 Thanks very much for coming back on a Friday morning and I should start with an apology because yesterday there so I was as you could tell I was running out of time and I think I did a totally messy job with heavy quirk symmetry so I will spend whatever whatever I will have to skip at the end I want to do a little bit more justice to the topic and and sort of talk about it for 10 15 minutes that gives you an idea about the power of the theory so that so that it's not it's not it's so that it's a little bit less confusing than it was yesterday so the idea was to try to separate and I still want to encourage you to interrupt me at any time you know if I whatever I wanted to talk about if I don't cover it I much rather have lots of questions then then go through all my notes so the idea was to try to separate the large and the small momentum components of these heavy quirk systems so I will be a little bit technical in the next five minutes but maybe that will still give you a help build up an intuition about what's happening so so that the formal construction of the heavy quirk effective theory uses so you want to separate out from the heavy quirk feel the large momentum components so that the dynamics covariant derivatives only act on momentum components which are of order the QCD scale and we saw before that so so the heavy quirk goes whatever if you define the heavy quirk velocity as V mu equals P mu over M heavy quirk and Q will be either B or C throughout this discussion then in the infinite mass limit the light degrees of freedom and soft QCD interactions have to leave this velocity invariant and this allows you to define sort of modified fields well now this moment whatever this velocity acts acts as a label on this field and I defined this by pulling out the large components of the momentum and I use this projection operator as 1 plus V slash over 2 and and and you see sometimes one minus V slash over 2 so this is the full QCD field and I pull out this face factor and I will also define P plus minus just to introduce some notation so I want to pull out the large momentum components so when I X with the derivative on this it pulls down MQ and you'll see why this is good and we said before that in the rest frame of the big work one plus V slash over 2 so in the rest frame V is just one zero zero zero so this is one plus gamma zero over 2 and that's a projector on the quirk rather than the anti-quirk degrees of freedom and you can define another field which is as you could maybe guess sort of the qualitatively at leading order you can think about it as projecting on the anti-particle degrees of freedom of this four components Pinoy and then you can sort of invert this and write Q of X as e to the this is sorry this is plus and so once I define this and I look at the QCD Lagrangian which is just Q by ID slash minus MQ Q and I plug this in you see that the derivative acting on this exponential factor will end up canceling this MQ term and after a few lines of manipulation that I don't want to write down here you end up with that with the Lagrangian just for sort of the big components the heavy-quare components of the field which will just look like ID slash sorry IV dot D times Q of V and when I said and of course there's some higher-level terms which are suppressed by inverse powers of the heavy mass scale and in the numerator there is some typical QCD scale and if you wish you could have started from this Lagrangian and derive that the propagator is just one plus V slash over two times I over V dot K there are sort of so now this covariant derivative so the moment of this field does not scale with the heavy-quare mass that's the whole point so the dynamics so you have a couple of the dynamics which kind of scales with the heavy-quare mass as you take the heavy-quare limit and the soft QCD interactions and dealing with this Lagrangian is much easier than dealing with full QCD and that's what results in a lot of simplifications and again once you go to subleading order I just want to say that this this is a formalism which then allows you to do pair to a but if QCD corrections and so you can separate QCD corrections that the big black mass scale at the time scale and and ultimately parametrize the low-energy physics so just to give you an example I was waving my hands yesterday that's when you look at some elliptonic decays so you look at the B decay to a D and the left on and the neutrino where these style and the left on and the neutrino the only kinematic variable on which strong interaction can depend on so this guy has momentum P this guy has momentum P prime there is the variable Q square equals P minus P prime square and it turns out so this is a neutrino sorry and unfortunately my knees and my visa almost indistinguishable even from this distance so let alone from where you are so again the physics is that there is a heavy quark in a mason and the weak current can change its spin and it can change its velocity but nothing else happens in some sense and there is this left on neutrino pearl which is produced from from the weak interaction but as far as the heavy mason is concerned all that happens is that you change the spin of the heavy quark possibly or you leave it invariant and you can change the velocity and sort of the physics of where a big part of the predictive power of heavy quark symmetry for these systems where these transitions comes from the fact that if but in the case where P over mb which I will call V and P prime over m charm which I will call V prime so in the case where V and V prime is the same then in some sense you haven't done anything to the dynamics of this of this bound state of this B mason or a D mason so so so let me just work this out so Q square is mb square minus m plus md square and okay that's it and so here is where the spun starts so we said that on the heavy quark symmetry this is a spin one sorry a spin 0 pseudo scalar mason this is a spin one vector mason but they are doublets of this heavy quark symmetry and you can combine these two fields into something that is for all practical purpose purposes like a super field something that has two different spin two different angular momentum states in one field as 1 plus V slash over 2 times gamma mu times so m star is the vector mason in that case it could be a D star if it's a chime system so this has some velocity and some polarization tensor and this guy is the pseudo scalar and you can show that there is a unique form of this expression which contains both the D star and the D and has the right transformation properties under Lorentz symmetry and under heavy quark symmetry and the reason this is going to be sort of a beautiful is because if you are interested in some current so let's say we are interested in the current that the C by gamma mu B transition between so you start with the B mason with velocity V you end up with the D mason with velocity V prime and you could end up so you could ask what is the matrix element of this current or what's the matrix element with some other current with some other Dirac structure or you could ask what happens when this final state is not the D but the D star and all of these different things so changing the spin of the final state changing the Dirac structure it's all related to one another through heavy quark symmetry and you can work out so basically the formalism uniquely determines what is the form of this matrix element want to use the whole blackboard for heavy quarks because then we'll talk about other things so you can write in sort of general any of these matrix elements as so that curly field M I will put the label on it so now this is the D or D style because it contains a chime quark with V prime there's a C by gamma mu B and there is the other guy sorry that this the B mason which I can embed it in sort of its own super field which is different than this but it has the same structure and heavy quark symmetry tells you that this matrix element can be written as the trace over some function of V dot V prime because there is no other kinematic variable times those tensor structures that that that encode all the Lorentz and heavy quark symmetry properties of these states so this is M V prime I can put here some arbitrary general gamma matrix and that's useful because then I automatically get the relations between the vector current and the axial current and so F is just the most general thing I can write down so the only thing I have at my disposal is V and V prime and they are dot product which is so V dot V prime I should I write so V dot V prime which people usually call W is just given by it's basically proportional to minus Q square and it is just MB square plus MD square minus Q square right so this is it kind of just comes from this equation that this is M B times M D times V dot V prime so you solve for that so so in this sense the kinematics is easier described in terms of W but it's just really a rescaling of Q square and this function f cannot depend on anything else then it has to have a form of F1 of some Lorentz invariant object which is the only thing that there is is Q square you can write down another term which is F2 times V slash or you can write down a term which is F3 times V prime slash or you can write down a term which is F4 times V slash times V prime slash and there is nothing else you can do because because both V square and V prime square is one and and any anything else which involves more Dirac structures can automatically be reduced to this form and what heavy quarks symmetry the reason heavy quarks symmetry becomes so powerful is because it tells you that between between the V current and the heavy meson states you cannot insert any other Dirac structure in this form so it kind of uniquely determines the form of the matrix element and also because this one plus V slash over two is a projection operator so it is its quail is itself you can show that one plus V slash over two times M times one minus V slash over two is the same as M so in some sense you can send which M between projection operator is one plus V slash over two and one minus V slash over two and these don't do anything on these on these fields and what that allows you to do so effectively if you look at this trace and you remember that a trace is cyclic then after you calculate the trace this functional form will have the same effect as if it was sandwiched between these projection operators so you see that I can insert here sorry there should be a buy on something someone should have yelled at me right so I can put a one minus V slash over two here where you can put a one plus V slash prime over two here and again using this totally straight for a vertical algebra you can show that P minus sorry yeah so I can I can put a one minus V slash over two here and because this is the m bar I can put one minus V slash prime over two here right because when you do the Hermitian conjugate the weather reverses and you can show that between one minus V slash over two and one plus V slash over two you could write down these four different functions but they all reduce so for any matrix for for any matrix element that you care about it's not an identity in general but for any matrix element it is this complicated mass is just F1 minus F2 minus F3 plus F4 it doesn't matter what the structure is the only point is that there's only one linear combination that matters and that's it and and sometimes people call this combination C of V dot V prime this is often called the Isgui vice function in the literature and and and what it tells you is that all of these matrix elements and I said yesterday that in full QC there are six different functions of Q square that parametrize these matrix elements heavy quark symmetry allows you to relay them to just one function of Q square so so instead of six functions that describe these transitions you only have to worry about one function and then the rest is organized in terms of corrections which are suppressed by the QCD scale over the heavy quark mass moreover because a B-meson is stable under QCD interactions it's only weak interactions that can change a big quark number you can use the fact that so the big quark number current which is just B biogama 0 B between equal velocity or equal momentum B states is so in terms of QCD interactions this is a conserved current it's only weak interactions which can change the heavy quark number so depending on the favorite normalization of the meson states this is just given by a number like typically chosen to be two and if you use relativistic normalization it would be like 2p0 and in HQET it's people usually take out the heavy quark mass from the normalization of the states anyway it's just given by a number and I can also calculate the cut this matrix element using this formalism and the comparison of the two allows me to conclude that this function at zero recoil so in the point where the B-meson and the D-meson has the same velocity is called sometimes zero recoil because in the B-rest frame the D-meson doesn't recoil at all so this is just given by unity so so all the hadronic physics is embedded in just one function and the symmetry allows you to determine the value of that function at a special kinematic point which is zero recoil which is equivalent to maximal Q-square so that's kind of how much I wanted to dig into this and maybe it gives you a little bit more of an impression or whatever a little bit more understanding that there is really a very well-defined machinery in effective theory that allows you to work out the consequences of heavy quark symmetry and systematically address subleading corrections any questions so in the remainder of my time I wanted to say a few things about flavor and new physics and maybe I will be a little bit more agnostic about what new physics might be then some other lectures in these two weeks and so I want to treat the standard model as a low energy effective theory of some higher of some high of some completion which is valid at higher energies and then from this low energy effective theory point of view the question is do we see evidence for some higher dimension operators that that come from integrating out some new physics at some higher scale and people have looked for it I mean we have looked for it experimentally for lots of possible higher dimension operators that that could correct the standard model and when you and and of course you can restrict yourself to operators which are invariant under the standard model gauge symmetries I mean that's just what we always do and so people have looked for operators which could contribute to better your number of violations so three quark fields and one left on feel one one one L field and this would be suppressed by some heavies the quark mass sorry have some what I mean talking about some heavy new physics scale and we know empirically because of proton stability that if you add to the standard model such an operator with order of one coefficient then the scale has to be greater than something like 10 to the 16 g e v we talked about the flavor of physics that you could write down again operators not generated by the standard model for example q q bar q q bar and and deviations from the standard model for such operators are constrained to be sort of at the TV to the 10 to the 3 4 TV scale depending on depending depending on what you assume is of which particular operator you take whether it's a CP violating term or not etc and of course we have looked for precision electroweak corrections so for example they could be related to an operator and I'm just giving some examples so this would show up in precision electroweak measurements and we know that the scale of this precision electroweak corrections are sort of between the TV and 10 and the 10 t so sort of at the few TV to the 10 TV scale that we have that that that order of one coefficients are restricted that the order of one coefficients lambda is restricted to be greater than some scale which is several TV so this is thank you so the so so so the tension between these electroweak precision measurements and seeking new physics sort of below at the TV scale is what was sometimes referred to as the little hierarchy problem and so these are all dimension six operators and as you have probably heard before it's amusing that of course the lowest dimension operator that you can add to the standard model is not any of these but there's a unique type of terms which is dimension five and it just looks like l five square and these are precisely the terms that after electroweak symmetry breaking they give rise to Majorana mass terms and new the Nini and they also naturally give you an explanation why these masses would be parametrically of whether the web square over the new physics scale so there's a very nice story how neutrino masses may likely to come from this dimension five terms that you can add to the standard model low energy effective theory and I just want to emphasize that this is really I think almost everyone's prejudice in the field including mine but ultimately it's an experimental question because I can also accommodate neutrino masses by simply adding a right-handed singlet field right-handed singlet neutrino fields to the standard model and then neutrino masses could be generated in exactly the same way as as quark masses are generated and so I just want to emphasize that whether we have seen higher dimension corrections to the standard model this dimension five terms or not that crucially depends on the nature of neutrino mass and it is only something that can be determined experimentally not theoretically so neutrino masses bring to me to another topic that I wanted to say a few words about and that's a charge left on flavor violation that I think is a very important topic and there are lots of experiments and they will improve immensely in the next decade and they are interesting to know a little bit about so if the state is so in the standard model if neutrino masses were zero then the standard model would predict left on flavor conservation we know because of neutrino masses that even in the standard model no matter how you extend the standard model to accommodate neutrino masses left on flavor is not a conserved quantum number and what I was saying here is that whether left on number is conserved or not that's an experimental question but we know for sure that left on flavor is not conserved because neutrinos neutrinos oscillate so if so if you have new physics at the TV scale or at the higher scale since the standard model already violates left on flavor there's no reason to impose left on flavor conservation on any extensions of the standard model either and so if you have some say some TV scale new particles that carry left on number for example slaptons in supersymmetry then they very naturally and automatically have their own mixing matrices so they can give rise to left on flavor violating charge left on flavor violating processes and probably the most celebrated of them that people have searched for is mu2 e gamma in the standard model mu2 e gamma does arise due to neutrino masses so I can write down a diagram a usual penguin diagram between them that mediates mu2 e gamma transitions and if you work out what this branching ratio is just like flavor changing usual currents in the quark sector you will get mass square differences of the neutrino mass eigenstates so so this will be proportional to neutrino mass squares and putting and because of dimensional reasons the only suppression the suppression factor is going to be G for me or mw square so a hundred g e v square and as a result of this if you look out the numbers you find that the standard model predicts for this branching ratio mu2 e gamma to be of order 10 to the minus 52 and actually I don't know probably the uncertainty could be as much as plus minus one order of magnitude because of the mixing angles and the uncertainty is in the mixing angles and and also in the overall neutrino mass scale but you see that this is an exceedingly small number the current experimental bound so this is the standard model prediction the experimental bound is that this branching ratio is less than something like 6 times 10 to the minus 13 and the point is that for example if you have weak scale supersymmetry then you have a whole suite of diagrams and I'm just giving you one example with some so you could write down some diagram with the some neutrino and slap tons again depending on the flavor parameters of this new physics actually 10 15 years ago before when the bounds on mu2 e gamma were orders of magnitude worse than they were today there were lots of papers predicting that supersymmetry could have TV scale supersymmetry could have given a signal already at the current level of sensitivity we see that that has not happened but these type of experiments will again improve by orders of magnitude in the next in the next decade or so in the next round of experiments so sort of mu2 e gamma is really just the tip of the iceberg a whole suite of other important constraints on new physics in in charge laptop flavor violation so people have also searched for mu2 3e or things like tau2 3 mu tau2 3 electron or 2 electron and the mu1 or 2 mu1 and then electron and it's just something that's important I think to watch out for because they're really very well motivated models that could give signals that could be observed in the next generation of experiments and of course if you see any one of these processes experimentally then it's a whole program because then you will want to map out all of these different couplings and to understand which how suppressed which processes are and I'm in just to give you some impressions there is so in on mu2 3e that's a process where the branching ratio currently is constrained at the 10 to the minus 12 level and there is a planned experiment called mu3e which I think on the 10 year time scale will push this limit to be less than 10 to the minus 16 so you know every time any of these limits improved by several orders of magnitude that is really quite exciting because if you fix the couplings in any of these diagrams these rates go like so here the standard model is completely negligible so what this bounds is a new physics amplitude square the new physics amplitude goes like the one over the energy scale of the new physics so this branching ratio predictions would go like one over some heavy mass to the 4s power but if you improve four orders of magnitude in the experimental bound that gives you an order of magnitude improvement in the mass scales that are probed by these experiments so there is a very broad program of doing these measurements both in Europe and Asia and and and and and and and in the United States possibly connected and possibly disconnected topic to charge left on flavors is electric dipole moments yes please so did so let me repeat the question the question is how does this compare with the possible sign of Higgs to tau mu at the LHC and I'll come back to it in about 10 15 minutes it sorry I managed to turn this on maybe I should I can't turn it off now I'm trying yes so there is obviously a connection okay so let me jump forward so we'll come back to electric dipole moments in a few minutes so what happens if you see any of these processes and as the gentleman commented there is a hint of a possible signal of Higgs to tau mu this would of course be incredibly exciting and this is clearly not something that sort of the standard model or the type of new physics scenarios that most theorists and vision would predict but if the experimental signal becomes robust then we have to figure out what that is and there is an obvious synergy between those things because if you have Higgs to tau mu then I can write a diagram which would contribute to something like so this is now the Higgs I could put here the the usual Higgs coupling which is flavored diagonal if there is an effective Higgs tau mu coupling I can put here sort of this this coupling and I can attach for example a photon to this so then this is still tau here and I can attach a photon and I can actually translate between the claimed Higgs to tau mu branching ratio and if that's if I just take the central value on face value and I assume that there is an evidence for this then I can calculate what is tau to mu gamma in this model or in this scenario and I think that the conclusion is that so the amusing thing is that while mu 2 e gamma is constrained extremely well experimentally the tau processes right now are much weaker constrained so okay so my notes are completely sloppy on this but I believe the I believe the answer is that the direct search for tau to mu gamma at with the so there are Baba and Bell limits on tau to mu gamma I think at the 10 to the minus 8 level I'm not 100% sure but I think that they don't exclude the possibility that this diagram could be present meaning that if you maybe Michael knows this all the top of his head but my under my recollection is that if I take the central value on face value that I get enough suppression that I don't violate the current how to mu gamma bound and of course this is going to be fascinating to watch because in the Bell to experiment things like tau to mu gamma will improve a couple of orders of magnitude compared to what the current limits are so should this signal survive there will obviously be an interplay between doing tau to mu gamma doing tau to 3 mu 1 or mu we or any of these things and and and if you and and and there's obviously a connection between the two yes thank you I should them using thing is that the situation is totally different if my notes are correct if you saw a Higgs 2 so so there is a hint for this and let's just call it a hint I would I would say that this is a signal that I would want to see more than 5 sigma before I really believe it because it would be like so spectacularly unexpected but if you saw Higgs 2 mu e at an experimentally observable level and I think this is true all the ways through the high luminosity LHC era then the story would be different in the sense that I think the constraints on mu 2 e gamma now and what the next generation of mu 2 e gamma experiments will achieve which I think one way to wear those of magnitude improvement on this would essentially imply that such a contribution to mu 2 e gamma would be inconsistent with any observation of Higgs 2 mu e even in the high luminosity LHC era by 20 30 something unless your new physics can introduce some consolations and of course that caveat is always there that whenever we look at new physics which occurs in loops in principle you can build a richer new physics sector that would give consolations in these loop diagrams any other questions so back to electric dipole moments so electric dipole moments violate so they violate p and they also violate cp and so if you have an elementary particle it can't have an electric dipole moment because the spin sort of the only vector that we attach to an electron or a quark or whatever is p even an electric dipole moment is p odd so an element so an elementary particle cannot have a non-vanishing electric dipole moment without cp violation and so so I should just say that again historically it's extremely interesting because for example so because we don't understand why we haven't seen electric dipole moments experimentally as we said on Tuesday the current bound on the neutron electric dipole moment which is something like so the electric dipole moment of the neutron is experimentally constrained to be less than something like 3 10 to the minus 26 electric charge time centimeter that's kind of the standard unit in this field so once I'm talking about experimental data let me also write down the electron limit so it's the electron and the neutron limits which are the strongest and for the electron the bound is 10 to the minus 29 e centimeters and again this is extremely exciting because there is a planned next round of experiment that will push these limits by orders of magnitude and so I just okay so if there was a tetok ucd term that did not that wasn't extremely small sort of this bound on the other neutron electric dipole moment tells you that tetok ucd is constrained to be something like 10 to the minus 10 and I apologize but I don't care about whether one numbers where the arguments for the purposes of this talk it the bound on the neutral electric dipole moment tells you that some parameter that we have several scenarios but we don't really know why it is so tiny has to be not or the unity but of whether 10 to the minus 10 or less but we have seen CP violation in the standard model in the quark sector so you could ask the question what happens if you just take the CKM source of CP violation and that's an interesting story on its own because you can show that for a quark so if you take say a down quark then a down quark sorry quark EDM in the due to the Kobayashi-Masukawa phase of the CKM matrix only arises from three loop diagrams and so you have to do something like you need need to involve two W bosons and so there are contributions from diagrams like of this type so this is like a WW glue on and they are extremely suppressed in the standard model by virtue of the fact that they come from three loops they also have to involve the third generation so one of these lines have to become the top quark right because if you only had the first two generation in this diagram the answer would still vanish so you can see that once you have to draw something like this and it's a three loop and it involves the top quark and essentially it's a zero momentum external state this will be extremely suppressed there is a substantial uncertainty in what the standard model predicts for the neutron electric dipole moment but most people say that the standard model should be less or not greater than something of whether 10 to the minus 31 is centimeter so you see that there is several orders of magnitude room where discovery of an electric dipole moment would be a clear signal of new physics to make things even more intriguing for the electron and non-zero electric dipole moment in the standard model would not arise at three loop only at four loop because kind of you need an extra loop to start involving quarks so the electric so the electron electric dipole moment in the standard model is even several orders of magnitude smaller than this bound and again this is a kind of fascinating because if you have TV scale supersymmetry then you can write down diagrams with some e-nose what do I want and some sphermions and attach a photon somewhere so there are one loop diagrams in the MSSM that do not vanish I think in most MSSM scenarios actually the leading contributions to EDM's would come from not the one loop but but some two loop diagrams and again this is like just some scraping the surface of a huge body of literature studying electric dipole moments for example in the MSSM and the conclusion is that with the current LHC bounds putting in TV scale reasonable SUSE models you could see an electric dipole moment signal anytime the experimental measurements improve so so it would not be in any way surprising to see electric dipole moments show up due to new physics first any questions I'm just going to spend the next 20 minutes on some other snippets of what I think are interesting topics and each of these are really sort of fields on their own so Michelangelo told you that the LHC is obviously a top factory at design luminosity it's producing I don't even know what like something like 10 to the 70 t-bipers in a year so so you can do very precise measurements of top decay rates and you can also search for a top flavor-changing new tool currents which are again extremely small in the standard model the current so so the next five minutes will be about top flavor-changing new tool currents the best current experimental bound comes from CMS and it so they found that t to Q z the Q is either upward charm is less than something like five times ten to the minus four and again if you fast forward to ten years to the future these bounds will improve by something like two orders of magnitude so multiply that number by ten to the minus two if you wish and again it's kind of interesting to look at could new physics give rise to a signal like this and what does it constrain how would you understand it and the issue is that again if you do it the standard model calculation of course the standard model allows for processes like t to C z the dominant contribution again comes from fingering diagrams but now the internal line internal line in these diagrams is a down type work not an up type work right because I have put up I I start from a top so this is D or S or B and again I have a gym mechanism which will suppress these loop contributions by the quark mask well over the W mask well just like what we thought that the beginning that KK biomexing is suppressed by M try M square over MW square compared to the naive word of magnitude that you would have expected not knowing the gym mechanism and so if you do the calculation and I encourage you to play with this because it when you can write down the right order of magnitude of the answer in in probably it once you have done it once you can do it the second time in ten minutes and the standard model prediction for these type of branching ratios that is now constrained and ten to the minus four level maybe the limits will reach ten to the minus six the standard model prediction is something that on the order of ten to the minus twelve or ten to the minus thirteen again give or take an order of magnitude I don't need to care about it because what matters is that and that this predictions have no hadronic uncertainties right this is a fully perturbed calculation and the difference between the standard model and the experimental sensitivity is many many letters of magnitude so any signal would be new physics and so the way the experiments are done is that you produce a TT by a pair you look at one of the top quarks decaying into a B and the W and sort of you use this then the normal the conventional top decay to take the event and of course on the other side you look for a Z goes to L plus cell minus with some jet which is so some some quark jet and it's a reasonably clean search which is why the limits will improve to the ten to the minus six level hopefully in the next ten years and if you just think about this the formula representations of the standard model it's obvious that there has to be an interplay between this and B physics because the left-handed top quark and the left-handed big work is the part is a part of the same SU2 week doublet so should I have any of these transitions at a non-zero level I can play all kind of games like I could I can stay aside with a big quark this could be a top quark right this is a W I can generate believable changing neutral currents from this effective interaction so this could be a Z-style or a gamma so if this is C this is S so this is nice because I have I if there is such an interaction I have to put it in a loop to get some B physics process so that loop will give you a suppression however now this CKM element is one this CKM element is one and there is no gym suppression in this in this in this diagram where there's so there is there is no CKM suppression because the CKM elements are one so so I yes I have to pay a loop suppression but I'm evading some other suppressions that occur in the standard model for a beat so for example the process could be B to K or K-style mu plus mu minus if it's a Z-style or just B to K-style gamma and these contributions in the standard model would have a VTS here and in the radar would be a VTS square VTS is point oh four so I'm paying the price of a loop but I'm evading a CKM suppression in these diagrams so so that tells you that there is a non-trivial interplay and if you see any deviation in one so if you see a deviation a possible signal here then you could ask the question of course if you see a signal you want to understand what is the structure of the new physics which which operator is responsible for this transition because it would tell you something about the high energy theory that generates this and so for example you can write down different operators and this is sort of a similar game as what we talked about before in the context of tau to mu gamma and Higgs couplings that for example if you write down an operator with two doublets so this is a third generation doublet D and B and C and S so the left-handed doublet fields H dagger D mu H so if this is the gauge invariant operator well this comes from then you can use B physics constraints to say that the coefficient of such an operator from existing B physics constraints would have to be so small that the maximal signal in T to QZ that they could give rise to so they so if this is the new physics operator then it gives you branching ratio of T to CZ that is bound from B physics data to be less than something like 10 to the minus 7 so if you see this you know that it's definitely not coming from such an operator on the other hand if you write down some operator which involves the right-handed quag fields times the same then you conclude that the that low energy constraints from flavor of physics are actually very loose on this type of new physics operator and in fact a signal at the level that CMS and Atlas could see could possibly be due to such an operator without violating any of these flavor bounds so so again this is a big body of literature that I had worked on other many other people have worked on you can also look for a T to Q glue so involving strong interactions and you can actually do a full classification of the SU 2 cross U1 invariant gate as that's for the standard model gauge invariant effective operators and you can sort of make a map of what are the constraints which what are the possible new physics operators that could still give rise to a possible signal should you see this at the LHC please there are constraints on it from DD biomexing absolutely yes so DD biomexing is I didn't plan to talk about DD biomexing but of course that's a that's a fascinating topic on its own maybe I should talk a little bit about DD biomexing so let me say a few words about DD biomexing yeah so clearly anything that you do with flavor changing neutral currents in the up sector in top decay would have natural connection to flavor changing neutral currents that is processes like so there are searches for D to mu mu things like D to pi mu mu none of these things have been seen again because this flavor changing neutral currents just like the top flavor changing neutral currents are suppressed by a down type what die a down type quark mass quail over the weak scale squared because the because in the loop diagrams it's B S and D that can propagate I think there are plenty of other reasons why DD biomexing is very interesting and also these flavor changing neutral currents involving the D sector are very interesting I shouldn't I don't remember the number so so here that so for this process there is a possible issue later on with long-distance physics so I so this is actually I wouldn't see this as a particularly good search for a new physics but D to mu mu is a process which is which is quite clean again the standard model predictions are whether of magnitude below the current sensitivity and I don't remember the number of the top of my head although I my last paper had a constraint from this and I don't remember the number I think that there is an LHC B bound at the 10 to the minus 8 level maybe on this branching ratio and and that's quite constraining in many models so the point about DD biomexing that I that you may have heard about so let me step back all DD case to a good approximation are given by the first two generation of the standard model and the third generation the influence of the bottom and the top work in that in the D system is extremely suppressed by small CKM elements and therefore for decades people have said that CP violation in DD case are very sensitive probe of new physics this turned into a very interesting story about three years ago the LHC B reported the three Sigma evidence for CP violation in some particular difference of it was called the Delta ACP problem which so the measurement was the CPA symmetry in D to so let's call it ACP D0 to K plus K minus minus the CPA symmetry in D0 to pi plus pi minus and you could ask why on Earth look at this observable and the reason was that some systematic uncertainties cancelled and you look at this difference and that's what LHC B first reported measurements on and the amusing thing was that the central value of this was near the percent level whereas all previous theoretical expectations were below the 10 to the minus three level and if you're interested in this topic then ask me later because it's it's it's there was a lot of interesting work on the subject also DD biomexing is so so DD biomexing was the for the four neutral meson systems the K on the B and the B sub S it was the D system while mixing was discovered for the last time and it's very different than the other systems because in the standard model the DD biomexing arises due to intermediate down type work so this is D is the only neutral up type meson so in these box diagrams you get DS and B in the context of supersymmetry it's kind of the opposite that if you take in many cases the dominant contributions come from squark gluino diagrams so there's KK bar and BB biomexing comes from down type squarks this comes from up type squarks so there's sort of obviously a complementarity between looking for a new physics contributions in the D system and in the other cases actually I did want to say a sentence about DD biomexing so there is another part of them of so actually the combination of DD biomexing oh no I don't want to say this now sorry any questions so we said a little bit about Higgs that I wanted to come back to but I really don't have much more to say so Michael gave a very nice lecture yesterday summarizing the standard model properties of Higgs decays and predictions and of course and again you see dozens of papers in the last three years written on sort of related subjects that when you probe for new physics effects in couplings of the Higgs that are present in the standard model you naturally ask are there any is there any evidence for couplings of the Higgs that are absent in the standard model such as Higgs to tell you and there's a very rich experimental program and again depending on your favorite new physics model lots of new physics scenarios would not give things like Higgs to tell you but but but but but there is also many models that can that can have such an effect and of course it's a fascinating to look for it because because because you can look for it experimentally the sensitivity will improve a lot and it would be a very clean sign of of of new physics there is there is just absolutely no background you don't need to know anything about PDFs if you see this signal you know that it's not the standard model so I said a few words about this just now that the so for example in the context of low energy supersymmetry which has been most theorists favorite new physics scenario and because we knew from KK biomexing that they're very strong constraints on how much new physics contributions you can allow for example to Delta MK or Epsilon K I just wanted to say that that since these constraints will allow the known for basically since the late 60s early 70s in some sense all new physics scenarios have some suppression mechanisms built in to deal with constraints from neutral meson mixing and I think it's fair to say that sort of historic sorry if you just look at what is the constraint from again this is very much oversimplified but if you just write down this quirk quirk gluino contributions to KK biomexing then you find that sort of this Susie contributions divided by Delta MK measured experimentally if you have TV scale supersymmetry with order one mixing elements between the quarks squarks and the gluino of different generations and with very large mass plittings then you would violate you would you would get the contribution to Delta MK which is orders of magnitude greater than the standard model then then the experimental measurement so there are many ways to suppress these contributions you could have heavy squarks and so for example when people talk about like split models that's so one way to add to suppress those contributions that instead of the squarks sort of the scale of Susie being the TV scale if you push it up to the 10 to 100 TV scale then obviously you are suppressing these contributions you can also suppress these contributions by reducing the mass plittings between the squarks so for example if the first and second generation quirk sorry squark mask well differences sort of between so if the mass plittings are much smaller than the squark mass scale itself then again that suppresses these diagrams just like so sort of similar to the gym mechanism where you could and or you could suppress the mixing angles or make them may make them aligned to the standard model so that this quark squark gluino mixing is exactly happening in the same way as the standard model so sort of a sort of possibilities alignment where you make those mixing matrices standard model or CKM matrix like and there are classes of models which utilize each of these suppressions so for example gauge mediated Susie breaking is one way to suppress these contributions but the point I wanted to make is that because of these flavor constraints on KK biomexing many of the Susie searches actually almost all of the Susie searches where you see the so when people say that squarks are excluded from the run one data to something like 1.2 or 1.4 TV that usually assumes that the up down strange and charm squarks so those eight states are all degenerate and that's motivated to a large extent by the flavor of physics constraints and actually this plot is from that paper from many years ago and it's just driving the point home that the experimental searches really have this optimization of these degenerate squarks of the first two generation if you really relax that assumption and you assume less degeneracy of the squarks then in fact these mass bounds come down by almost a factor of two and of course that's qualitatively a very big difference whether you say that squarks are excluded to nearly one and a half TV so this is this is an analysis that was done by Josh Ruderman and collaborators a few years back using five inverse femtobank of data so the bounds since then have improved but the general picture has not changed that that the standard analysis quote some square mass limits and if you don't assume this degeneracy then the limits are much much weaker and of course that's interesting because there is this sort of this interplay between hiding flavor signals in the flavor measurements and hiding the LHC signals and sort of as you complicate the flavor physics you can make the LHC limits weaker and vice versa and so so so these games can be played in lots of different ways any questions so I should okay so I wanted to say okay I'm going to talk about minimal flavor violation for five ten minutes and then finish by ten twenty and then we have ten minutes to discuss before the discussion session so I don't want to leave you with the wrong impression in the sense that there are lots of ways you can spin this story so if you take the MSSM the most general form of the MSSM it has forty some new CP violating parameters and has something like eighty new flavor parameters in all these different mixing matrices but in fact there are very motivated models where the flavor changing neutral currents connected to these new parameters are naturally suppressed to acceptable levels and not only in supersymmetry but in a large class of models you could kind of ask the question what is the minimal reasonable deviation from the standard model due to some new physics that occurs at some scale lambda which is some high scale and there is a formalism which allows you to do sort of effective theory type analysis of these questions and sort of the key observation is that it's a kind of unreasonable to demand that all the higher dimension operators that could contribute to flavor of physics are exactly diagonalized in the way that the standard model operators are so that there is an exact alignment between the standard model and the new physics but so we said at the beginning okay let sorry let me step back so in the standard model that you cover couplings I shouldn't say anything about this in front of Andrea so in the standard model we said that in the absence of you cover couplings there would be a large symmetry in the quirk sector there would be a u3 cube symmetry because you are allowed to rotate the left-handed doublets the right-handed singlet sorry the yeah the upright and the D right by set by separate u3 transformations and you can view the you cover couplings as so-called spurions whose background value ends up breaking the symmetry in the quirk sector to just bury on them bill so if you have some other higher dimension operator coming from new physics then you can assume or it's a or you can impose on the new physics that this global symmetry is only broken even in the new physics sector by the standard model you covers by the new covers that that described the quirk masses and and this gives rise to a very nice formalism called minimal flavor violation well but you can kind of do order of magnitude estimates of of how well new physics has to be aligned or how many physics can be aligned with the standard model and and then and gives you a framework to to study these questions um so I think there is no way I have any sorry I realized that what I said in the last minute probably doesn't make any sense unless you know something about the topic so and and there is no way I can fix that in the next 10 minutes so so so sort of the punchline of what I wanted to get across if there was a little more time is that it gives you a framework well sort of flavor changing you to the currents automatically have the suppressions by CKM elements just like the standard model contributions things like B2S gamma which we didn't talk about but it's a very important constraint on you constraint on new physics and B2S gamma in the standard model is suppressed by the beak work you cover coupling in these MFV models that will come out automatically so it's it's a nice framework that you can impose on any new physics that will that is plausible and would give the new physics contributions to flavor physics to have the same kind of suppressions as the suppressions in the standard model by by by by by small you covers by CKM mixing elements etc so actually one of the things I will tell you in the next three minutes is that it's it's kind of a nice framework that I am actually finishing a paper that uses this I said yesterday that we said yesterday that this claimed anomaly in the B2D and D star tau neutrino rates is inconsistent or at least at the 2-3 sigma level their measurements are inconsistent with a charged Higgs contribution in the type 2-2 Higgs doublet model the amusing thing is that the data is actually consistent with just having an enhancement of the standard model operators so for example you could imagine having some W prime particle which could give rise to a I just wanted to write down an effective Lagrangian which is some coupling suppressed by some heavy scale and if I write down the same operator as the standard model then actually such an operator gives you a good fit to that data now you and then the coefficient that you need for this so you need C over lambda square to fit the data to be something like 0.2 over TV I can write 0.2 as VCB times 5 over TV and for the purposes of these lectures 5 is the same as 4 so I can also write this as VCB times 500 GeV square so what I'm saying is that if you write down such an operator and it's generated by some 500 GeV particle with order of one coupling and the same VCV suppression as the suppression of this operator in the standard model then that could explain the data actually and there's a little problem with something like this is that it's dead on arrival because if you look at what are the constraints from the LHC some W prime which couples to up and down quarks the same way as the W is constrained already to have a mass which is greater than something like 1.8 or 2 TeV so clearly it's an example of doing an operator analysis I would say oh I know what explains the data but the LHC tells me that that's impossible and you can do so MFV minimal flavor violation allows you to do again to play amusing games I don't think this is the explanation of this data but for example you could have a flavored W prime so if you assume that the W prime has some non-trivial transformation properties under these global symmetries then actually you can write down a theory where you can suppress the W prime couplings to the first two generations and get rid of this bound from the LHC while having a viable possible explanation of how this operator can be generated so so there are lots of things one can do I probably should stop here so what I wanted to tell you is just some examples that flavor is really a strong constraint on TeV scale new physics despite the huge progress for decades in many of these flavor changing neutral current processes the new physics is only constrained to be less than 20 30% of the standard model so there's still a lot of room for a new physics to show up the experiments both in the quirk and the lepton sector will improve by orders of magnitude and there has really been a very interesting interplay between theory and experiment and I gave you some indications yesterday that and the day before that in many cases theoretical questions that were irrelevant at the experimental level of sensitivity of the last decade will be relevant in the next decade so there is a lot to do and I think it's fun and thank you for your attention