Top measurements at HL-LHC and Higgs factories and EFT fits - Victor Miralles 
>> Welcome, everybody, to the topical group session. So our plan for today is to start with the talk on a topic that is very central to the mission in our session, and writing of our report, and then after the talk, we will move on to discuss the report itself. So, Reinhard, my co-convenor is connected as well. Víctor Miralles will tell us about top quark measurements at HL-LHC, and worked on together with EF04. So, Víctor, please go ahead. 
VÍCTOR MIRALLES: Thank you for your presentation. Exactly I will talk about the top quark measurements we have included in order to perform a global fit on the top quark sector. So, since this is our EF03 talk, I will mainly focus on the measurements that we have. But, yes, I mean, the global fits will be a contribution for the EF14. So, yes, and then basically our main goal here was to perform a global fit of the top quark sector. And basically, in order to do this global fit would be we used the HEPfit package which had been extremely convenient for this kind of global fit, and here we focus on the estimates which we include which are the different observables that we include in the high eliminate not ity HL-LHC, and in the e+e- colliders, and saw later - I show later some of the results. In order to talk about the measurements that we have included, we - we first need to know for which we need these measurements. And I will just briefly talk a bit which are the co-efficients that we want to constrain, so here are the definition of the different operators that we have included. We will constrain some linear concentration of them, so seeing briefly them. Like we have here two fermion operators, two lepton and two quark operators and here we will focus on the top sector, and you will see that we have for instance here the coupling you have the top with the W boson, and some of them. We will find constraints on the linear operators which are shown here. Here, basically, these two quark operators are mainly affecting the top quark couplings, and we have here the top to have ... the four quark operators are basically affecting the coupling of the top quark and the live quarks. And also the two lepton and two quark operators which we will be able to constrain in the context of e+e- machine, are basically par ram terrorising. So basically here considering the top quark sector will also have considered the bottom quark sector because the top and bottom quark belong to the same two, so we want to consider the top quark. We also need to consider the bottom quark s sector. So here are the observables that we have observed in the LHC, from the Tevatron and the LHC. These first observables, all of them, but the last two, come from the LHC, and they will be proved in the context of the high-luminosity LHC. So, basically, here, I just want to point out that, including the e+e- to b b bar measurements, we include Rb in the quark symmetry. We are able to constrain some of the proton quark operators that we have to introduce because we are doing this general global fit, and also this proton-proton, single production of the top quark in this channel coming from the Tevatron, it has still ... to the same process in the LHC, so we included this process too, although for sure in the high-luminosity, let's say, these will not be - they really aren't any more. We point out here the proton-proton tt bar differential cross section as a function of the invariant mass of the tt bar pair, and for this one, Reinhard will have 15 beams, we are able to split the last beam, because in that point, we will have ... in order to split these last beams, so for the high luminosity LHC which we will have considered some additional beams with respect to that, and this thing happens for the symmetry. So let me basically summarise which are the effects of - these different processes in our fit, in our Wilson co-efficients, and basically we have that the proton-proton tt bar differential cross section is essential if we want to constrain all the four fermion operators, and the - so this process really constrains a lot, - these four fermion operators, and the C ... we need the pp to ttH, and this is the one that can constrain the ... for constraining TkW, we find - CtW, we find that the helicities and the pp to tt bar are relevant, and these cross sections are veal want to constrain TkZ. For that, - CtZ. The cross section becomes very relevant too, and this one can also con strain CphiT. The observables can contain the Wilson co-efficients and we want them if we constrain these operators with the highest precision. But, the linear combination of this Wilson coefficient, so we need to add some additional information, and for instance, pp to tZq, we were able to get these blind directions. The other observables messaged here are relevant for the fit, and these ones are the most important that the most relevant ones that we have by now. We can talk and discuss later if we can include something else in order to do it better. So, in order to determine who this - how these measurements will improve in the high luminosity LHC, we have considered that the theoretical uncertainties will scale by a factor of two, and we will have the information of the high luminosity available, and with respect to the experimental uncertainties, we have divided them into the modelling part, the pure experimental systematics, and the statistical ones. And we have considered that the modelling will scale with a factor of 2 as the theoretical uncertainties, and that the pure experimental systematics will scale with the square route of their luminosity. So, here, I show an example of the inclusive cross sections that we have included, and also on the ... you can see the errors that we have and they will be proved in the context of the High Lumi LHC. You can see that most of them, or a lot of them, are dominated by the statistical uncertainties, or their statistical uncertainties, are competitive with other - competitive in a way like also, are very similar to the ones of the model, for instance. But, if we scale the modelling only by a factor of two, and the statistical ones with square route of the luminosity, we will find that in the context of the High Lumi LHC, the main experimental uncertainty will come from the modelling, so it is interesting to see if we can improve it more than a factor of two. Also in that case, the theoretical uncertainties, and the total experimental ones, are quite similar in many cases, so it may be also interesting that the theories go a little bit beyond the, on improving these by only a factor of two if we want to reach the maximum potential of the High Lumi LHC. So this is for the High Lumi - let me show you what we've included. We've included observables in the e+e- to b b bar process, and basically, we have included the inclusive cross section of e+e- and mine b b bar, and the foreground - we have considered the most updated benchmarks for the different colliders, and this information is extremely useful because the same reasons that we are including the information is also very interesting, because it can constrain the bottom quark-related Wilson co-efficients that appear in another way in our analysis. So basically, if we are below the tt bar threshold, we can constrain only a linear combination of CphiQ1 and 3 and Cq phib. If we go high in energies, 250 GeVs, we will also be able to constrain the two quark and two lepton operators. Basically, the two photon and two electron operators which is something that has not been much gift in there. In order to constrain these new - this four fermion operators, it is - the sensitivity with the energy in this case. So, now the focusing now more on the top quark sector. Here, we have this to include the optimal observables, the statistical optimal observables, and we follow the analysis of the number here, which is an interesting analysis made by Marcel Voss, and also [inaudible]. And also, basically, then the interesting part of this optimal observables is that they exploit the differential distribution of bw, so they have this different distribution and they can basically achieve the highest precision with this optimal observables here. Basically, with them, we are able to constrain the two fermion operators, the top quark fermion operators, we have the C phi q minus here which is complementary to a linear combination I've shown before, which is this one, so including the information of the e+e- to tt bar, we can fully explain these. And also, with these optimal observables, we will have very strong constraints on CphiC. And it will include the information of the e+e- to tt bar at two different energies across and above the tt bar threshold. We can also constrain the two quark, two-lepton operators. All these operators here which couple the top quark with the electron can be constrained, but only in the case in which we have two energy points above the mass of the tt bar threshold mass. So, basically this is one of the reasons why we should go beyond the tt bar, and also in different energies. So, as you can see here in the context of the FCC, these two energy s of the tt bar threshold are quite close, and these will generate that the constraints are poor for these operators in this case, although still they can - this machine can contain all of them. Let me discuss briefly the results here. I show the constraints that we have in the first, the current constraints, that we can reach with the current accelerators. After that, we have the constraints of the HL-LHC, and after that, the constraints of the e+e- working below the energy of the tt bar threshold, and finally, the constraints of our e+e- machine working above the tt bar threshold, but just with one energy above the tt bar threshold. And, yes, as an example, we have chosen here the ILC benchmarking, but something similar will happen with the other colliders. I know that the shallow ones are the constraints from the global fit, and the solid bars are though that we find from the individual constraints. And basically, we can see here how with these observables that we have included in the context of the HL-LHC, we would be able to improve our constraints by a factor of three more or less, 2.5 for some, 3.5 for others. Working below the tt bar threshold, the improvement is not so strong. We can find some improvements on the bottom quark operators, especially in the individual constraints, but also here, for C phi B, the constraint is huge. If we go above this threshold, it is the point where we are really able to constrain all the top quark weak couplings with our extremely good precision. So now it is interesting to add this second energy, and compare, we find including just one energy above this tt bar, and two energies. So in this case, when we include the additional energy above the tt bar threshold, we have done on also all this seven four fermion operators, the seven, two lepton, two quark operators, and we can see how even though we have included a lot of additional operators, the relation is not present, and indeed we have even an improvement. So it is very interesting for the machines it would be able to constrain all these operators. And now let me show you how the different machines are compared, so, for instance, if we have an FCC run ing energies off FCCE, as I said before, the energies above the tt bar are quite close to each other, and the constraints of this, of this four training operators are not as good, thus in the case in which we include these two energies, and but in any case, since in this machine we have the - we're able to constrain the operators you can see at the bottom like C phi Q- even though it performs better. With CLIC, we will have similar results. It is a bit better for the - and the ILC is better for the electro wave top quark couplings, we see more luminosity, but for the four fermion operators, we are probably better with the ... because it performs - because it reaches higher energy. So that is more or less everything. That is a summary. I did my 20 minutes, just a summary. With the HL-LHC improved by a factor of three within limits. With e+e- we are able to improve the bottom quark and also the top-quark operators if we work above the tt bar. And as it were, collider that works with very - with very close energies of the tt bar threshold, can improve the top quark operators by a factor of two with respect to the HL-LHC, but with the - and the achievement is probably a factor of five. The, the linear colliders operating above this tt bar threshold, can provide they good constraints for fermion operators and since they are working on - energies, so that is everything. Thank you. 
>> Thank you very much, Victor. Are there questions here from the audience? For Víctor? 
>> If I could make a comment: the point that Víctor made about the degeneracy of the top-quark gauge couplings in the four fermion operators involving top is a very interesting one. I mean, it's modelling-dependent. Which of those is expected to be the largest effect? I guess I was pretty surprised when I studied this problem that actually in e+e- the four fermion couplings are the larger effect, and it may be it is not so surprising because they're not suppressed by gauge interactions, but to distinguish those two as quite subtle, it requires multiple energies above the top quark threshold, as Víctor said, and this is one of the real benefits of being able to have a 500 GeV and then even a higher energy run in an e+e- machine. So that point should certainly be emphasised. 
VÍCTOR MIRALLES: Thank you. 
>> Thank you, Michael. That's important to emphasise this in the report. Are there any other questions from the audience before we turn to Zoom? Reinhard, do you have any hands up on Zoom? 
REINHARD: I don't see any hands up yet, but I actually have a question on exactly that topic. FCC, FCCE doesn't come by itself. Some decades later, we will have FCCHH, you don't have it in the slides, it is not a straightforward extrapolation, have you thought about how to include FCCHHH? 
VÍCTOR MIRALLES: I think I will discuss that later, but we finally, yes, we decided not to go there, but, yes, I agree that it will be like extremely interesting. I don't know, to be honest, I don't know if ... is in the audience? 
>> We started out with the electroweak couplings only, so, the focus on e+e- was sort of motivated by that. I think it is interesting, but there are no official projections for FCCHH top measurements. They're not available for High Lumi LHC, either, if you take it strictly, but we have some guidance of what the Higgs group did. I think one can make reasonable assumptions and get reasonable prospects. For FCCHH, one would expect those four quark operators to improve, but how much is very hard to guesstimate right now. If anyone is daring to go there and provide projections for those measurements, we could include them in the principle. 
>> Thanks, so then the other comment, just on the organisational structure, right, which I think you had very nicely on your very first slide, Víctor, which this is really a topical group spanning exercise where the EFT results and the details of of the combined fit, and then even putting this into a global EFT fit is all in conjunction with the EF04 but the top-quark measurements related things which will go in our report and EF03, it is nice that you have the full list, and we will be asking you either to send us a write-up, or something, because if - it is going to be very helpful to us as well. I agree with what Marcel said, that, you know, to have the assumptions there is good, because it makes it all very consistent. 
VÍCTOR MIRALLES: Yes. I think we should definite ... like, for next - this is possible for next week, for sure, and we will also make it and send it to you. 
>> Okay, are there any other comments or questions on Zoom? I don't see any. Okay, thank you, Víctor. 
>> Thank you, Víctor!