will talk about a few examples where it even even anomalies which look like observables that have nothing to do with flavor physics when you try to build some model around it that would explain it then very often flavor will be a constraint on the models that could accommodate some experimental data so I think that there is a very strong case that whatever the LHC will find in the next run that we all hope to understand what the underlying physics is flavor physics in my opinion will be important to understand what the new physics could be or what the new physics is not and since I think one of the things which has been fun in the last 10 years or 20 years about about this physics is that sort of the development experimentally and theoretically has gone hand-in-hand there was a lot of data from the b-factor is at slack and in Japan now there is the LHC experiments of course Atlas and CMS and also LHCB which is providing a wealth of information there are new K on experiments both in Japan and that's on that are turning on so there is really an incredible development source there's the issue about experiments improving in some cases by a factor of 100 in some cases by a factor of 10,000 the 10,000 is the interesting case of mutual conversion where the current bounds are expected in the next round of experiments to be conducted at Fermilab and at Jay Park to be improved by a factor of 10,000 and so this give you access to distance scales or energy scales that could give rise to deviations from the current expectations sort of an order of magnitude higher scale than what we have access today and of course whenever you can access an order of magnitude higher energy scale that is quite exciting so and of course there is the other issue that we really understand kind of surprisingly little about flavor physics that so there's something that people call the standard model flavor problem that we really have no idea why there are three generations what gives rise to the hierarchical parameters that you will see in between the quark masses and the mixing angles why is it that the neutrino parameters that professor Smirnov talked about I do not appear to be similarly hierarchical and of course in the context of the new physics I mean whatever I will hope to find new physics at the TV scale in many of the new physics models there are new physics flavor problems and when people talk about that we usually refer to the fact that the hierarchy problem indicates or I suggest that there should be some new physics at the TV scale so that we can understand the Higgs mass why the Higgs mass is so light and this scale seems to be substantially smaller than sort of what would be a natural expectation of sort of the new physics flavor scale if you just look at bounds like this so certainly you can there are lots of ways to reduce this tend to the three TV to a TV but you have to do something so that it happens it doesn't happen automatically I wanted to say one more thing about the experimental improvement so because sort of this tend to the four improvement is really an extreme case but if you just look at LHCB and and Bell 2 which is the upgrade of the Japanese E plus E minus B factory they will have a quarter of 50 times the data that they have gathered so far and the scale of new physics that they are sensitive to in that case goes like the first route of the integrated luminosity in that case it's 50 and the first route of 50 happens to be some number like 2.7 so even sort of the most conservative way of how the energy scale that you are sensitive to where the distance scale that you are sensitive to by in the next round of experiments improves by a factor of several so so I think it's quite interesting because the experimental precision will improve a lot there is of course related set of questions in which case can this is the theoretical understanding good enough that you can make use of this improved experimental precision to really learn about short distance high energy physics rather than rather than just QCD and of course sometimes people ask what are the expectations for the deviations from the standard model in all these measurements and of course on that there is a differing set of opinions depending on what your favorite new physics model is but I would say that sort of any deviation beyond the current limits are possible that have certainly been a huge body of literature which has predicted bigger deviations than where the current bounds are right now one of the important messages that will come repeatedly in these lectures that so for example here in KK biomexing even though this looks like an extremely precise field if you ask what is the bound on how much could new physics still contribute to the observed value of KK biomexing delta MK then the answer is that we know that surprisingly poorly so so something like a 30 40 percent new physics contribution to the measured value of delta MK from new physics is something that is certainly still allowed and and and so so so this will come back and it's going to be important that that despite the fact that the sometimes that is highly precise measurements at the percent level at the few percent level when you ask how well do they constrain new physics in many cases new physics to this flavor changing interactions can still be 20 30 percent of the standard model so so in some ways it's a very precise field in some ways there is still room for a large deviations and that's interesting I think any questions so I wanted to so what should you expect I think that in the rest of today's lecture I will talk about flavor and CP violation so if we're using abbreviations but I write slowly so the flavor and CP violation in the standard model I don't know how this will go until probably it will slip into the second part something sort of constraining new physics in in mixing so it will turn out that neutral meson so there are four neutral mesons the K on the D meson and the B and the B sub S meson so neutral meson mixing will play a very special role in this story so I will explain how well we can constrain new physics in in in these neutral meson systems in the third lecture I will probably talk about some of the sort of strong interaction or QCD or effective field theory methods that will allow to understand some of this hadronic physics and in my last lecture I will talk about sort of flavor at the TV scale sort of whatever top work so sort of top flavor properties maybe leptons so charged left on flavor violation maybe a little bit about Higgs maybe a little bit about super symmetry and flavor who knows is this font size okay from the back so so you so it wasn't here yesterday but I'm sure you heard or you know very well that there are several ways that we know that the standard model is incomplete we certainly have very strong evidence or I mean it's beyond doubt that dark matter must exist and we don't know what is the particle nature of whatever makes up dark matter we also don't know exactly how neutrino masses should be added to the standard model and what I mean by that is that we don't know empirically whether neutrino masses violate or it don't violate lepton number what people sometimes refer to as the may run or a dark nature of neutrino mass and there is also I think and an equally strong argument with the billion asymmetry of the universe that you may have heard about that we know in the in the current universe that if you look at sort of the billion number the ratio of whatever you know that the world around us is made up mostly of billions the density of anti billions is negligibly small sorry so so if you look at the number of density of variance minus the number of density of anti billions divided by the entropy density of the universe then we know today that this is about 10 to the minus 10 and this is roughly a constant in the expanding universe and what this means is that soon after the big bang when the temperature was so high that quarks and anti quarks were in thermal equilibrium at the very beginning there was a corresponding so sorry not at the very beginning that's actually important there was an asymmetry that formed in the only universe between the number of quarks and that and the number of anti quarks that later resulted in this billion asymmetry and it was sorrowful first formulated a set of three conditions that is required to generate this billion asymmetry and if you if you wish you could ask well if if if somehow so the point is that okay so there actually it's a little bit of a complicated story because you could ask that somehow at the very beginning at the big bang that could have been some asymmetric initial condition that formed more billions than anti billions but the point is that if inflation happened and there is a very strong evidence for inflation then inflation would have washed out whatever asymmetry there was from the initial conditions so the very only symmetry that we see now is presumably dynamically generated through the thermal evolution of the universe and for that to generate a very on asymmetry you need very on number of violating interactions you need because otherwise obviously there would be always equal number of billions and anti billions you need C and CP violation because without that you would always even in the presence of very on number of violation without C and CP violation you would still generate equal number of particles and anti particles and you need deviation from thermal equilibrium because again in thermal equilibrium even in the presence of very on number violation and C and CP violation because of detailed balance you would form you wouldn't be able to generate an asymmetry and the interesting thing is that within the standard model you can actually do a calculation you all these three ingredients are present in the standard model but you find that the prediction of the standard model is something like ten orders of magnitude smaller than the observed value in asymmetry in the universe and so one of the conclusions of this is that to make this work you need a stronger the so in again in the standard model there are several problems why this doesn't work one of them is that during the electrophobic phase transition the deviation from thermal equilibrium is too small and that could be fixed for example by a more complicated Higgs sector or low energy supersymmetry or anything or not anything but many new physics scenarios and also you need stronger CP violation so these considerations give a very strong reason that very likely there has to be CP violation beyond the standard model and and that of course is a strong reason to look for a CP violation beyond the standard model interestingly enough if you take the standard model there are several places where CP violation could occur it can occur in the quark sector that we'll talk about throughout these lectures and there is one such parameter that is an observed source of CP violation it can also occur in in in in the QCD Lagrangian itself if if the QCD Lagrangian contain the term which goes like F mu nu F mu nu dual that such a term would violate CP it would give rise to for example electric dipole moment so this is this is the term that usually it's written as its coefficient is parametrized as that of QCD times I guess 16 or 32 pi square which I always forget but someone will correct me so if that of QCD were non-zero that could give rise to for example electric dipole moments for the neutron on which there are extremely strong constraints and we know that this parameter for reasons that we don't understand but the plausible theories for it and you'll hear about some of them next week has to be smaller than something like 10 to the minus 10 and since the neutrino masses that was discovered in 1998 or so we know that there could also be CP violation in the neutrino sector and that is something that we have not found yet but but but but of course the also all these reasons I think I saw a strong motivation to to look for additional sizes of CP violation beyond what we have seen so far yes I am I am searching I am looking for a process that violates the variable number and violates the CP and the C what about deviation from similar equilibrium does with this process in some way I think is this depends on the universal scale it's in the universe is what yes so some I'm not sure I precisely understand the question about we wish to give you back the microphone so so there has to be some process which gets out of thermal equilibrium during the thermal evolution of the universe so for example so for example in in leptogenesis model so for example like something like super cooling so if you if you have some what's what's a good explanation for this if but it's a property of no no no so it's certainly for some process well where these phenomena can take place so you're right that in the case of electroweak value genesis the question is whether the electroweak phase transition when the Higgs acquires a vacuum expectation value is that a second-order phase transition is that a first-order phase transition and how the how how that phase transition takes place so yes it is it is dependent on the on the process in that sense maybe I still don't understand your question it's related to to the it's related to some interaction that would generate so for example in the context of the standard model it would give you some constraints on the Higgs mass that if the Higgs mass were lighter than what it is experimentally is do I get it backwards or not I think that the Higgs mass would have to be substantially lighter in the standard model to make the electroweak phase transition first or at all so that some electroweak process during that phase transition can can produce a billion a symmetry so in the in the context of the standard model with the electroweak value genesis it can be written as a constraint on the Higgs mass so it's in that sense that and if you have some beyond standard model scenario again looking at which processes remain in term like equilibrium and how quickly certain processes occur at a certain energy scale that can give you constraints on parameters of a model so okay maybe we should continue afterwards yes related to non perturbative effects because always we see if that if no if if do I do I love it's a dimension for a term that you can write down so you should write down and and so sorry in electromagnetism if you only had you one then you you can show that that term is irrelevant so it's it's a it's a it's a boundary term it's it's it's it's in the electroweak theory that that there are physical consequences of that term so just in QED it would be inconsequential any relation between this term and instantons and non perturbative possible I mean so one of the explanation for this term why the term is dynamically so small is for example if there is an axion and there will be a whole set of lectures next week on axions so I'm sure that this will be explained better next week someone else had a question yeah my questions related to that I'm just wondering why you've listed that as CP violation beyond the standard model since that term is a generic feature of this yeah so I shouldn't say beyond the standard more light but what I what I meant to I would say that that's a part of the standard model and we just don't understand why the coefficient is so small so I don't I don't know what the standard model is anymore with neutrino masses because we don't know whether the right-handed light neutrinos or not and to me that's an experimental question there's a very strong prejudice that among most theorists including myself that neutrino masses come from a dimension 5 term and it's a Majorana mass but we don't know it empirically so but yeah I would certainly say that that term is a part of the standard model because we can write it down and we just don't understand why the coefficient is so small anyone else yes excuse me how much the CP violation phase is needed for explain this barion asymmetry so in the quark sector in the standard model there is no phase even if it's maximal phase I mean it's not enough so the problem is that in the standard model from the CP violation that occurs in the quark sector the the effect its consequence for the billion asymmetry is not only related to the CKM parameters and like the sign of the CP violating phase but you also get a product of the mass quark mass square differences so what suppresses the standard model so badly is not really the smallness of CP violation but that it comes in a combination with the quark mass square differences which are much smaller for most of the quark mass square differences than the electro weak scale and the origin of that you you can understand because we'll come back to you that in the two-generation standard model there would be no CP violation so what's called the Yarskog invariant if that's familiar to you that contains all the separately all the three up type work mass square differences and the three down type work mass square differences and if any of those two words any of those maybe I can write it down and if any of those were zero then the standard model quark sector it would not have CP violation and so it's really this quark mass square differences which make the answer extremely small because what is in the denominator is the MW square at a weak scale and in the smallness of the quark masses in this invariant which make the answer so tiny yeah in in the standard model it it's not enough but but how much is enough for for the for produce this asymmetry I'm not an expert on that question I think that usually the standard model is quoted to give less than 10 to the minus 20 so it's like 10 orders of magnitude too small and and and the details depend on lots of things that would lead us to some direction that probably some of you know more about than I any other questions so so okay so in the standard model we have left-handed quark so left-handed quark doublets which go like under SU 3 it's a triplet SU 2 doublet and it has a hypercharge 1 6 we have right-handed quark singlets which are SU 3 triplets singlets under SU 2 and have hypercharge 2 3rds right-handed singlets which have 3 1 minus a 3rd lepton doublets which are 1 2 minus a half and the right-handed lepton singlets which are 1 1 minus 1 and so for most of these lectures I will ignore the lepton sector but so to me the definition of flavor of physics or what is flavor of physics is basically any interaction that distinguishes between the three generations of this fermion representations so why why why why why three fermion representations and then what what makes the first and the second and the third generation different and of course we know that in the standard model everything comes from the you cover couplings of the fermions to the Higgs field so there is the down quark you cover couplings which couples cube bar to the Higgs field to drj and there is the up quark you covers which couple the left-handed quarks to phi tilde which is something like I so to I conjugate what to j and then for the lepton sorry so it's a coupling between these left-handed doublet so it's always coupling a doublet to a singlet with the Higgs field and so these you cover matrices I had some three by three complex matrices which are completely arbitrary as far as we know and after electrophic symmetry breaking so this doublet field the complex doublet field acquires a vacuum expectation value and you get masterms well the down quark masterms will have a matrix which is just coming from the web the Higgs web times these you cover matrices and now these couples to the left-handed and the right-handed down quarks and they similarly a term for the up quarks and again these are still arbitrary 3 by secret 3 complex matrices and as you may know any 3 by 3 complex matrix can be diagonalized by multiplying it from both the left and right by some unitary matrices so I'm going to insert the unit matrix here written in some funny form Vdr dagger Vdr and here Vdl dagger Vdl so these Vs are just some unitary matrices so this is the identity and this is the identity and they are chosen such that if I look at this 3 then this is a diagonal diagonal matrix which is just md ms mb and if you can and if you figure out what are these unitary rotations these two unitary matrices that diagonalize the mass matrix then by definition these transformations on the left-handed down quarks and the right-handed down quarks will give you the mass eigenstates for the quarks and similarly for the up type quarks there is this is another 3 by 3 matrix so it's a two unitary matrices from left and right that can diagonal diagonalize that matrix and a priori those unitary rotations have nothing to do with what they're with the matrices that diagonalize the down quark mass matrix so this is Vul dagger Vul and Vdl dagger Vdl so again Vul times Mu times Vdl dagger is the diagonal matrix for the up quarks so m up m time m top and and Vdl times Uij is the mass eigenstates sorry is the mass eigenbasis for the for the up quarks and the point is that yeah so for example I was not writing I should have some index on these things because these are the weak interaction eigenstates and these are the mass eigenstates but what you can see is that this left-handed quark doublet contained an up quark a left-handed up quark and the left-handed down quark and you see that they diagonalizing matrix for the for the left-handed up quark and the left-handed down quark is just two matrix which are unrelated to one another so this field Ql which was an Su2 doublet Ul and dl in the weak interaction basis now when you diagonalize the mass matrix for for the quarks then you have to use different have to apply different unitary rotations for the Ul and the dl guys which will part of the same Su2 doublet and so the Ul the left-handed up quark is diagonalized by Vul DeGal so I pulled that out and what I'm left with I should put so these are interaction eigenstates weak interaction eigenstates I should have put an after index I on all of these for weak interaction eigenstates I'm sorry for being sloppy and here we get a Vul Vdl DeGal times yeah so I want this to be ij this is jk I guess this must be j then okay good so so it's it's kind so it's really kind of a simple story because this mass matrices are diagonalized by different unitary rotations for each of these fields we end up with sort of this misalignment that when we go to the mass eigenstates where the up and the down quarks the left-handed up and down quarks then we pick up this unitary matrix that that that gives you a misalignment that that that in the mass basis the the su2 doublet field will not only contain an up quark but it will contain a linear combination of all the down quarks and so it's really this matrix which is usually referred to as the ckm matrix and since it's the product of the unitary matrix and the two unitary matrices this matrix is unitary as well and what it tells you is that the weak interaction which started out if you just write down the kinetic terms in the in the in the weak interaction basis weak interaction eigen basis it was so the W in this basis couples diagonally to the quarks after you go to the mass eigen basis which really tells you what are the states that what are the propagating degrees of freedom which have a well defined time evolution then now the W no longer couples just the same generation up and down quarks but it couples an up quark to a linear combination of the other three down quarks so so the physics of this is that you get what's called the charge current weak interaction interaction of a W plus with so for example if you produce here you I then this guy can be any of the D of the three different kind of down quarks and the coupling is going to be g2 the weak coupling times the ckm matrix ij and it just comes from the fact that it's different that the mass matrices are diagonalized by different transformations for the up and the down quarks and so an important property of this is that you are getting that you get this the W interactions change the quark flavor at the same time when you look at the interactions of the Z boson what else did I want to say so you can go through this diagonalization because the so so the interactions of the Z boson remain flavor diagonal so they only couple to whatever Uli to Uli or Dli to Dli whatever left or right and so you just one second so you get charge current interactions at three level the Z remains a flavor diagonal the coupling to just the same quark anti quark pairs without any what's called flavor changing neutral currents and if you want to so for example if you want to have some decay say k long to mu plus mu minus which was actually historically important because that's really so there was a puzzle in the late 60s that k long to mu plus mu minus was not yet seen experimentally and the theoretical calculations would have predicted it to be seen in at that time we only knew about people only knew about three quarks the up down and the strange and so if you if you want to do this kind of flavor changing if you want to get this kind of flavor changing neutral currents then you need to have what's called a second order of weak interaction so you have to have two electro big gauge bosons involved because you cannot get such a flavor changing neutral current at three level in the standard model and it's kind of the same story for K long to mu mu or KK by a mixing that we started with over there that from this point of view doesn't matter so so here you are changing a down type work to another down type work that's why it's called a neutral current and and these type of interactions in the standard model only occur as a as a second order process with the with with with with with two at the loop level not not not at three level there is another so there's an important aspect of this so here in all these loop diagrams you can have three type of internal quarks and if you calculate this amplitude it's going to look like what else can it be as a sum of three terms so V us VUD star time some function of M up plus V VCS VCD star time some function of M chime for the chime piece and the cell the cell term is VT S VT D time some function of M top so this is I haven't really computed anything I just denoted this loop integral the only difference between these processes is between these diagrams is the identity of the internal quark in this diagram so there is some dependence on on on on on the quark masses and you can see immediately that because the CKM matrix so it was VUL VDL dagger so what is so you see immediately that that VCKM times VCKM dagger that's also the unit matrix because it's nothing else but VUL VDL dagger times VDL VUL dagger so so this is one and where that times that is also one so because the CKM matrix is unit is unitary that tells you that in the limit of when the quark masses if the quark masses all vanished then you would have V us VUD dagger so let me pull out f of zero symbolically times VC S VC D dagger plus VTS VT D dagger plus there will be terms that go like so what I'm imagining is just Taylor expanding these functions of the quark masses about zero and you see that the leading term sorry the first term which the quark mass independent term gives me this sum of CKM matrices which has to vanish because the CKM matrix is unitary so then the next terms which go like the uptype quark mass squares those will be the leading terms which are non-zero but these will always be when you write down the result will always give you terms which go like some mi square minus mj square over the V scale square because these are because the dimensionality of the answer doesn't change and I you have to go to second order in the quark masses to get an on-zero answer so so any flavor changing useful current process in the standard model is proportional to some quark mass square difference over the V scale and of course you see that there is an important caveat that when so in processes where the top quark can play an important role then this is not a suppression factor at all for for for for processes where the top quark dominates but for processes well the first two generation dominate then these type of factors usually get give you a very severe suppression like in the case of KK by mixing that we started out with so so you see that this flavor changing neutral currents really in some sense very directly probe the differences between the three generations and and they are always suppressed except when the top quark can dominate some particular process so so this will be relevant for many processes in the in the B-meson sector and a few cases in K on the case well where the top quark diagram plays the dominant role in the case of so K long to Mu Mu is actually an interesting case because it's a combination in fact of the top diagram and and long distance contributions that determine the answer so so let me say a little bit more about the CKM matrix before we finish so it's obviously a 3 by 3 matrix and I'm not going to write it out once we know what are in the corners that's all I can remember and so basically this so this is a 3 by 6 3 complex matrix which is unitary and and and and and and it's a very different set of experiments that can give you information on the magnitudes and the phases of these of these nine complex numbers we know empirically that in the so this this may mixing matrix in the quark sector has an approximately diagonal structure so that the entries so that the W interaction is almost flavor diagonal but not quite and so it is a useful parametrization that was introduced by Lincoln Wolfenstein to to parametrize this matrix by by by by four parameters I should I should have said it before so so a 3 by 3 unitary matrix in general depends on nine parameters right three mixing angles and six phases and you can show in lots of different ways we can talk about it afterwards or you can ask me that five of these phases can be removed in the quark sector so there is one complex phase and three real mixing angles that parametrize the this mixing matrix and just so the magnitudes of these elements are physical quantities they are phases depend on conventions and and just to keep track of the weather of magnitude of of the different terms so lambda c is usually called a cubby boy where it's actually so lambda c cubby boy which is something like 0.2 to 5 or so and and usually it is quite useful that you can put the CP violating phases into this smallest whatever five of the diagonal entries of the CKM matrix and so for many processes it is actually useful to think about just VUB and VTD to carry a complex CP violating phase but you should remember that to get something face convention independent that is CP violating the result always has to depend on four CKM elements you cannot have a CP by any CP violating physical quantity has to depend on four CKM elements it cannot depend on few well and of course because this is a unitary matrix if you take the scalar product of any two rows i and j that has to give you delta ij similarly the dot product of column 9 and and two different columns have to give you delta ij and what do I want to do in the next five minutes I saw that I would get a lot fired also so so let me just say one more thing that of course the interesting question is not measuring this element whatever these parameters they are just some couplings in there in in the standard model Lagrangian the real question is how can you do measurements which test this structure where sensitive to to be on standard model phenomena and because there is really a lot of different measurements which are relevant for answering this question it has sort of become a useful language to get a graphical representation of constraints on on the CKM matrix that is called a unitary triangle and I it's it's kind of you should really think about it as as as a way to compare lots of independent constraints on the CKM matrix so what it comes from is taking the scalar product of the first column and the and the last column so so one of these unitary relations tell you that VUD times VUB conjugate plus VCB times VCB conjugate plus VTD times VTB conjugate has to be equal to zero and this so these are the sum of three complex numbers adding up to zero that is some that you can represent as a sum of three vectors adding up to zero that's also called the triangle and it is conventional for entirely historical reasons so 20 years ago 30 years ago people had a fairly good idea of what is the magnitude of this term and therefore it has become customary to take this relation and divide out by this term so then you get another relation which is one and now you can draw this this triangle but this is zero zero this is one zero and so this is the VTD VTB side and this is this and it and and and in that parametrization the coordinates of the apex of this triangle is rho and eta and I guess we'll get to it only tomorrow that so so so instead of me trying to draw all these constraints there is a sort of the state of the plot and and and we'll just go through a few of these measurements so that's what I by I meant that the unit is triangle is really just the language to compare different constraints because you can do measurements of the sides of this triangle using both three level processes and for some of the measurements you can do loop level processes so the consistency of those can test possible new physics contributions in in in in in in in processes which in the standard model only occur in loop diagrams and by studying CP violating phenomena so this angle is usually labeled as gamma of beta by studying CP violating observables one can also get direct information on the angles of this triangle in fact one can do different measurements of the same angle which is sensitive to new physics and we'll see some examples of this tomorrow or on sales day so probably I should stop and continue from here next time so what do I want to say so okay so so just to talk about this for a minute so so the most important constraint so that if you haven't seen this before so so there are direct measurements for example of this angle better which is this angle and we'll go through how why that is so precise and how can that be independent of QCD effects to an extremely good accuracy tomorrow there are also some measurements of the angle gamma which is going to be very important partly because so all of the all the angles alpha and better I measured in processes which are loop processes in the standard model they involve BB biomexing gamma is special because it can be measured in three level processes and similarly on the when you measure when people measure the sides of this triangle they can be measured from processes involving BB biomexing or processes such as semi-laptonic decays the new physics is very unlikely to influence the standard model results so you see that the complexity of this is in the fact that you're really putting a lot of measurements some of them are insensitive to new physics some of them are sensitive to new physics and you are trying to compare whether they give a consistent determination of standard model parameters or whether there is some tension between them which could indicate the presence of new physics or where our lack of understanding of something that we thought we understood but basically this is sort of one of the flagship flagship plots of the of the last 10 years of B-factory progress and what I will explain next time is that even though this plot looks like you know like a dozen measurements or something like eight nine measurements having an extremely good consistency just like where we started in the chaos sector despite the fact that the very consistent results if you assume the standard model from the beginning if you allow for a possible new physics for example in BB biomexing then these then the constraints on the new physics parameters are actually much weaker and sort of the conclusion will be that also in BB biomexing just like in KK biomexing we can still have 20-30% of the standard model contribution that could come from new physics processes so we'll talk about neutral meson mixing and CP violation tomorrow and we'll see how far I can get tomorrow.