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Are you gonna slide? Yes Can you try to go
fullscreen? yes to that

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is fine.

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Yes. So please stop when ready.

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Yeah, thanks a lot. So, I would

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like to thank the organizers for giving me
the opportunity and for inviting me to

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give this talk at HCP. So, this is a talk
which is similar in lines with the others

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that we have listened to in this in this
series. However, I will be taking a little

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bit different approach from the from the
theoretical point of view. So, this talk

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is based on these four works. So, three of
them published and one just to be

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published very soon. So, now coming to the
to the motivation for standard model

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effective field theory. So we want to ask
some pertinent questions. So some of the

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questions that we want to ask this, how do
we reconstruct a TV scale a graduate from

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The available data or the data that will
become available in the HLS at the next

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question that we want to ask is how do we
extract the best observables to study the

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effects of some particular operator and
for particular processes. So, we know that

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new vertices come about from effective
field theories and can produce novel or

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enhanced effects in several parts of the
face face. So, many of these questions can

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actually be IP address very well in the
regime of either or high energies and

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luminosities. So, when we talk about
effective field theories, so, it is a

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bigger theory actually, which is which can
be either weakly strongly or moderately

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coupled, and is assumed to supersede the
Standard Model above a high cutoff scale

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lambda which is the scale of the mass of
the heavy new physics. at the perturbative

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level, we know that all the heavy degrees
of freedom above this cutoff scale lambda

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are decoupled from the low energy theory.
So, there are several Ways to write down

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effective field theories. So, here I will
be taking the approach of a linear

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effective field theory, which I write down
in terms of several operators at different

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mass dimensions. So, starting with the
dimension for standard model and Ranjan,

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we go on to higher dimensions in mass and
this is how we parameterize the

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Lagrangian. So, there are several
important goals of the LSE and one of the

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most important goals at the present is to
precisely measure the Higgs and other

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couplings like gauge couplings, several
other couplings. So, if history is our

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guidance we know that we can get indirect
constraints to much higher scales tender

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tender president running of the of the
collider, so, st parameters being prime

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examples during the lab round. So, the
questions that we want to address are can

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the Large Hadron Collider compete with the
left Collider in constraining precision

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physics and whether or not it can provide
any new information. So we know that from

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EFT correlated variables left had already
constrained certain anomalous x coupling

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Even though the Higgs was not discovered,
so, from z pole measurements or triple

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gauge coupling measure measurements that
at the left could already constrain

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several couplings and in LHD, we can
actually use the high energy and the high

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luminosity to to constrain these couplings
further.

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So, now coming to my first case study, so
this is extra volume with the Large Hadron

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Collider. So, this is a Higgs being
produced in association with a W or Z

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boson. So, these are the various modified
Fineman diagrams and the black blobs

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essentially show us the modifications. So,
we can have modifications in the W or Z,

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CT CT vertex, the Higgs WW, the Higgs Cz
vertex, and we can have a whole new four

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point interaction. So, this is essentially
the Lagrangian the dimension six of

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aggrandizement which which encapsulates
this, these these diagrams. So, the terms

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in blue are essentially modifications of
the terms which are already there in

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standard model. So, you see that these
terms even though they are new, they have

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One limitation is that they do not grow
with energy and are suppressed with

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respect to the contact interactions, which
are mentioned in in red. So you see that

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the contact interactions of the four point
interactions and because of the absence of

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a propagator in the in the Fineman
diagram, these actually grow with energy

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we'll see how in the later slides. So,
I'll quickly flash the operators which

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contribute to the above Lagrangian in the
in the word services. So, these are the

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various operators that contribute to the
to the Higgs trialing processes and modify

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the Higgs vv star and the Higgs D FF bar
couplings. So, coming to the topology that

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we are considering, so we produce a V h,
where V is either a W or a Z, and the VD

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case to a pair of leptons and the Higgs to
a pair of big quarks, which essentially we

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take as a fact check. So there are several
angles at play here, which which will be

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very important in the discussion of this
of this talk. So please note the angle big

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teacher Which is the two to two scattering
angle and this is in the V eight center of

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mass frame. Then we have an angle small
theater, which is the angle of the of the

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of one of the leptons say the positive
charge leptons with respect to the rest

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frame of the V boson. And then we have the
angle phi which disc which describes the

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planes the angle between the these two
planes of the V Ll and the V eight system.

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So the question is how much differential
information can we extract from this

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process. So here it is essentially a three
body process because we are treating the

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Higgs is a fat jet. So there are three
times three minus four that is five

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kinematic variables that completely define
our our system. So if we if we ignore the

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boost factor, the variables that we have
our square root is at the end of three

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angles. So if we consider 10 bins per
variable, so then for every energy bin, we

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will have 10 to the power three, which is
Thousand numbers have been stopped in the

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full information. But we will see later
that this this number thousand can

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actually be reduced to nine per energy
bill. So this is the beauty of this method

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that I'll be discussing, which is called
the method of moments. So please bear with

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me. So now, as I discussed before, the
differential cross section for the

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processes, pp to z or w, h is a
differential input variable, so, we can

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write it as d sigma d d Big D small to
define. So, now just focusing on the Z h

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for the moment, here we do a full cut
based and an MVA analysis, and we see that

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the major background is z BB bar, we use a
boosted substructure analysis and by a

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shoddy cut Bates cut based analysis, I
didn't do a very optimal optimized cut

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based analysis we see that we get a signal
over background ratio of the order of a

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quarter. However, with an MV optimization,
we can take it further to half. So, we see

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that so, Be changes from one over 40 to
other one, and we still have like close to

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35 evens even at 300 inverse femto bond.
So Nan Lu actually discussed very, very

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nicely possibilities for upgrades, like we
can take be tagging to even up to four,

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which I'll be looking at the plot on the
left actually shows the ingredient mass of

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the Z eight system for the various signal
and background samples. And we see the cut

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have been imposed for one of these and the
right plot, which is the table which

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actually shows the cut paste analysis and
the various cuts applied. So coming to the

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result for this part, so, because I
discussed before that EF T's are

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essentially correlating various variables,
so we know that even we are when we are

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studying PP to ch we have correlations to
triple gauge, Bo's uncoupling, so delta

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Kappa Gamma and delta G ones there are two
well known Triple H couplings and we show

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the results in this plane. So we see that
the greenery Essentially is what what lead

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had found between these correlation
between these two variables. And then

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another paper by Francis Can you at all
actually found the pink and the pink

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region from the W Zed measurements from
the W's analysis at the high luminosity

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Elysee and we further went on to study the
Z h process and overlaid it on it. So

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because these are all correlated
processes, we see that the overlapping

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region is essentially the green region
which will survive. So, now I won't be

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discussing more but there's the Goldstone
goes on equivalence through which we

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should study the four processes ZHWHW W
and W z in conjunction and we will get

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different directions on the same same plot
and we will get a very small region to

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probe the triple gauge couplings. So, if
you look into the right panel, so we get a

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direction in terms of the universal
observables. So, in terms of the four

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couplings that They discussed before the
for contact interactions is that you will

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Jesus dlg that you are and she said Dr.
And we find permit level constraints on

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various couplings and you see that these
couplings, these measurements that we

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find, rather the bounds that we find, are
very well in comparable to left and

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sometimes even doing much better even by
an order of magnitude at the high

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luminosity latency. So now coming to the
olicity amplitudes quickly, so for a two

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to two process, we can write down the
olicity amplitude for the transfers and

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the longitudinal parts using these
expressions. So, I'm not going into the

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details, but you can see clearly that the
longer you depart with with the with no

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suppression due to the one by square root
that is the leading term. However, we want

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to constrain all these various couplings
like Kappa v v, Kappa Delta V, V and so on

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all these couplings which modify the
lorien structure, and for those we need an

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interference between the longitudinal and
transverse terms but We'll discuss later

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if we are not careful, the longitudinal
and the transverse terms, these these

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terms vanish and we are unable to
constrain these couplings. So now

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including the decay level, we can actually
modify the amplitude by including the

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Wigner functions which are described here.
And we can actually translate these in

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terms of the positive olicity left on fi
hat and theta hat. But we know that

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polarization of the electron is
experimentally not accessible. So we do a

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trick. What we do is we translate the
positive velocity criteria to a positively

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charged criteria and add the latency or
add other colliders we can definitely

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measure the charge of leptons and we use
the relations between left handed

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cardinalities and right handed
cardinalities and flip for the for the

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required required reasons. And we get we
can dissect the amplitude squared into

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these two parts where we have a left
handed part and the right handed part here

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and once we expand this amplitude square,
we get these beautiful nine structures.

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So, you see that we have a longer term
little piece which is completely longer

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term which depends on the sine squared of
the two Peters, we get transverse pieces,

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and then we also get terms which are
longer to the load and transverse pieces.

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So, what are these coefficients a Ll to
att prime Tilda, so, these are the nine

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Angular moments and these are these are
given in terms of the various

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coefficients. So, you see that inside
these emails, these are all functions of

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energy. And you can see that these are
also functions of the various EFC

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coefficients. So, you can write it in a
very beautiful and compact way in terms of

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these nine functions. So, as anticipated
the parametrically largest contribution to

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the longitudinal transfer transfers
interference terms comes about from a lt

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two and H il t to Tilda, so, these are the
CP od and the CP event done Now, mind you,

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if we integrate any of these terms,
because these are all sines or cosines,

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and not squares of them, all these terms
will completely vanish. So in one of the

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papers, what we did is how do we extract
these, so we did a rudimentary thing. So

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what we did is, when we encountered a
negative sign into these couplings, we

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just flip the signs and we retain the
positive condition. However, in one of our

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later works, which I'll be showing in the
next slide, we use the sophisticated

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Method of Moments which actually preserve
these things. Now, we do expect CP od and

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CP event structures when we do these, when
we perform these and and rightly so, we

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see that for the LD two we regain CP, CP
even structure which is the blue one and

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for the CP odd which is sine phi we get we
get the red curve. Similarly, for the wh

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process we get, I just want to remark one
thing that these distributions also remain

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positive served for any low distributions
for anello effects when we include

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radiation showering, experimental cuts,
etc, at least for azimuthal angles they

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remain preserved for other angles, there
are small shifts, which are there in

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details in the paper. So now, coming to
the differential in angles so what what is

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the method of moments, so, I'll be just
saying very quickly, So, essentially, it's

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an analogue of the Fourier analysis, which
is utilized to extract the aforementioned

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Angular moments a Ll through a TT prime.
So, what we do is we square the amplitude

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and we can write it in terms of the A's
and the F's. So, A's are essentially the

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moments which are functions of the energy
and F's are the functions of the angle.

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So, then we look for weight functions,
which which essentially form an inner

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product like this and we get a chronicle
delta and then it is easy to pick out the

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angular moments. So, we when we when we
extract the matrix, what we find is some

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Very nice, we find that the weight
functions are proportional to the to the

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00:14:03,929 --> 00:14:09,089
angular functions barring the first and
the third rows. So, where we have a mixing

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00:14:09,209 --> 00:14:13,229
and then we essentially rotate the one
three system to an orthogonal basis, and

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we use the following criteria of a m as a
sum of the weight functions over the

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various bins. And we use one of the
variables which is the invariant mass of

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the final state. So, for the Z eight
system, we use the Z h invariant mass for

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the wh system we use the W h invariant
mass and we can find the invariant masses

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the angular moments for all these nine
terms. So now coming to the results. So,

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so, we have previous results, one is the
first one is essentially the contract

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terms. So the contract terms with the
remember the terms that I showed in red,

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which essentially the four point
functions, so we have limited our

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calculations to own include only the
interference terms and have checked

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explicitly that the squid jobs are
especially for us small. So the four point

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contact vertex is constrained by Using the
energy squared dependent terms, and as we

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00:15:03,359 --> 00:15:08,219
discussed before the A Ll term dominates
because it is not suppressed by square

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root esat and we get less than per mil
level bounds on the four point

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interactions of the GH WQ and the GH said
F at the design luminosity of three to one

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inverse for the Z h. On the other hand for
for discussing the modified lorien

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structure we find a we define it a 2d
plane plot for delta G h Zed Zed and Kappa

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Zed Zed and similarly for delta G h WW and
Kappa WW and we find that we get person

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level bounce for the opposite side versus
the delta G h Zed Zed and Kappa ww versus

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the delta G h WW. Similarly, we find
single bounce on the CP odd quantities and

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upon assuming a linearly realized
electroweak symmetry, we get a combined

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plot through which we get person level
constraints. So, this is just an Just

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coming very quickly to the case two, this
is just one slide this is week goes on

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fusion, which is preliminary. So, we study
the processes p p to H plus jets and p p

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to h in the dye photon and the dye towel
channel. And here we see the cut based

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analysis and on top of the previous plot
we have overlaid the direction or given by

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the Vf study. So, we get a separate
direction which coincidentally is very

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similar to the W direction we will be
optimizing this further, but we get a

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different direction. So, this is a work
coming soon. So, now quickly coming to the

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SD axis, which has been very well
discussed previously. So, SD access is

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essentially evolving from from the run one
which usually which essentially used

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signal strength and was using the Kappa
framework a lot. So, this is a more

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differential analysis and allows for
combinations of measurements and several

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decay channels. We, we have several stages
proposed and here we measured the

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crustacean Instead of the ratios of signal
strengths, so, we have various stages here

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at stage zero essentially corresponds to
the production mode category. Stage one

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defines complete set with potential bins
merging. So, we have like several

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categories in terms of PTs and other
variables. And with accumulation of more

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and more data we can go into more
granularity and we can be more and more

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differentiated. So, this is an excellent
slide from from Steven Jenkins, which I

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really liked yesterday. So, this is from
like resolved and boosted analysis in the

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VH VB and that these two are not
orthogonal. So, now coming to the last

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slide here, so that the SD access method
evolves with increasing statistics and

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requires intuition and systematic
understanding of the of the data. We have

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various stages of binning. As I said
before, an SD access gradually moves

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forward to a fully differential analysis
with shape information and can be

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connected to effective field theories,
copper frameworks, various bsm scenarios

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matrix element method is one of the most
powerful tools to discern the full

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structure of any processes. On the other
hand, the method that I propose that we

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propose here in this talk the method of
moments, as described in this talk has

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comparable sensitivity the matrix element,
it is very transparent. It exploits the

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full Angular structure for the squared
amplitude, and it combines the advantages

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of both SD access and the matrix element
method to a certain extent. Coming to my

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summary slide, the high Lumia AC can
strongly compete with left and can be

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considered a very good precision machine
at the moment. The effective field

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theories sense actually shows that that
many animalistic couplings were already

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constrained by left through various
measurements, we can essentially exploit

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the full tensor structures of the Higgs
gauge bosons by using differential

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information and sophisticated techniques
like the method of moments. We also

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studied complimentary directions like the
week goes on fusion. We discussed that the

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simplifying template cross section is a
very powerful tool that gains in

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sophistication with more data
accumulation. And one should explore the

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complete comparison between these three
methods. Also, stay tuned for an upcoming

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work in the GG to H to z star, the golden
channel with the method of moments. So I

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thank you all for your attention and
welcome you for any questions or comments.

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Thank you very much.

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So thanks a lot for the nice talk and also
eliminating food, new technique and new

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possibilities. So we kind of have a hard
limit in the sense that the next session

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will start in seven minutes but we
certainly have a bit of time for question,

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comments as these talk nicely rub up
current result with the experiment of

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sensitivity and so on. Okay, so I do have
a question from Ricardo.

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Please go ahead.

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Hello. Can you hear on slide 12? You say
that you extracted them independent from

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the CPS coupling. Yeah, how do you do
this? Because it's

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Yes. So, as I said like CP the CP even
couplings. So, if you come here into the

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the distribution the various nine Angular
moments here. So, you see that the seven

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terms of are actually like correlated like
you have the GS correlated, but except for

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the CP od terms the Ei l one tilde and the
L two Tinder. So, these do not depend on

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any standard model like modification. So,
we do not have any standard model

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interference with the with the CP od term.
So, whenever we are putting any bounds,

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they are just coming out by themselves.

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Okay.

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Okay, thanks a lot more questions.

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So I have prepared a zoom link here if
someone is interested later on. So I'll be

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there online for a few hours.

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Thanks. So maybe I could ask you
obviously, questions that you might expect

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Given your last two slides, which is use
show, it's a nothing nothing approach to

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that probably the best limit on this
coefficient at the same time you also show

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the SD access, which is kind of building
up more and more differential. And one

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more question that is that if you have a
feeling of well obviously access at the

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moment, fewer information, but we have a
feeling of well, how much more bins maybe

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just in PD or in other direction as access
could go to be competitive with the

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proposed approach or if this will still
remain much read say. So I read in

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exploding information,

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right. So this is a very good question,
because so if you see these nine Angular

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moments, so if we, right if we write down
and we try to compute the number of events

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and each of these terms, we see that like
some of these will have some of these will

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require more luminosity in order to
extract some level. So, some of these

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Angular variables can already be extracted
with the present luminosity of of the of

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the order of hundred and 50% or so, at the
moment if I'm not wrong, because I am not

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following I have not followed SD access
studies very well. But if I know like most

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of the most of the bins are in terms of
pts, and like repetitively, over the like,

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I might suggest that some of these bins
can even be in terms of these, these

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angles that I proposed here like the
structures here. So if the bins can be

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done in these ways, like including these
these structures, so for example, the bh h

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to BB which is already done very well. So
if the SD access can include some of these

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bins in the sine squared theta sine square
theta and cos theta cos theta kind of

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terms, so you will already get a very good
mapping between SD access and the method

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of moments that we proposed. So these are
essentially our nine bins. So if you use

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these in SD access, some of these will
have less sensitivity but some already

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have Good sensitivity in my opinion.

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Okay, thanks. I mean I'm aware of a pure
theoretical paper for the end of last year

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unfortunately remember the names and in
any case, I will not be able to quote all

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of them. So I prefer not to quote any it
was suggested to extend the sex sex into

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the kind of transverse mass direction,
which is one also the variable that you

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were you were plotting so I assume that
some extent that might be similar, but

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right, yeah,

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are these angles actually like a very,
very transparent like, unlike the matrix

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element method, which is extremely
powerful tool, but it is kind of like a

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box. But these these you get a pure
feeling about these like you, you can use

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your full year analysis to get all these
structures.

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Okay, thanks for your answer. Yep. I think
Well, okay, we can take one final question

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which I assume being a follow up and then
we can Rose. Okay,

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Ricardo, a second, I wanted to ask you a
question more on the technical side. So,

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to construct these observables, you, you,
you need to reconstruct the full form

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factor of the vector boson. In the case of
W where you have the problem of the

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longitudinal momentum of the material,
well defined, how do you do that

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reconstruction of the Exactly, exactly.

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So, yeah, I was wondering, someone would
ask this question. So, I didn't show the

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plot here. So, the W reconstruction
actually gives a nice reconstruction for

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two of the three angles, but there's an
ambiguity in the third angle by 50%. So,

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we will get we will lose some efficiency
in that sense. So, we use the piece of

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reconstruction, as we have been in in
many, many papers. So, in one paper we

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were actually trying to, to use machine
learning techniques to extract the pieces

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of the new You know perfectly but we
didn't manage to do it and we are still

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looking forward to it. So there is still
an ambiguity for the WWE exe process and I

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agree and we are actually planning to
study the W two hydrants and the Higgs to

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Taos so that like we get more handle over
so till now we have only studied w two l

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new and Hicks to be barred. Thank you.

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Okay, so