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All right so

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um so the best of luck on film is out in
the maze on the case show some interesting

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hints of physics with hints of physics
beyond the standard model. And while these

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are not conclusive to to a number of
people, they are compelling but when taken

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together, and they may well go with it
with a new analyses and proved techniques,

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experimental techniques. However, the main
premise of this talk is that they hint

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physics beyond the standard model. And,
and then the clear call for theorists is

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to do a bottom up model building
adventure. So, what I mean by this is that

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we should first try to, I will try to
guide you through a number of steps to

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establish the so called infrared
consistency checks and meaning Can we have

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new physics that a explains the anomalies
both in charge in little currents and B

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pass all experimental constraints that
have been that are out there in particle

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physics? So, the the question zero is to
try to find an explanation within the so

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called the Standard Model effective field
theory, which is a motivated framework to

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to parameterize many different short
distance new physics models. So, if this

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can can be done, then we should go and try
to complete the effective operators by by

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identifying the emerging set of new heavy
mediator particles that generate these

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operators. Then we will arrive to a new
set of consistency checks for instance, do

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these heavy mediators pass the Direct
searches at the LSE. Once we have all this

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then we can go off and try to work try to
try to write down a full fledged model a

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prototype, which is fully calculable hence
we can really calculate many many

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observables and cross check and to
establish the IR infrared consistency

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checks and we would like to this model to
be to be able to extrapolate it to high

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energies. At that point, we are ready to
try to make connections with the

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ultraviolet physics and try to ask
questions How does that construction fits

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into the UV picture? In other words, is it
linked to to open problems so, the

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standard model for example, the hierarchy
problem the flavor puzzle etc. And then we

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can also ask questions about the
connections and links which come out from

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those constructions with other sectors of
high energy physics in general. And, and

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to make predictions, where should we look
further? All right. That's this slide

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defines what I would call a bottom up
model building. So, the zero exercise is

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to perform the analysis of su to gauge
invariant dimension six operators. We know

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that the basis of these operators is quite
big into there are a huge number of flavor

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parameters and input flavor parameters. So
the the way to navigate through this huge

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parameter space is to employ flavor
symmetries and symmetry breaking patterns,

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which serve as the organizing principle.
So we were able to To identify a coherent

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picture of new physics based on two
assumptions, the first one being that the

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new physics come in specific dimension six
in a few dimensions six operators

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basically in semi electronic for firm
operators, which involve left handed cork

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and leptons tablets and they are written
in the Lagrangian on this slide. And

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second that the the flavor structure of
these ij k l tensors follows the U to Q

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cross u 12 favorite symmetry which has
been which with the minimal breaking

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spurious This was quite surprising and
very was, you know, very interesting to

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see that one can explain the anomalies in
such a minimal framework and Be safe with

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with respect to other constraints of low
and high energies.

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And the structure which emerges the flavor
symmetry in particular, is something that

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was proposed before the anomalies to try
to address the problem of the puzzle of

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from your masters and mixings youtube
youtube flavors symmetries. So, that I

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will leave the more details we can on this
slide and links to to to a few references.

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And, and just to mention that, for
example, well young constraints are high

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at from Atlas and CMS were important in
this exercise as well as radiative induced

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effects. And let me mention that, here we
do not consider right handed current, and

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the current data doesn't tell us whether
we have them or not. However, they can be

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added And they can in some cases they can
be useful and future data. If this turns

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out to be new physics future there are
ways to say whether or not we have right

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handed currents

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alright. So, now we are good good to go

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more towards higher energies and try to
find

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towards the model. So, new having
mediators we generate these new family

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interactions at three level at least can
be nicely that we can have we can have a

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we can basically make a catalogue of them
and they are given in this slide. So,

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these particles are like a w prime or or
scalar and vector laptop work. Their

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standard one quantum numbers are given in
the brackets. So, models where you have a

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single mediator particle are very
predictive. So, they for example, they if

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you exchange one mediator then you have a
clear prediction between effective

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operators at low energies

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okay.

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In fact they are so predictive that only
one of them can is a successful

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explanation of all of both charging local
current anomalies and is consistent with

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other with other constraints and this is
the so called vector laptop work singlet

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So, it's like so it is the most successful
single media to model and, and its mass is

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around TV scale. And it's coupling to
third generation is of order one so it

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also makes it a perfect candidate for
direct contact dl hc which is also quite

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exciting. Let me also mention that Other
simplified models were put forward in the

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literature, which contained multiple medic
mediators playing the dominant role in the

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anomaly, so giving a significant
contribution for to formulate the

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prototype model, I will go with the vector
laptop work option. And the first thing

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which which comes to attention is the the
quantum numbers of this particle. It is

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actually the party salame laptop work
Quirk. It's the first Leftwich work that

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was

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proposed in the literature and studied in
the literature.

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And this rings a bell as to a profound
question, an open problem of the standard

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model, which is the puzzle of the charge
quantization. The party Salam is one of

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the you know celebrated extensions of the
standard model which which resolves the

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charged quantization puzzle by cork left
on unification this connection comes comes

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comes with the vector electric work
solution. So, however the the vanilla

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potty salon the original pet salon cannot
be directly used here because because we

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need a T scaler laptop work. And there are
constraints from K on decays for instance

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k long to new e on the original party
Salaam. So, the The question is we have to

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modify party Salam and the question for
model building is how to achieve a

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successful TV scale cork left on
unification. And the answer to this

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question goes under the name of the so
called four three to one models which were

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quite popular in recent years and in This
slide you can find links to some selected

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references. And if you would like to have
to, to, for for more references, I will

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give very quickly the the main idea of the
41 model, which is to say that we haven't

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extended gauge symmetry at the TV scale
broken down to the standard model. And in

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this breaking we basically generate a
massive electric vector electric or as a

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massive gauge boson of this

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of this symmetry.

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Now, the there are now there are two
options to embed fermions. In this model,

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they can either be all three sample
generation charged under the three to one

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gauge group, in which case we need the
regenerate interaction with the laptop

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work through fermion to mix With the heavy
fermions. Or we could for instance dialect

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directly couple, a third generation to su
four gauge group and then we the third

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generation directly talks to laptop work.
Now the given the time constraints, I just

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want to make the point that this model is
really, it's a normalizable model with all

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details specified, it's weakly coupled.
And one can calculate observables with it

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and and do an exhaustive phenomenological
studies, some of which were done in the

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literature and calculate, for example, one
new contribution to nasal mixing or some

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exotic signatures at dl hc. So far, we
think we have the working prototype model.

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All right, so where does this lead us in
terms of insights about the US Physics.

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One possible answer to this could be the
so called flavor deconstruction. So let's

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go one step back and think about what
leptons flavor universality is, well, long

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distances, gauge interactions. And the sea
electron Yuan and Tao the same and the

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only difference between these three
particles is data mass, otherwise they

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look the same. This is left on play with
universality. However, this might not be

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true at short distances. In fact, we have
a a great example. And so like the long

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long wavelength photon sees positron and
proton the same but we know very well when

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we go to short distances to high energies.
These are far apart. from each other. So,

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flavored quantum number could be an
indication that when we go to high

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energies there could be this
deconstruction where we have a gauge group

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for each generation of fermions. So, the
model that was put into literature it goes

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under the name of parties alarm cubed,
where there is a participant gauge group

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per family. And then there is a series of
hierarchical symmetry breaking, which then

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go down to the fourth one model at a TV
scale. Now this construction seems like a

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horrible complication when you go to high
energies, they're much more than there are

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many particles, however, and the natural
realization of this idea will go in in

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extra dimensions and you'll follow the the
idea of deconstruction in extra dimension.

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And once again, it is not the number of
particles which is a measure of

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complexity. It's it's basically our
simplicity. It's basically the number of

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symmetries that we have in the, in the, in
our theory. So we're what kinds of

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connections we can make out of this. For
instance, one obvious is the neutrino

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mass, that where this neutrino is in the
same multiplet as the top Quark, for

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instance, then we have a disastrous
prediction that the neutrino mass should

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be of the order of electroweak scale. And,
in fact, we are forced to, to have a very

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specific nature of the neutrino mass
something which goes under the name of

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university so mechanism which were the
neutrino masses protected by electron

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number.

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And my final slide is another interesting
connection which has to do with the

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gravitational waves. So by studying the
cosmological history of this model, one

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can realize that in large parameter space
of the model, you can undergo a

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hierarchical strongly first order phase
transitions in the early universe, and

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this can give you a footprint which is a
stochastic gravitational wave radiation

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that has this characteristic three peaks
signatures per family. And the ratio of

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the peak frequencies is related to the
rate to the hierarchy of, of mass of Quark

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masses. And this is interesting for as you
can see from this plot to future

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gravitational wave interferometers.
Alright, so, this brings me to my

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conclusion, which is very simple. A B
anomalies show the power of data to

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sparkle, new ideas and theorists are
thankful to their colleagues for you know,

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delivering fantastic results and looking
forward It not only opened a new

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directions in model building it also
provided new connections and and new

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spectacular signatures. And the footnote
in the conclusion is that yes working

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model exists. However the final judge is
the experiment. Thank you

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very much mirror question toward me.

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Raise your hand

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Okay, maybe I should start. So, that gives
me some time. So,

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regarding regarding the Smith discussion
admin,

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yes. So, you you focused on

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for farming operators, right, which
essentially match directly to the usual

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operators that we have and you know, after
we integrate this into W and so on, and

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does this mean are you doing this because
you know, that the others

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cannot do the job like, you know,
operators with the To send and engage

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pauses and so on or just to start
somewhere, well also those were studied

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and then it showed that they cannot do the
job. So, I see you can have a god operator

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which goes there is a semiotic current
times a gauge boss on with the with the

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Higgs current. And those are so, not to
say basically, you can't pass the

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constraints from the modified gauge
imposed on vertices like WD case and I say

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things and these particular models
essentially are a realization of the setup

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right.

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So, yes, those other operators are much
more suppressed. Well, so, there are other

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So, so, as you go more towards you know,
UVI then you are getting more and more

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consistency checks for instance. Then,
then you have for example, for cork

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operators like delta f To transitions and
in particular in particular model what is

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a quite important constraint is DD by
mixing for instance. Yeah. And so as you

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you know, and then you have more
complicated direct search constraints. For

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instance, color on is one example you have
this particle which you don't see before

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constructing the model, etc, and goes on.
In even if you go to, you know, the first

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site of party Salaam then gives you flavor
changing the flow currents in K on the

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case, so then you have to be careful where
we're teason

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Okay, see, there is another question from
Giovanni. So just, we should be able now

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to, to speak to try. Yes, much. Thanks for
the nice talk. So my question is how much

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these models are already constrained by
direct searches, I mean how much parameter

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space is still free to explore to be
explored. Alright. So,

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yeah. So, so, the, the precise answer to
this question is, I believe in one or two

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of these references where you can really
show the plots that put combined together

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the direct searches for the lepto Quark
and the parameter space and they try to

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you know, go through the parameter space
of the of the of the, which is a, you

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know, predicted from the from the
anomalies and and there is still there is

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still some, you know, large fraction of
parameter space which is not not explored.

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So, you can have Have a lepto quirk which
is three TV for example, and has a

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coupling of another one.

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Yeah, so So

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yeah, so I cannot claim that this model
can be ruled out by the LFC searches. But

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if we were to have some kind of future
Collider, then like, let's say even

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doubling the energy will be will be quite
good. We actually done prospects for the

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report for the high energy Collider, it
really covered a lot of parameters. And of

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course, this also depends on on the the
statements that I make right now depends

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on the on the on the status of the
anomalies. For instance, before the the

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latest bell to update is the model this
was much more constrained because the the

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anomaly was more profound, but Then the
anomaly went down in the parameter space

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is all of a sudden more relaxed. So yeah,
I hope it is scan by by the detailed

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answer to these questions can be found in
these references.

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Thank you.

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Thank you very much. Other questions?

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seems not. So, we are in time so I think
that we can close the session. Thank you

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very much again to all the speakers