Are you gonna slide? Yes Can you try to go fullscreen? yes to that
is fine.
Yes. So please stop when ready.
Yeah, thanks a lot. So, I would
like to thank the organizers for giving me the opportunity and for inviting me to
give this talk at HCP. So, this is a talk which is similar in lines with the others
that we have listened to in this in this series. However, I will be taking a little
bit different approach from the from the theoretical point of view. So, this talk
is based on these four works. So, three of them published and one just to be
published very soon. So, now coming to the to the motivation for standard model
effective field theory. So we want to ask some pertinent questions. So some of the
questions that we want to ask this, how do we reconstruct a TV scale a graduate from
The available data or the data that will become available in the HLS at the next
question that we want to ask is how do we extract the best observables to study the
effects of some particular operator and for particular processes. So, we know that
new vertices come about from effective field theories and can produce novel or
enhanced effects in several parts of the face face. So, many of these questions can
actually be IP address very well in the regime of either or high energies and
luminosities. So, when we talk about effective field theories, so, it is a
bigger theory actually, which is which can be either weakly strongly or moderately
coupled, and is assumed to supersede the Standard Model above a high cutoff scale
lambda which is the scale of the mass of the heavy new physics. at the perturbative
level, we know that all the heavy degrees of freedom above this cutoff scale lambda
are decoupled from the low energy theory. So, there are several Ways to write down
effective field theories. So, here I will be taking the approach of a linear
effective field theory, which I write down in terms of several operators at different
mass dimensions. So, starting with the dimension for standard model and Ranjan,
we go on to higher dimensions in mass and this is how we parameterize the
Lagrangian. So, there are several important goals of the LSE and one of the
most important goals at the present is to precisely measure the Higgs and other
couplings like gauge couplings, several other couplings. So, if history is our
guidance we know that we can get indirect constraints to much higher scales tender
tender president running of the of the collider, so, st parameters being prime
examples during the lab round. So, the questions that we want to address are can
the Large Hadron Collider compete with the left Collider in constraining precision
physics and whether or not it can provide any new information. So we know that from
EFT correlated variables left had already constrained certain anomalous x coupling
Even though the Higgs was not discovered, so, from z pole measurements or triple
gauge coupling measure measurements that at the left could already constrain
several couplings and in LHD, we can actually use the high energy and the high
luminosity to to constrain these couplings further.
So, now coming to my first case study, so this is extra volume with the Large Hadron
Collider. So, this is a Higgs being produced in association with a W or Z
boson. So, these are the various modified Fineman diagrams and the black blobs
essentially show us the modifications. So, we can have modifications in the W or Z,
CT CT vertex, the Higgs WW, the Higgs Cz vertex, and we can have a whole new four
point interaction. So, this is essentially the Lagrangian the dimension six of
aggrandizement which which encapsulates this, these these diagrams. So, the terms
in blue are essentially modifications of the terms which are already there in
standard model. So, you see that these terms even though they are new, they have
One limitation is that they do not grow with energy and are suppressed with
respect to the contact interactions, which are mentioned in in red. So you see that
the contact interactions of the four point interactions and because of the absence of
a propagator in the in the Fineman diagram, these actually grow with energy
we'll see how in the later slides. So, I'll quickly flash the operators which
contribute to the above Lagrangian in the in the word services. So, these are the
various operators that contribute to the to the Higgs trialing processes and modify
the Higgs vv star and the Higgs D FF bar couplings. So, coming to the topology that
we are considering, so we produce a V h, where V is either a W or a Z, and the VD
case to a pair of leptons and the Higgs to a pair of big quarks, which essentially we
take as a fact check. So there are several angles at play here, which which will be
very important in the discussion of this of this talk. So please note the angle big
teacher Which is the two to two scattering angle and this is in the V eight center of
mass frame. Then we have an angle small theater, which is the angle of the of the
of one of the leptons say the positive charge leptons with respect to the rest
frame of the V boson. And then we have the angle phi which disc which describes the
planes the angle between the these two planes of the V Ll and the V eight system.
So the question is how much differential information can we extract from this
process. So here it is essentially a three body process because we are treating the
Higgs is a fat jet. So there are three times three minus four that is five
kinematic variables that completely define our our system. So if we if we ignore the
boost factor, the variables that we have our square root is at the end of three
angles. So if we consider 10 bins per variable, so then for every energy bin, we
will have 10 to the power three, which is Thousand numbers have been stopped in the
full information. But we will see later that this this number thousand can
actually be reduced to nine per energy bill. So this is the beauty of this method
that I'll be discussing, which is called the method of moments. So please bear with
me. So now, as I discussed before, the differential cross section for the
processes, pp to z or w, h is a differential input variable, so, we can
write it as d sigma d d Big D small to define. So, now just focusing on the Z h
for the moment, here we do a full cut based and an MVA analysis, and we see that
the major background is z BB bar, we use a boosted substructure analysis and by a
shoddy cut Bates cut based analysis, I didn't do a very optimal optimized cut
based analysis we see that we get a signal over background ratio of the order of a
quarter. However, with an MV optimization, we can take it further to half. So, we see
that so, Be changes from one over 40 to other one, and we still have like close to
35 evens even at 300 inverse femto bond. So Nan Lu actually discussed very, very
nicely possibilities for upgrades, like we can take be tagging to even up to four,
which I'll be looking at the plot on the left actually shows the ingredient mass of
the Z eight system for the various signal and background samples. And we see the cut
have been imposed for one of these and the right plot, which is the table which
actually shows the cut paste analysis and the various cuts applied. So coming to the
result for this part, so, because I discussed before that EF T's are
essentially correlating various variables, so we know that even we are when we are
studying PP to ch we have correlations to triple gauge, Bo's uncoupling, so delta
Kappa Gamma and delta G ones there are two well known Triple H couplings and we show
the results in this plane. So we see that the greenery Essentially is what what lead
had found between these correlation between these two variables. And then
another paper by Francis Can you at all actually found the pink and the pink
region from the W Zed measurements from the W's analysis at the high luminosity
Elysee and we further went on to study the Z h process and overlaid it on it. So
because these are all correlated processes, we see that the overlapping
region is essentially the green region which will survive. So, now I won't be
discussing more but there's the Goldstone goes on equivalence through which we
should study the four processes ZHWHW W and W z in conjunction and we will get
different directions on the same same plot and we will get a very small region to
probe the triple gauge couplings. So, if you look into the right panel, so we get a
direction in terms of the universal observables. So, in terms of the four
couplings that They discussed before the for contact interactions is that you will
Jesus dlg that you are and she said Dr. And we find permit level constraints on
various couplings and you see that these couplings, these measurements that we
find, rather the bounds that we find, are very well in comparable to left and
sometimes even doing much better even by an order of magnitude at the high
luminosity latency. So now coming to the olicity amplitudes quickly, so for a two
to two process, we can write down the olicity amplitude for the transfers and
the longitudinal parts using these expressions. So, I'm not going into the
details, but you can see clearly that the longer you depart with with the with no
suppression due to the one by square root that is the leading term. However, we want
to constrain all these various couplings like Kappa v v, Kappa Delta V, V and so on
all these couplings which modify the lorien structure, and for those we need an
interference between the longitudinal and transverse terms but We'll discuss later
if we are not careful, the longitudinal and the transverse terms, these these
terms vanish and we are unable to constrain these couplings. So now
including the decay level, we can actually modify the amplitude by including the
Wigner functions which are described here. And we can actually translate these in
terms of the positive olicity left on fi hat and theta hat. But we know that
polarization of the electron is experimentally not accessible. So we do a
trick. What we do is we translate the positive velocity criteria to a positively
charged criteria and add the latency or add other colliders we can definitely
measure the charge of leptons and we use the relations between left handed
cardinalities and right handed cardinalities and flip for the for the
required required reasons. And we get we can dissect the amplitude squared into
these two parts where we have a left handed part and the right handed part here
and once we expand this amplitude square, we get these beautiful nine structures.
So, you see that we have a longer term little piece which is completely longer
term which depends on the sine squared of the two Peters, we get transverse pieces,
and then we also get terms which are longer to the load and transverse pieces.
So, what are these coefficients a Ll to att prime Tilda, so, these are the nine
Angular moments and these are these are given in terms of the various
coefficients. So, you see that inside these emails, these are all functions of
energy. And you can see that these are also functions of the various EFC
coefficients. So, you can write it in a very beautiful and compact way in terms of
these nine functions. So, as anticipated the parametrically largest contribution to
the longitudinal transfer transfers interference terms comes about from a lt
two and H il t to Tilda, so, these are the CP od and the CP event done Now, mind you,
if we integrate any of these terms, because these are all sines or cosines,
and not squares of them, all these terms will completely vanish. So in one of the
papers, what we did is how do we extract these, so we did a rudimentary thing. So
what we did is, when we encountered a negative sign into these couplings, we
just flip the signs and we retain the positive condition. However, in one of our
later works, which I'll be showing in the next slide, we use the sophisticated
Method of Moments which actually preserve these things. Now, we do expect CP od and
CP event structures when we do these, when we perform these and and rightly so, we
see that for the LD two we regain CP, CP even structure which is the blue one and
for the CP odd which is sine phi we get we get the red curve. Similarly, for the wh
process we get, I just want to remark one thing that these distributions also remain
positive served for any low distributions for anello effects when we include
radiation showering, experimental cuts, etc, at least for azimuthal angles they
remain preserved for other angles, there are small shifts, which are there in
details in the paper. So now, coming to the differential in angles so what what is
the method of moments, so, I'll be just saying very quickly, So, essentially, it's
an analogue of the Fourier analysis, which is utilized to extract the aforementioned
Angular moments a Ll through a TT prime. So, what we do is we square the amplitude
and we can write it in terms of the A's and the F's. So, A's are essentially the
moments which are functions of the energy and F's are the functions of the angle.
So, then we look for weight functions, which which essentially form an inner
product like this and we get a chronicle delta and then it is easy to pick out the
angular moments. So, we when we when we extract the matrix, what we find is some
Very nice, we find that the weight functions are proportional to the to the
angular functions barring the first and the third rows. So, where we have a mixing
and then we essentially rotate the one three system to an orthogonal basis, and
we use the following criteria of a m as a sum of the weight functions over the
various bins. And we use one of the variables which is the invariant mass of
the final state. So, for the Z eight system, we use the Z h invariant mass for
the wh system we use the W h invariant mass and we can find the invariant masses
the angular moments for all these nine terms. So now coming to the results. So,
so, we have previous results, one is the first one is essentially the contract
terms. So the contract terms with the remember the terms that I showed in red,
which essentially the four point functions, so we have limited our
calculations to own include only the interference terms and have checked
explicitly that the squid jobs are especially for us small. So the four point
contact vertex is constrained by Using the energy squared dependent terms, and as we
discussed before the A Ll term dominates because it is not suppressed by square
root esat and we get less than per mil level bounds on the four point
interactions of the GH WQ and the GH said F at the design luminosity of three to one
inverse for the Z h. On the other hand for for discussing the modified lorien
structure we find a we define it a 2d plane plot for delta G h Zed Zed and Kappa
Zed Zed and similarly for delta G h WW and Kappa WW and we find that we get person
level bounce for the opposite side versus the delta G h Zed Zed and Kappa ww versus
the delta G h WW. Similarly, we find single bounce on the CP odd quantities and
upon assuming a linearly realized electroweak symmetry, we get a combined
plot through which we get person level constraints. So, this is just an Just
coming very quickly to the case two, this is just one slide this is week goes on
fusion, which is preliminary. So, we study the processes p p to H plus jets and p p
to h in the dye photon and the dye towel channel. And here we see the cut based
analysis and on top of the previous plot we have overlaid the direction or given by
the Vf study. So, we get a separate direction which coincidentally is very
similar to the W direction we will be optimizing this further, but we get a
different direction. So, this is a work coming soon. So, now quickly coming to the
SD axis, which has been very well discussed previously. So, SD access is
essentially evolving from from the run one which usually which essentially used
signal strength and was using the Kappa framework a lot. So, this is a more
differential analysis and allows for combinations of measurements and several
decay channels. We, we have several stages proposed and here we measured the
crustacean Instead of the ratios of signal strengths, so, we have various stages here
at stage zero essentially corresponds to the production mode category. Stage one
defines complete set with potential bins merging. So, we have like several
categories in terms of PTs and other variables. And with accumulation of more
and more data we can go into more granularity and we can be more and more
differentiated. So, this is an excellent slide from from Steven Jenkins, which I
really liked yesterday. So, this is from like resolved and boosted analysis in the
VH VB and that these two are not orthogonal. So, now coming to the last
slide here, so that the SD access method evolves with increasing statistics and
requires intuition and systematic understanding of the of the data. We have
various stages of binning. As I said before, an SD access gradually moves
forward to a fully differential analysis with shape information and can be
connected to effective field theories, copper frameworks, various bsm scenarios
matrix element method is one of the most powerful tools to discern the full
structure of any processes. On the other hand, the method that I propose that we
propose here in this talk the method of moments, as described in this talk has
comparable sensitivity the matrix element, it is very transparent. It exploits the
full Angular structure for the squared amplitude, and it combines the advantages
of both SD access and the matrix element method to a certain extent. Coming to my
summary slide, the high Lumia AC can strongly compete with left and can be
considered a very good precision machine at the moment. The effective field
theories sense actually shows that that many animalistic couplings were already
constrained by left through various measurements, we can essentially exploit
the full tensor structures of the Higgs gauge bosons by using differential
information and sophisticated techniques like the method of moments. We also
studied complimentary directions like the week goes on fusion. We discussed that the
simplifying template cross section is a very powerful tool that gains in
sophistication with more data accumulation. And one should explore the
complete comparison between these three methods. Also, stay tuned for an upcoming
work in the GG to H to z star, the golden channel with the method of moments. So I
thank you all for your attention and welcome you for any questions or comments.
Thank you very much.
So thanks a lot for the nice talk and also eliminating food, new technique and new
possibilities. So we kind of have a hard limit in the sense that the next session
will start in seven minutes but we certainly have a bit of time for question,
comments as these talk nicely rub up current result with the experiment of
sensitivity and so on. Okay, so I do have a question from Ricardo.
Please go ahead.
Hello. Can you hear on slide 12? You say that you extracted them independent from
the CPS coupling. Yeah, how do you do this? Because it's
Yes. So, as I said like CP the CP even couplings. So, if you come here into the
the distribution the various nine Angular moments here. So, you see that the seven
terms of are actually like correlated like you have the GS correlated, but except for
the CP od terms the Ei l one tilde and the L two Tinder. So, these do not depend on
any standard model like modification. So, we do not have any standard model
interference with the with the CP od term. So, whenever we are putting any bounds,
they are just coming out by themselves.
Okay.
Okay, thanks a lot more questions.
So I have prepared a zoom link here if someone is interested later on. So I'll be
there online for a few hours.
Thanks. So maybe I could ask you obviously, questions that you might expect
Given your last two slides, which is use show, it's a nothing nothing approach to
that probably the best limit on this coefficient at the same time you also show
the SD access, which is kind of building up more and more differential. And one
more question that is that if you have a feeling of well obviously access at the
moment, fewer information, but we have a feeling of well, how much more bins maybe
just in PD or in other direction as access could go to be competitive with the
proposed approach or if this will still remain much read say. So I read in
exploding information,
right. So this is a very good question, because so if you see these nine Angular
moments, so if we, right if we write down and we try to compute the number of events
and each of these terms, we see that like some of these will have some of these will
require more luminosity in order to extract some level. So, some of these
Angular variables can already be extracted with the present luminosity of of the of
the order of hundred and 50% or so, at the moment if I'm not wrong, because I am not
following I have not followed SD access studies very well. But if I know like most
of the most of the bins are in terms of pts, and like repetitively, over the like,
I might suggest that some of these bins can even be in terms of these, these
angles that I proposed here like the structures here. So if the bins can be
done in these ways, like including these these structures, so for example, the bh h
to BB which is already done very well. So if the SD access can include some of these
bins in the sine squared theta sine square theta and cos theta cos theta kind of
terms, so you will already get a very good mapping between SD access and the method
of moments that we proposed. So these are essentially our nine bins. So if you use
these in SD access, some of these will have less sensitivity but some already
have Good sensitivity in my opinion.
Okay, thanks. I mean I'm aware of a pure theoretical paper for the end of last year
unfortunately remember the names and in any case, I will not be able to quote all
of them. So I prefer not to quote any it was suggested to extend the sex sex into
the kind of transverse mass direction, which is one also the variable that you
were you were plotting so I assume that some extent that might be similar, but
right, yeah,
are these angles actually like a very, very transparent like, unlike the matrix
element method, which is extremely powerful tool, but it is kind of like a
box. But these these you get a pure feeling about these like you, you can use
your full year analysis to get all these structures.
Okay, thanks for your answer. Yep. I think Well, okay, we can take one final question
which I assume being a follow up and then we can Rose. Okay,
Ricardo, a second, I wanted to ask you a question more on the technical side. So,
to construct these observables, you, you, you need to reconstruct the full form
factor of the vector boson. In the case of W where you have the problem of the
longitudinal momentum of the material, well defined, how do you do that
reconstruction of the Exactly, exactly.
So, yeah, I was wondering, someone would ask this question. So, I didn't show the
plot here. So, the W reconstruction actually gives a nice reconstruction for
two of the three angles, but there's an ambiguity in the third angle by 50%. So,
we will get we will lose some efficiency in that sense. So, we use the piece of
reconstruction, as we have been in in many, many papers. So, in one paper we
were actually trying to, to use machine learning techniques to extract the pieces
of the new You know perfectly but we didn't manage to do it and we are still
looking forward to it. So there is still an ambiguity for the WWE exe process and I
agree and we are actually planning to study the W two hydrants and the Higgs to
Taos so that like we get more handle over so till now we have only studied w two l
new and Hicks to be barred. Thank you.
Okay, so