Hello, everyone. And my talk is going to be about the issues related to the
application of the effective field theory in the search for new physics in vector
boson scattering processes at the LSE. What I am going to show is based on
studies and work done by several people, including CMS physicists, such as myself,
and as well as theorist. I'm not a theorist. So it's maybe too much to say
that this is a theory talk, but it will be somewhere in between the experiment I hope
that will be suitable for everybody. So let's move on to the second page. I have
one slide of introduction about the vector boson scattering, which I don't really
think I need to go through in the details, but let me just say that in terms of the
EFD expansion, in principle, we can say that in vector boson scattering processes
we can probe. The dimension six operators that affect the triple gauge couplings,
the Higgs to gauge couplings and at least some of them affect only also the quartic
couplings. And we can probe the dimension eight operators that affects only the
quartic couplings. Now, traditionally VBS analysis are focused on the dimension
eight operators and the related quartic couplings because they are the best
processes to study them. And I am not going to discuss this issue of how much it
is justified to to omit dimension six and go directly to dimension eight because
opinions differ already at that point, but for for the purpose of this talk, I will
just assume that we are interested here in the quartic couplings and the associated
dimension eight operators Okay. And yes, so let's go to page three. And of course,
the important issue that we immediately have to face is the problem of unitarity.
So let me just briefly recall that there's been two main philosophies that has been
been in used by by experimental groups, how to deal with this problem of
unitarity. In GPS data analysis. The first approach is what we what we used to do in
CMS, at least up to now, okay, which is simply to disregard the unitarity limits.
So, so to to, to apply the EFT expansion as if the unitary It was not a thing. And
of course, as long as what we want is to have some some mathematical tool to to
quantify the precision the relative precision of the data and the degree of
agreement or disagreement with the status The model this is fair enough, but
unfortunately in this way we give up the physics interpretations the numbers we get
do not have the right physics interpretation in the EFD framework. Of
course, there would be no difference then no no problem at all. If the if the
unitarity limits were so far away that we would not see them anyway, but this is not
the case unfortunately, in within the range of parameters that we are sensitive
to unitarity violation happens well within the measure branch, okay. And the other
philosophy was to apply some kind of unitary ization technique, like for
instance, the favorite technical class was was the K matrix, the technique that
assumes amplitude saturation at the unitarity limit, and this is usually sold
as the physics significance of this is described The maximum possible signal
related to a given operator. The problem is that there is no unique prescription to
the unit unit derive the amplitudes. And again in the parameter range that we are
sensitive to your result is driven mainly by whatever you assume. Extra. Okay, so so
it's like part of a more complex model. So the first question that I would like to
address in this talk is how to render the experimental numbers more difficult, but
at the same time to keep them as model independent as possible. And the next page
please.
So first, let me focus on on some facts about the EFT validity catalog. So by
construction, EFT validated stops at the scale of lumba, which is supposed to be
the scale of new physics, and lambda is not equal to the unitarity limit, but it's
rather it may be maximally equal to the unitarity limit, but it may as well be
arbitrarily lower than that theory actually does not predict the value of
lambda n the only way for us to get to know the value of lambda is to deduce it
from the data. So, that is one thing, then I will not insist on whether lambda is one
value for all the higher dimension operators or there can be different
lambdas for different operators. I mean this I guess it depends on the underlying
physics. But I will insist because this this follows from from construction that
for a given operator, lambda is just one value and it applies to all the individual
amplitudes that are affected by this given operator. Even if the individual unitarity
limits of the single amplitudes are are much larger than that and this is relevant
for instance to to the to the individual amplitude of the different Felicity
combinations of the initial and final state as I will show in the next slide or
maybe the next to next and this is also relevant to different processes if they
probe the same coupling and if, if they are sensitive to the same set of higher
dimension operators. Why is this important? Well, because for instance in
the WWE process, we have the same sign WW and we have the opposite sign that the
process experimental is may be more interested in the same sign process
because it's it has much less background, but it happens that both of them probe
actually the same coupling and it is the opposite Same process that breaks
unitarity faster than the same same process. Here we have three examples of
that and you can see that the difference is actually quite large. And even the from
the experimental point of view, we are only interested in the same same process,
we have to consider the unitarity limits that follow from the opposite sign
process, which are the limits that are relevant for us. And by the way, the same
also goes for w z and z z, because both processes probe the same quartic coupling
ww z z and usually zz brakes unitarity faster than w z. So, this defines the
unitarity limit that is relevant in this case. Then on the next slide, this is
slide five now, I am showing here the the energy dependencies of the cross section
In the same sign WWE scattering process this is calculated for on shell W's in the
presence of an anomalous Quark the gauge coupling for different dimension eight
operators and for for each dimension eight operators there are several values of the
corresponding Wilson coefficient depicted here.
The standard model is of course, this this purple curve which is which is falling all
the way down okay and the relevant unitarity limits are marked here with
ethical lines for for every value of supply efficient and what we observe here
is that the whenever the cross section starts to deviate from the Standard Model
value in a in a measurable way so to say we immediately hit the unitarity limit so,
the measurable bsm effects are confined to A very narrow origin which is just before
the unit article and essentially either you measure nothing by nothing I mean the
standard model in this case or we immediately run into trouble with the
unitarity limit. So, already at this point, we see that the we may we may have
a difficulty here, then the next plot I would like to show on page six is this is
again the energy dependence of of the same sign WWE scattering process, but in the
presence of the FT one operator for some arbitrary bug to have it, but this time
this is decomposed into the individual Felicity combinations of the initial and
final state. So, in principle we have three to the fourth come in fellas and the
combinations which is a the one that if you consider all the symmetries related to
the fact that it's for identity apart because we ultimately end up with certain
amplitudes that are really independent of each other. And they are listed on this
table here on the right hand side. So what we see here is that the individual energy
dependencies are very different from each other. And also from this table we see an
important fact that the individual unitarity limits for this individual
amplitudes vary quite a lot. Okay, so if you were to unit there is every amplitude
separately on its own, you could even end up with a completely different signal
estimate which is however, not consistent with the principles of the EFT which
requires to make a one cutter for them all. In this particular case, the
unitarity limit calculated from t matrix diagonalization is marked by this vertical
line on the plot which is just below three TV and this is the value that is relevant
everywhere here in this case, five minutes. So, yes okay. So the fact is that
the page seven please So the fact is that the FT does not provide any predictions
for above lamda. So the best thing we can do is not to use this region if we want to
do EFT description. So what does this imply in practice for zz it's relatively
easy because the invariant mass is known it is measured so we can simply place a
cut on the data remove events, which light above the assumed cutoff value and either
set limits or feed bsm accordingly for w z and wV Well, here the situation is tricky
in principle, we can recover, try to reconstruct the invariant mass of the
system but there are two problems to deal with somehow one is the the The jet PT
resolution that that limits the resolution of the environment mass determination. The
other one is that the kinematics of the neutrino, which was the reconstruction, it
has a quadrat is subject to a quadratic ambiguity. So, there are some ideas how to
solve this ambiguity and this is under progress now in CMS, but as long as we
don't have that, then the situation becomes similar to what we have in WWE
here that this problem is serious, because we have two new trainers with which means
no experimental access to the invariant mass. So, the measured signal is in
general always a sum of the region below lambda and above lambda where one region
we can apply the EFT in the other region you cannot. Okay and the only way to
correctly use the FT to apply the data is to make sure this the second region does
not contribute significantly to what we measure you never know it from the data,
but you can verify it from the simulation. Next page and this is this is what happens
for for the same sign w for the for the WWE process in general. So in general,
normally what we do is we measure the distribution of some physical observable,
which is not the invariant mass because we don't have access to that, but which is
whatever variable offers the best sensitivity to new physics. And we can
define the DSM signal as the enhancement over the standard model prediction in
terms of this distribution.
So, what we measure is always a sum of the regions from zero to lambda and where the
which is the EFD control region and from lambda to infinity, which is some tail.
Okay, we don't know what to expect, but realistically there will be some signal
There, but ideally what we would like in order to apply the EFT is what was called
here the EFT signal which is defined by analogy but only restricted to the EFT
controller engine above lambda, you put no additional signal which means only the
Standard Model distribution and the two must be indistinguishable within
statistical errors in order for the EFT description be viable for for what we
measure and this is only true in a very restricted range of f lambda. So, if we go
to the next page one minute. So, if you draw this plane f versus lambda or lambda
versus f from from the top you have origin which is forbidden due to the unitary
condition from the left hand side, you have a region where The bsm signal is not
significant enough to be detected and in addition, this EFD consistency criteria
imposes an additional bond. So, from the right hand side we have a region where yes
we can measure VSM signal but we want to be able to describe it using the EFT
because there is too much coming from this from the region above lambda. And this has
been the sub the subject of a detailed simulation work and I will just just
quickly flash the result on the next page this is so what is left is some what I
call EFT triangles mainly because the region is bound from from three sides but
of course the shape can be more fancy than that. So for the individual dimension
eight operators, it looks like that so there are some ranges where this is
possible, but they are rather narrow and better. mind that this is just a generator
level study. So the sensitivity is still bound to degrade significantly once we
plug in the full detector simulation. Okay, and now the second the next page.
The second case is one more related to what we're currently doing CMS because we
have not observed any bsm signal so far. So how to set limits on vsms so that it's
useful to the theory community consistent with the EFT. And here again, the EFT does
not predict what's happening above lambda, but only the most conservative signal
estimate will provide the limits that are guaranteed to be true. Anything else we
assume might not be true. And the most conservative signal estimate is what is
given by this, this so called clipping technique that maybe I don't need to
explain because it's or you can ask me if you like, but since I am running out of
time, I will only show them Next page which is page 12. Okay, in the brand new
paper coming from CMS that appeared like two weeks ago or so, the clipping
technique for the first time was was implemented okay here, we use the events
clipped at the respective unitarity lemons This is a combination This is a new
analysis of the same sign w W and W see the channels and their combination from
data collected during the entire run to and the novel feature is the
implementation of this clipping technique. Not unexpectedly the impact on the results
of considering the unitarity limits is quite large okay because in this range of
parameters that we are sensitive to the unitarity limits are rather low of the
order of 1.5 TVs. So that's well be well within the measured range. Okay, let me
very quickly just show the results page 13. Here you have the the current limits
on dimension eight operators on top you have using using this standard CMS
procedure which is disregarding the unitary condition on the bottom you have
the same table but with the clipping
applied at the unitarity limit as you can see, the difference is really large.
Generally the bounce the limits become weaker by a factor like four or five Okay,
so in some in some cases, the bounds are pretty weak I mean if the Wilson
coefficient is much larger than one then of course it brings up other problems, but
this is where we realistically are okay and this is the way that that we are going
to follow. So I am ready to conclude now and what I was trying to show Is that the
usefulness of the EFT to study in PBS? The data is rather limited for several reasons
that I outlined here. But we are implementing the clipping technique, which
in my personal opinion is the correct way of analyzing the data. If we want to go
for for physics interpretation, eventually it would like to learn something about the
underlying physics from it. I didn't say my Yeah, thank you. Okay. Yes, that's it.
Thank you.
Yeah, thank you. Me, huh. We have maybe time for one question.
And the question and so I mean, I would like to know slide 14 how a mature Pareto
analysis can overcome the Should that you show the slide the slide? The issue that I
show once, I mean the fact that the space in which you can say even CFT in a
sensible way, it's that limited how much you're very nice you can overcome because
at the end you say that
we want them with a very thorough analysis.
Well, actually, well, a multi operator analysis is more flexible, generally
speaking, I don't know if it will overcome this particular problem. Maybe it won't.
But of course, in real life, it is more likely that if we observe bsm effects, it
will be a combination of different higher dimension operators rather than then it
will be driven by just one higher dimensional uppers. So in this sense, it
is more flexible, simply I mean, we're more or less Likely to Succeed, but then
for technical reasons this is only possible if we combine data from from
different processes, because in a single process you end up with terrible
correlations you get this flat directions and here you are bound to 111 dimensional
treatment like one operator at a time
I thought the namely that implement more operators it's just worse because you have
the end of all the triangles, no.
Well, in principle, you may imagine that you may find a combination of different
operators that well for sure the area will be many dimensional okay. So, there may be
some some places where you, you may end up with a measurable say No, but you will not
violate unitarity anywhere. Maybe I am not saying that it will be like this, but you
have more flexibility, I think.
Oh, ah, thank you.
Okay, so let's take me how again and we can maybe move to the next clip.