 Okay, I think we're going to go ahead and get started. So I'm going to hand things over to Pavel to introduce our speaker for today. And I have this in case you want to cheat sheet. Okay, so, okay, well, hello everyone. So I think today I'm very happy to see our great SMU friend who came to coming back to give us a seminar about his recent work. Now, for those of you who don't know keeping, so keeping got his PhD from Beijing University in 2014. And then he came and finished a PhD degree in our theory group here at SMU between 2014 and 2019. And then keeping went to university of peace work, which he where he's a postdoctoral researcher in a very well recognized group working on phenomenology of elementary particles. Now, keeping, I would say it's, well, you want to know him better, right? So if you want to know him is to come with us for dinner tonight. So, but he really has a very diverse range of interests. He's a master of all trades. And now he worked with me on the structure of the protons and continues working with me on this. He also did some research on models of non-standard Higgs boson interactions. And today he will tell us about his other recent work, which is dedicated to bread and butter physics at immune colliders. So please welcome keeping. Okay, so thank you Pavel for this nice introduction. It's always good to come back to meet our old friends, all of you. So today I will talk about this the muon colliders. Of course, there is a lot of things we can do about the muon colliders. I will mainly focus on the physics side. Of course, there is a lot of technology side. I think the gym ball knows much better than me about that. So we will focus on this physics. This work has done in two scenarios. First one is about this standard model physics and high energy muon collider. You more general or left hand collider. And of course, we want to move forward. I will also cover a little bit about the BSM started in muon collider. Take this muon Higgs, you cover coupling in. So this work was done with my postdoc advisor, Tao Han and his students, Yang Ma. And this BSM is done also with few German fluency. So this is the outline of this talk. We mainly two parts, actually PDF, so this is BSM Higgs. So let's first ask about why we think about this muon collider at high energies. Of course, it's a great interest to think about something always beyond what we can go. And especially about this, we, everybody knows this proton collider, hydrogen collider and electron collider, we are familiar with that. And muon collider is great to have both advantage of a hydrogen collider and electron collider. So it can get a very high energies, which is the proton collider can give us. But it's all simultaneously, it can also give us a very clean environment to measure something we want, especially when we think about the BSM physics. So left on colliders, it's great for us to probably show distance physics. So I'm thinking about the history. We have a scholarly history about the electron collider. Many big discovery they have made by this electron collider like the charm tau or even gloon was discovered at the electron collider. And of course, in the future, we are proposing some future electron collider like FCCEE or CEPC, or even then this has been discussed about 30 years about this international linear colliders. And the muon colliders have these features. Also, muon collider as the other advantage we have mentioned about this can give us very high energy like up to TV scale. And the more optimistic it can even give us 30 TVA or even someone think about this 100 TVs. And this was provide us a great advantage to explore this BSM physics like we can measure this multi boson hex or even multi hex production at high energies, which can never be achieved at a proton collider at a very clean background. So I need some of them here, but we can discuss them more if we want. So let's move forward. So think about what's a portable high energy muon collider to think about the size of these colliders. So here I need to talk about these few colliders we have already below very familiar. First of all, the size of this formula, you can say this kind of size. And at the same time, you can say this brook heavens, roughly same size. And you can say this current energy say this light yellow light blue circle. So currently this energy say roughly 26 kilometers. So think about this hex factory for muon collider. You can say we can only see every tiny size we can which is this get this muon colliders build. Of course, think about this even higher. So this is such as the 400 GV muon colliders or 30 GV muon collider, you can say this size. So we don't need to build some big tunnel to in order to make this. So just do the existing one, even the Fermilab TerraTron tunnel is already getting enough to us to just to feel this muon being there. We can get this externally out of this high energy. Yeah, and the luminosity I need to hear which is which we are talking about. Of course, currently all these are just estimation. So we have, we can open up the mistake to side to have some energy dependence and luminosity which is those as your energy squares behavior. Of course, consumptively, which is we have some technology issue which will constant this luminosity but still we can get as high like 10 inverse anubars. So that's a basic setup for us. So let's think about what we can do based on this muon collider. So first of all, we should do to everybody should be aware about that to mechanism or to kind of physics will show up in muon colliders. One is about this vector motion fusion, one is annihilation. I show us some typical standard model cross section like a WW production, TT bar or TT bar height production at high energy muon collider at a multi TV energy range. So you can say on the left plot, there are two kind of curves. One is downward, one is go upward. They are not very typical. So one is about this annihilation, all of them go downward because this is one over S behaviors, just S channel, you have one over S suppression. So at high energy, when your energy is going high, all this crossing decreases drastically. But on the other side, we also have fusion, which you behave as logarithms of your energies. So when you have very high energy as a muon collider, you can see that all this vector motion fusion processing goes very quickly and very soon you should dominate by your cross section production. So all of this standard model process we are dominated by your vector motion fusion process. Similarly, I will have this one some others like a coca bar or you can think about the jet production in. And we have to think about some realistic the detector configuration, like this is corresponding to 10 degrees of your detectors are in the forward directions. So the behavior system. So the question is for us, we have this enhancement because of this vector motion fusion. So same as WW as a reference, and we have this the high energy electric wave physics or low energy QED or QCD, this one. So you can say this one, this is about this, this WW fusion or WW production, similar as here. So that's roughly the size of give us this, the weight. So the question I proposed here is how can we treat this W and Z standard model particles or add high energy to the left hand criteria or property because of this vector motion fusion or this globally then collinear enhancement. So that's the way we should provide us the answer to this one. So think about the electric wave physics at high energies. So because the energies become so high all the standard model particles like WZ essentially become massless. So this massless give us exactly the same behavior as QCD. So when we get this logarithm enhancement, so the electric wave symmetry just restored, gradually restored. So we get the fully symmetric standard models at high energies. So all this gauge boson, so almost gauge boson, it actually exactly behaves like your hex. So we have goldstone equivalence theorem and of course we have a violation, goldstone theory of violation, which is behaves like your population to our mass. So this is exactly the same way which is used already in QCD like high trace term behaves as a power suppression of your lambda QCD. So we know this is splitting behavior. So we have already been familiar with this characterization of the QCD, so we have quantum PDF. Similar situation will also happens at this electric wave center. So we will have electric wave PDF and for the initial state of addition for the final state of addition we will have some similar as the fragmentation function or which can be simulated with a pot of shells. We will talk about it later. And other aspects which doesn't show up in QCD is about this QCD is a nice symmetric SU2-3 SU2 symmetric which is unbroken. However, yet Rick physics is first one is Cairo theory. So all this left handed and right handed the Fermin behaves very differently because the interaction is different. So when we talk about electric wave bosons get away so you need to be aware about this polarization of the electric boson also with your Fermin. And another interesting is about this Yukawa coupling because the top part of Yukawa is roughly other one which is significantly enhanced compared to others which is not legible which doesn't show up in QCD or we'll never see that. So that's a general picture about electric wave physics and high energy. So think about this contradiction in what they just do mimic about this QCD splitting. So how we do this splitting behavior? So we can think about the process like something A splitting into B C because it's which and in the collinear region B C almost get the same direction as A. This is the final state of radiation or similarly for the initial state of radiation is the right point one. So the cross-section in this collinear limits can be always the factor rise as your kind of hard part cross-section which you behave as like this is part only crossing sigma X. And another part which is collinear part which is we can say this A and a splitting to B C similar to for this initial state of radiation. And we have this kinematic variable. This collinear part can be behave at here. You can say it's always then at high energy over things just to behave like your collinear fakulation and the factor rise you have this momentum fraction of your daughter particle come from your mother particles. So count about this dimension as the splitting behavior. So either behave as a QT with some QT of your choice of your particle like B C or which we have think about this gauge boson like WZ they have mass. So your gauge boson is cut off lower cut off by your mass. So when we talk about this collinear behavior so we have either KT cut off or transverse cut off or mass cut off which is behave differently. To validate this characterization in theorem of fakulation formulae then we have to be aware about that your observable should be very safe. You cannot reconstruct some divergent observable which is not can be never measured. Of course, in order to make this work the leading behavior should be coming from collinear splitting. And that's what give us the correlation of your picture capture your main physics and which exactly happened in the collinear in this vector boson fusion. So just to think about that we have to talk about the initial state of radiation and the final state of radiation. So we similar which we should treat at them then this is the usual state of radiation to be with some as your pattern distribution function final state of radiation we similarly we should we start locally enhancement with as your circumcision function. And the leading order behavior of splitting which is already done 30 years ago about this we call as defective W approximation and longitudinal behavior of your wavelength because this mass of effect in this scenario can be levered so you go out. So this will give us a power suppression as your state think about this W mass of the mass which give us the same order of magnitude under this one and can be treated as a golden stone here golden stone equivalence. And that's one is the exact same as this high trace effect in this QCD scenario. So we will see that was how this in my follow up slides. So think about this let's come back to this effective photon approximation or effective W approximation which is exist for almost a century. So think about this photon we did it from your laptop which is the most simplest case we can think say such as when such as a symbol to your electron or laptop condition with some target like a here and the fusion process which is coming from your photon we did it from your beam particle your laptop. So the left on some cloud with your target can be factorized as your part part hard particle processing can look with your photon PDF. And the photon PDF is a well-de-traded which is certainly proposed by Fermi and followed by a wide acronym. So this is called also called wide acronym approximation and the behavior I show up at least for here. And in this same scenario the effective of W in a gauge SU2 gauge or standard model so gauge is same to it can be similar treated with the effective W processing which is a show exactly behavior as this one. And we have this the calendar splitting color comes of your logarithm enhancement and this logarithm also give you this the big cross section at high energy. And I show this diagram you can see that then think about the left on cloud or high energy beam on cloud. What happens there actually is exactly actually it's kind of gauge boson collider. So you mostly you are collider this gauge boson together and then you produce all the auto particles. Exactly as the proton-proton collider you have proton-proton beam coming and also the collision a hard crossing coming from your proton inside of the proton. So that's how mimic or how you think about this electron collider or a beam collider left on collider based on our knowledge of the proton collider. So this is which we know for 30 years already. So let's say, but we call we have I have given you some carpet about this electron or the standard model. First one is a standard model it's a chiral theory. The chiral theory you have this chiral interaction which is violated CPE symmetry. So some of the this PDF such as you have polarized dependence in your beam and also your your pattern like your method boson. So when you do this city transformation in both phase of the beam particle and your pattern you will not get this same exactly same PDF because your chiral theory, chiral violation is behavior. So for the QCD like or QED like your most simple the case we can have a well established unpolarized correlation which you can sum over of your polarized and get an unpolarized PDF. And then the yearly for the QED or QZD PDF we always talk about the unpolarized the proton diffusion but we should not have the case anymore because all of your PDF should be polarized. Now this is first feature we should be think we should be well treated in this scenario. Another scenario which is also never show up in QCD it's about this gamma Z or this interference between different patterns. Think about this same process. You can say under this just hard of this convolution of you get complex conjugate with another part. So you can have interference between the intermediate part of gamma and Z and then you can say in this diagram you can have one side is gamma from your initial beam and other side is Z from your initial beam. So in this sense, when we do federalization form for this diagram we will end up as a pattern as gamma Z same tendency as your pattern. So that's corresponding to the interference which gives us your mixed gamma Z states. So we have this interference, the PDFs which never show up in QCD or QED case. So this is another feature. And of course, one big problem is about this this correlation or this QCD is good because QCD is symmetric. QCD symmetric give us a lot of features about this as a gloom PDF think about the gloom in your QCD. You can never distinguish the gloom colors of the gloom or quarks of the gloom. So what is good observable in QCD? It's always the color-branding. Color-branding, since then you can't struggle with the observable of your case. So you need to always sum over all your color and then you get the formulate or your color-symbolic observable which is sure up in the detector. However, this is not a case in the electric wake theory because electric wake you can wear is typically neutral or from electron. And similarly for W and Z, you can observe W and Z well or resolve them. And however, think about this W and Z in gloom and in gloom, it's just different colors. You have eight kind of gloom. So you need to sum over all the gloom. But this is not a case in electric wake system because W and Z, they show up differently. So this gave us a big problem because when you have this kind of diagram you can say in QCD case, you need to sum over these two cases and get the cancellation down. But this is not a case in the electric wake theory because you can say this splitting electron beam give you neutral PDF while the virtual diagram give you electron PDF. And they are separated in two different PDFs. So this is a big problem for this one which is called block logic violation which requires us to reconstruct your PDF. In your QCD case, we need to see we have to think about this singlet case which is sum over your electron and then the divergence can be canceled in a singlet but not in your this color violation like this triplet cases. Go ahead. Yes. Right. Yes. Right. Right. Interference effect with radiation you mean we did a gamma and we did a Z. That's what we mean. Yes. Then you need to have different polarized PDF. And then your PDF becomes very complicated because we need to formulate a big basis which is refer to different PDF. For example, you have this one, you have polarized PDF which cannot be as your this one. Yes. Yes. Yes. One over two. We do have that tar but that tar will not as a collinear enhancement. You don't have collinear need logarithm house. And then of course, when you formulate this this is not the full picture. This only captured your logarithm enhancement tar. We will sum plus some power supply term or which is shown as a constant. So that's why when your energy become large all this power supply term just become legible. So this is, we have talked about this electric PDF. So we should go beyond the if actually equivalent photo approximation or if actually double approximation. So we need to come up with the full standard model PDFs. So you can see all this splitting I showed up here. So think about the leading order you kind of have splitting into photon or the sub-leading splitting you kind of photon can split into your left arm. Simultaneously you can have split into quark. So quark can go further split into quark and gluon and that when your energy goes even above your electric scale like they must when you cross this they must threshold you can have also W and Z as well. So finally all this standard model particle become your patterns as quark and gluon inside of the proton. So in the end we have everything every standard model particle as your patterns. So that's a full picture about this. So let's just do this is some little technique about how we treat this one. So we just only have just dig up we need to sum the logarithm which is done by this dig up equation to sum logarithm to your PDF. And we have nearly three regions and we choose some kind of threshold below some QCD or the region like lambda QCD which is some standardized scale which is quite slightly different with lambda QCD because lambda QCD is characterized as this. This is a 215 and we should be thinking about a little bit further. So we just to simplify it. So we just divide it into the different regions and then below some QCD range which we only have QCD. So in this sense in the below the QCD region we only have quark and we need a photon PDF or some lebson PDF but above this QCD region which quark and glue enters. And another standardized electric scale we choose as they must as you're as just the degree these two regions above the electric scale we have all this everything. So this is the four pictures. So let's go this technical one to think about this more interesting about this without how this PDF behaves at high energy. So the first one as I mentioned below your QCD, below your electric scale we have QCD. So we have quark glue, we have photon PDF we have valence PDF like this valence quark in the proton case simultaneously we also have quark and glue PDF. So we here I just need to do quark as an example. And we show this for electron beam or this muon beam and we choose two standardized scale like a 30 GV or 40 or 50 GV you can say this is one over S behavior or log X behavior of course the photon is the first we did it from your leptons, the photon PDF is the biggest one. And at this S going to one limits because that's four moment fractions carried by your leptons. So in this region it's all mainly coming from your valence. So valence will dominate with your axis moment fraction going to one limits in another false limits everything shows up at here similarly as the muon colliders. So I give you some give us some number about how large the size of it is. So think about this 30 GV for electron case at this 30 GV you can see almost all the moment fraction is carried by your valence and sub leading as your photon and the thing and the quark glue, et cetera. Let's go one step beyond above the electric scale and then we get all this electric and enters. So we have this all this is under models the particle as your pattern. So we have W there the simultaneously we have as I mentioned about the polarity effect. So we have to distinguish W and Z we also have to distinguish transverse and longitudinal W as well because it behaves very differently. And trans longitudinal W, longitudinal W Z which is the carrier is about your this blocking violation which does not have logarithm enhancement because all this is just your mass effect of your W gauge boson or W the gauge boson. So this behaves just to like blocking scanning. So we call this blocking scanning violation which is constant at a high energy. So this does not enhance at all but you can see longitudinal W involved because longitudinal becomes much larger than your or transverse become larger much larger than your longitudinal. So we also be aware about this electric wave sector will be given your collection to your low energy side like your U quark D quark PDF which is due to the QED effect. So at high energy we should come back consider about the four electric series not just the QED one. I give us some numbers like about 15 or 20% level about your scale certainly we quantify the big difference between your different scale choice which is here show these two scales here. So that's this PDFs we have got. So let's make some prediction about this what happens at high energy lebson providers. Think about this. We just do think about the election colliders in a third three TV which is kind of clinic or this clinic collider setup and the thing about 10 TV beyond colliders. And we show us some some bottom numerosity before we make some some prediction for this process. We show all this bottom combination like your beam particle variance quark variance left on and we also show all these combinations here. You can see how then we show some some keep it in mind about size. But of course this is the various one we'll show up as your take full energy of your election of your left hand beam. So it will blow up your with your all this energy got square root of tau going to one limit. It means that all the energy is carried by this by your left hand beam variance quark. But when you solve the quark, solve the limits like when your reflection goes smaller all this pattern shows up of course the largest one coming from your photon one photon and one your variance left on and sub leading is gamma, gamma and all these other sub leadings. So this is give us the size of this the bottom numerosity, but keep in mind this QCD QCD interaction is a strong company is much larger than your QED interaction. So consider about this one we will exactly the size of ball or which we will show this but about this in the left side what's how large your size of your QCD interaction and high energy colliders will behaves. Think about this we just come up with some kinematic cuts which is such as we show this the colliders about a five degree or 10 degree of a detector or of course we should think about some kinematics about the threshold cuts about your final state or some PT cuts some very generic generic cuts. So then we can give us some feeling about the cross section then take about digit production example and high energy electron colliders. So similar as before we show us the electron colliders 30 and a few your energy scale of new colliders. So you can see the largest cross section of the digit production actually is coming from the quark-quark initialized process which is exactly which is this pattern behaviors. So you have patterns inside of your left arm and this one will significantly contributed to digit production and high energy in left arm colliders. So you both in the electron case and in the muon case and the electron case is even more significant because the logarithmic enhancement is even larger because the electron mass is much smaller. So you have much larger logarithms in this electron case. You can see this one you can compare this total digit production compared with this gamma gamma is the photon-ed issue of the process. You get this two to three actually is two magnitude larger than your gamma gamma which is only QED effect. So your QED effect which you are like the quark-quark warm patterns initialized which gives you two magnitude larger for this muon collider case you get one magnitude larger than your photon-photon initial process. And then think about the sun model you actually we have mentioned before we take this WW production cross section as your benchmark as your number. So you can see the digit production initialed by your quark-loom patterns which goes even larger. So you have three magnitude larger than your WW production. So if we measure some yes-way physics or BSM physics all this digit production will come as your background contribute to your this process. So we have to treat this one very carefully if we want to get a precise prediction about this new physics model. So but however there is good news about that one it's the kinematics of the different process which is very differently. It's not like something experienced so let's think about some kinematics distribution like this environment mass or appearance distribution of your digit production or this WW process. You can see clearly that one all this GED production initialized by your quark-loom patterns peaks along this low energy scale. So it will go to very soft like your environment mass required to be very that few tens of GED all this jump will come together. But if we require your threshold to be higher think about this WW environment mass the threshold which is 160 GED just slightly beyond that one 200 GED example. You can see all this standard model of the digit initially with process we all excluded. So this is a big exactly the idea if we want to study some BSM physics or electric like WW electric physics at high energy scale we have to think about all this kinematic card to exclude all this junk. So one basic requirement is just to impose some environment mass card which will give us the safe scenario will give us we want at high energy. So this is the environment mass card and this the repeal of the cost repeal of distribution you can see for repeal distribution we show up these two scenario one is about this will be annihilation another is about the vector ball solution annihilation process is very sharp peak around this when you have this which is actually peak around the repeal going to zero maybe. However, all this vector ball solution will spread out but this keeping in mind this annihilation will be kicked by your one photo initial state radiation which is coming from this ISR because that's why you get this shape or slightly key spread out which is above cost a lot of spread as this your vector ball solution process or this pattern process. So that's the picture but all other kinematics like transverse momentum or energy or your ability of your pattern of your digest jet product process. Everything seems to be the same as before so we should think about this that some kind of minute to be hard enough to in order to get suppress all this digest or this solve the jet present. So another thing about this you can see the boost which characterized by your energy of your thing about a W. So your W, so it's both the both how large you both so we can have two in order to to remove this one. Actually it's not very high just to when your energy of your W kind of 100 GV is enough for us to to here I give us some in some number which 200 GV kind of same scale. So this is the idea about so what we what's the slow energy standard model digest block you want. So as we have already showed that one we need to move to high energy then we can study some BSM physics or electric physics and high energy. So let's think about some electric scheduling process like here I just need some some electric pattern distribution or electric luminosity and high energy 30 TV beam cloud example as similar before you can have this annihilation or balance will be on and all this this vector vector pattern electric pattern luminosity comes later. So so give a good idea similar before I give us some as some moment of reflection keep in mind how large you about this the size of this electric PDF will be here I take 3 TV or 5 TV as your quantified how large so we can say W boson only take of the 1% of your of your pattern moment fraction of your beam particles. So that's the basic size of this one. So let's just to make some prediction in based on this electric PDF here is the result. We have already showed this WW before which you show up once again but this is different from previous one because previous only coming from gamma gamma fusion but now we have all this electric wake as your pattern as well. So we have WW fusion the fusion gamma the fusion as well all entered into these pictures similar as others others all of them will come receive contribution from your electric wake or PCDF or electric patterns here included it right here. So everything now is the pattern and everything is kind of so fusion process now actually I get also show up as show up there before this annihilation which highly suppressed before so you can say think about this WW production example you can say this is 1, 2, 3 3 magnitude larger the fusion process than your annihilation so all this cross section mainly coming from this fusion process. So actually here one conclude to conclude to conclude this subsection with that with all this standard model or this heavy scattering high-range laboratories behave like your proton proton colliders or hydrogen colliders you have some colliders give us a kind of gauge boson collider actually which is cloud gauge bosons so that's the picture of this this high energy muon collider high-range lepton collider so similar as before if we show that some decomposition of different patterns like WW or gamma Z etc. or compare contribution to your or the whole total cross section you can say so of course gamma-gamma still contributes biggest one and all others come secondary like WW fusion or WF fusion we need to decompose into different polarization then and this can give us the size of different proton decomposition and this give us the kinematic distribution similar to before you can say I should normalize this distribution all these fusion processes show up as your threshold region and about along the collider energy region which is as is your beam energy scale it's mainly coming from your annihilation so that's so for this muon mass and weaponry similar to before we have a sharp peak about this this the weaponry here similar as WW or the Higgs or just repeat so so let's move to the next topic do we have some question based on this what do we have shown here before here I don't know okay so we have so we assume everybody knows some more Higgs we want to take advantage of the high energy muon cloud to do BSM physics to search new physics so we know all about the annihilation and the vector boson fusion which we are familiar with already so at high energies actually we have seen this all these Higgs boson fusion actually that will give us a great advantage if we want to put such as Higgs physics so all these Higgs we are coming from this scheduling and longitudinal think about this longitudinal behavior the Higgs boson or longitudinal of the Higgs boson which is exactly this is your Goldstone so we have Goldstone equivalent theorem which is give us the longitudinal double gauge boson G can be equalized by your Goldstones so we know that the muon cloud as gauge boson cloud we also know the discrimination of the annihilation and vector boson fusion we should take advantage of that to separate these two scenarios previously we have emphasized this variable boson fusion but now we want to switch another one to emphasize this annihilation so let's think let's see what we can do here so one example is that this muon Higgs carbonine which we will show up we show up because we consider both muon clouders so we can measure this muon Higgs carbonine and the grid position at the muon clouders so let's come up some models some models such as this buck or extra automation models which can give you division of your muon Higgs carbonine you can see based on your standard models or predictions so we show up here because the one is this we show just to show about this the running of your muon Higgs carbonine or the muon Higgs mass your muon mass running in based on the scale so here is the standard model prediction you can see it's run as here and then you can see we normalize to here this is red line but we have new physics contributions like these different models which can give us significant deviation from your standard model prediction so the goal of us is just measure how we measure this difference at high energy muon clouders and that's the goal so let's see how far we can go so first we need to quantify the BSM physics we need to know how much is the difference between the standard model and this BSM physics let's come up with some theory which we will use this effective theory parameterization we will think about how we can parameterize this electric this effective theory of course we can use some nonlinear Higgs effective theory or we can use some standard model effective theory we just to quantify all these BSM models BSM contribution with your new operators like for this Higgs effective theory all this one coming from the nonlinear realization of your Higgs boson so we say that this I give us an example about this left hand we cover carbonine which is muon here we can say all this muon Higgs carbonine we will see the correction based on this coefficient all these coefficients is coming from your BSM physics similar as this standard model effective theory you can just to take some black box so all these black boxes can contribute to this BSM contribution to your muon Higgs to cover and then all this muon Higgs to cover we behave that we use this this Wilson coefficients entered into the carbonine and you normalize into your standard model prediction which is this Y1 standard model we cover or here we just this is kappa you just take the ratio with the BSM contribution with your spec to a standard model then we will get this mu physics contribution which as your coefficients so we just want to say how much we can determine these coefficients at high energy muon crater so let's see this contribution between the standard model and the BSM physics so we have seen that before about this annihilation the fusion process and annihilation process first one let's compare about this Higgs cross-section the cross-section of the multi-gauge multi-boson production I need all the possible multi-boson production the triple boson or the four boson production and on the left part you can see we have already seen before one is going downward the annihilation which down upward that's the vector boson fusion at high energy this you can see same as before the vector boson fusion will dominate but we know this kinematically they are totally different because the kinematics behavior is very different we can take advantage of that to separate these two parts and here I show this standard model prediction and the BSM contribution here take some such as take this kappa we have shown this previously before this kappa is coming from your BSM and this think about some benchmark such as we take kappa which is equal to zero or one and which corresponds to kappa equals to one we correctly correspond to standard model prediction and we can think about some construct some model to kill this Higgs-Umu color so if we can think about some Higgs company having mu Higgs mu U mass without the U-Kappa company which corresponding to this kappa going to zero that's corresponding to this dotted line you can see and then the difference will become very significant at high energy colliders at high energy mu colliders so this is the triple boson production and the four boson production you can see even more sphere you can see so at high energy mu collider we can measure this difference and then we can determine this Higgs company at very great precision so if we find this difference at high energy mu collider we can discover new physics so that's the basic ideas here so let's clarify this BSM physics actually I showed up what's the behavior of this all these different channels like for triple gauge boson production triple boson production in which everything actually behaves the same with the code of the equivalent theorem and so the only difference coming from your symmetry factors because your W and Z boson they have different symmetry factors and then you normalize to think about this double Higgs which is the largest cross-section triple boson production to normalize them then you can then all this one actually behaves similarly just a standard model just a standard ratio so here I give a ratio under this numerical value which is quite well so that shows up this difference between your standard model prediction under one different channels so similar to the four boson production actually as before you can see actually all this deviation from standard model just to quantify by this one parameter which is kappa so let's determine this kappa think about 10 T-vabion colliders so we take this double Higgs production as an example so this I show some kinematic distribution like a theta this angle distribution of your boson or environmental mass under this kind of separation between the different boson of three of them you can see one first one let's focus on this environmental mass and we have seen already before the very boson seen all of them show up around your threshold so peak around this low mass of the region but annihilation will peak all around peak of all your collation energy so they will peak about the 10 T-v colliders so you will peak around this 10 T-v range so if we can think about some kinematic such you require your boson to be like 80% of your condition energy so just to set events here and then all these vector boson fusion events can just suppress so then we can focus on this annihilation and then we can measure the difference between your standard model prediction and your BSM physics so I can show you this black curve and the red curve red curve creates our standard model prediction and black curve creates our BSM but you can see there is significant difference between these two curves so we can measure this difference so all other distributions come similarly so let's similarly for this z-hectic production we have all these similar features but let's compare some numbers so as we can put some card some typical cards here and then count of the events how many events we can measure at 10 T-v colliders based on the luminosity we have shown as before so we can say at 10 T-v luminocliders if we measure this double-double-higgs we can say that the standard model events corresponding to this one which will give us a few hundred events but BSM events will give us very significantly which is three or times larger than your standard model prediction so then you can see which way we have given as this signal over background ratio and for this z-hectic production the signal over background ratio is even bigger because your standard model events is much smaller but this is the BSM contribution which comes the same size as your WW1 then you will focus on this one we can even get better sensitivity so let's quantify this one how can we precisely determine this BSM physics so we think about this defining your signal, defining your background so let's do this systemally scanned how precise we can go so we just to show some different deviation some contribution from BSM one of course depending on primary choice let's parameterize it as one single parameter kappa mu just do this one is corresponding to standard model the two corresponding to BSM and one so you can smooth transition from this standard model prediction based on this BSM scenario so you can see all these colors are smooth transition from this color plot and the different color, different color like the solid dash or dotted one and they are corresponding in different cost kinematic cost so we can measure this difference which quantifies then let's see how much we can quantify this one so this is coming from our money plot so if we require your signal think about this deviation then your uncertainty of your standard model background which you should think about more so the uncertainty of your standard model will often behave like your square root of your event so that's your uncertainty the signal is many coming from the BSM physics so think about how many sigma we can get so we can just choose two sigma or five sigma think about two sigma events two sigma deviations then we can come up with how much of this that Muehn-Kleider will determine this this standard model this BSM contribution deviation so this one is a result you can see a different energy which we can measure this deviation between your standard model and BSM one up to very precise and so that we can even get 1% precision as your standard model as your Muehn-Kleider recover if we can we discover some more the events which beyond this one that's exactly corresponding to BSM which cannot be explained by your standard models or with your uncertainty so think about the five sigma deviations then we just to get some some events not very big with then we can get very easily to get this this five sigma deviation if we can build this Kleider so the conclusion will come so you will translate this Muehn-Kleider carbon deviation between the standard model to some BSM scale so think about this standard model EFT parameterization all this corresponding to your new physics scale then you can say actually for this 30 TV we can reach the new physics problem to 100 TV which means that you can use the 30 TV Muehn-Kleider constant BSM thing up to 10 to 100 TV so that's why we get very excited if we can build this Muehn-Kleider so let me summarize so I talked to standard model one is about this so what the standard model physics will behave at 100 to 1100 Kleider especially 100 to 100 Muehn-Kleider and one we talked about this BSM physics measurement at 100 to 100 Muehn-Kleider we can take this Muehn-Kleider as an example so of course so one thing about this all this standard model particle will become the patterns exactly we have as we show C as QCD case in this proton case then we have high energy Muehn-Kleider just an electrovec gauge boson volume of the high energy the proton Kleider like the high energy as you say so for the Muehn-Kleider if we have this Muehn-Kleider we can measure this Muehn-Kleider Higgs company at a great position and we can probably move physics up to 100 TV you will have the 30 TV Muehn-Kleider so let me stop here to take question I've also studied not with the the thing about the low energy T is your thing about you can boost the Muehn-Kleider into your rest plane so if you have some BSM particle which must much heavier than your Muehn-Kleider than your Muehn-Kleider must so in your rest plane the Muehn-Kleider cannot decay into some heavy particle so you just both see it so that will not affect this decay but of course radiation that one will affect but that one we have to show this one this standard model one think about this one this is standard model particles like a gamma, z, et cetera so if we have some BSM particles so it will come much below here even smaller than this so all of these new physics particles inside of your Muehn-Kleider should be smaller than the standard model sector standard model sector we have to show exactly how large your size it is so yes we can build some model like L, Muehn, minus L, tau then you can radiate this gauge boson which is new decay and then it's not decay just radiate a new gauge boson and then your Muehn-Kleider will become tau then you have this new particle your gauge boson which should be much smaller than here and of course here we let's go back a little exactly the same here we show this electron as you can see as this electron-Kleider or Muehn-Kleider similarly you can have this anti-electron we can also have this anti-muehn inside of your electron inside of which should be roughly the same size as this one because it's coming from the gamma-gamma radiation gamma-gamma is splitting with your electron here you can think about tau so the tau roughly size behaves like this one so if we have new gauge interaction new bosons so here I'll give you a size so that one contribution will be much, much smaller than this one so we'll interfere with each other, just go ahead yeah yes yes big symmetry, you mean CKM? no, that's becoming extremely first one the effect is extremely small we're not affected I have shown this you can see here this example this electron, this is Muehn-Bien we have this of course the biggest comb valence one electron valence, this black curve this is a neutrino neutrino effect is here but of course this is not coming from this your your this mixing matrix it's coming from this gauge boson decay or gauge boson interaction just think about this W W will interact and split into your neutrino which is this and then we can think about this one and all of this one the kind of PMC matrix will inside of this bin, inside of this band between this solid curve and basic curve that's one thing then we need to very precisely determine how large is the deviation and to give us quantification so that effect is negligible here actually it's already there no, no, no we didn't publish the PDF but everything is there we just haven't we want to write some big paper which is and then after the hour we will release this related to that question there's a small group of people within the community a Muehn-Bien or say broken as an upgrade to the electron so in doing simulations presumably you said the laptop PDFs are already available in LH so in principle we should be incorporating these into our center exactly, yeah that's very simple we're doing that okay, great actually I use this PDF as I work with Pavel I load this LH PDF and all of this is based on same combination just to release and then everything can be incorporated really so related to this as well this is a perfect slide to talk about these are all pure theories that we're looking at here, right? have you attempted to then extract these from existing E plus E minus collider data and see if they agree expect they should, right? but has anyone tried to do that? for instance gamma star, gamma star or gamma star Z star interactions at E plus E minus I have this one which back up very fortunately I put it here you can see this gamma-gamma actually this was done by Clicc Zeta, 30EV electron colliders of course gamma-gamma will induce into hydrons and you can see this is a simulation done by X-ray group you can see the spectrum this is PT and Zeta all these activities becomes Zeta because they're very small very small I put here one is about a PT 40EV this is horizontal one vertical is corresponding to 5 degree so of course below these two cars all this enters enters and beyond that one is in this small circle or this one actually low effect at all low effect at all that's it we want to go to this region of course we have to incorporate this one because all this junk coming from this non-properative interaction which we have to extract from data just to measure this data experiment and then failure but for this high energy region which is the perturbative region which it doesn't at all this is the branch which exactly which I show here in this region so what's the region where we it's in the extremely forward region lower left corner low PT low angle and there's no existence for instance I know that Favard and Bell were plagued by a gamma star gamma star not being able to simulate that very well I wasted a year of my life to simulate gamma star and just gave up that guy's thesis from 1970 you were in 19 early 1980s and everyone is that a genie pig genie pig waiting by by this guy this Barclay I was an experimental person maybe Barclay this guy Daniel Seward should be that one that looks familiar I know that code I did use that code to extract someone it's not of course a lot of way of waiting but it's doable what I'm wondering is data from SLC and infer some of the find a point on one of those yes we can't do that one no yes I'm thinking about that one but I need to talk with this Daniel Seward to do this because the third one is always well simulated already but we should smoothly transition currently these are just this one with two different scenarios in between we need to smooth transition and then get some consistency that part isn't that done yet we also there is big uncertainty there even when you can think about this there this is two scenario one is PCR simulation one is called SLAC done by Peskin and Barclay etc. they have done this one you can say of course kind of agreement but if we look in more detail this will give you significant deviation not as a precise high energy part yes yes this question Peskin always talk about this one because of course they are pushed by different group Peskin doesn't always want to push this IOC this linear and his answer is very negative but we don't think in that way and by other group the Brookhaven group actually it's kind of 30 years hopefully currently the big advantage we have big breakthrough is about the cooling and they demonstrate it's possible it's favorable, durable in the future of course there is a lot of another technology like intensity or how you do this make this high luminosity intense one yeah I'm not sure for that part as I didn't get into the detail about this yeah exactly yeah yeah yes I need of course I can need more but I just need three of them slow mass activity these two papers you can take a look which summarize this including the accelerator stuff and also the physics side yeah bronchiflexion yes but that bronchiflexion of course does not depend on how your energy is the tau the bronchiflexion is always your property of your leptone the middle tau and mu and then you can always boost it into your atmosphere yes I don't have the drought diagram but actually think about this you can see here think about this is the tau or mu then you can have BSM gauge bosons here you just talk about bronchiflexion of that actually it's just static so you can always boost it which is boosted into your rest frame and of course there is BSM contribution which is exactly this splitting picture which is not decayed bronchiflexion it's a PDF well let's go ahead and wrap up there as Pavel said earlier I think it's around until Thursday yes you're grabbing for a coffee or lunch or something like that he's sitting in Fred's office I'm sure Fred's not here so the perfect place for him to set up so you're going for keeping up a trail let's then keep him one more time