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We started directly with nobody with the
radical review of precision TriCity. Thank

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you for giving this talk amasa is on to
you. Okay, thank you for the for the nice

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introduction. And thanks to the organizers
for inviting me for this conference.

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Although, I guess I'm expressing the
feeling of almost all of the participants

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by saying that initially, I was looking
forward to a nice week in Paris with

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interesting physics, but also be in a very
nice city. Now, we still have interesting

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physics, perhaps even even more
interesting because we really have to

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focus and what I think we all have seen so
far of this conference is a real success,

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which proves that even online we can make
our community very, very lively and have

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nice Discussions Now, with this, let me
delve into precision physics precision

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UCD. And I think this audience don't
really need to need to motivate why we are

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doing precision physics. It's all about on
the one hand, testing the Standard Model

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finding tiny cracks in the standard model,
but also extracting, extracting the most

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out for data in terms of fundamental
physics parameters in terms of fundamental

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information. And at the same time also,
using QC D, not only not only to make the

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bridge between theory predictions and
experimental data, but really as an

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analysis tool for inference in data driven
background predictions are with new

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developments like substructure techniques.
So they Huge motivation really to do

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precision physics. And much of this
motivation is summarized in this in this

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cartoon, which shows the an overview on
all the star model cross section

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measurements that have been performed at
the nhc. Now, here, it's a CMS plot. Other

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places, it will also be Atlas plots, I try
to be more or less, more or less unbiased

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towards one or the other experiment. And
what we see here and what we will be

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focusing on in this talk is especially the
entries that are kind of on the upper end

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of the staircase, which are, which are
those processes that have a relatively low

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multiplicity, but at the same time, a
quite large, quite large cross section.

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And it's in there that we are really
striving for the highest level of

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precision. Now, state of the art precisely
dictions whenever you talk about precise

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making precise predictions, you have to
talk about using perturbation theory,

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making a perturbation serious expansion
and go to as high as high order as you

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can, given, given your resources and
technical capabilities and the current

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state of the art the current theory
default and this is already a major step

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as compared to previous generations of
experiments is that we now have a variety

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of automated tools at our disposal that
not only do leading order but also next to

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leading order predictions including next
to leading order effects both in Houston V

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and the electric theory and this has been
made possible to a large extent by an

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engineering type of approach that people
started 10 years ago to define standard

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interfaces between between programs. Such
that one could combine infrastructure from

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multiple apps event generator programs
with one amplitude calculations and really

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have an automated tools that that do all
these calculations to next to the order

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fairly often also combined with pattern
showers, which then allow you to get full

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event properties at next to leading or
accuracy on differential cross sections on

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fiducial perception. So whenever we're
talking about comparisons with

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experimental data, although this does not
show, kind of in the in the tiny dots

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here, all these are cross sections that
are defined for a certain set of fiducial

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cuts, so rapidity, acceptances, transfers,
momentum acceptances, and so on. You want

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to mirror these at the level of your
theoretical calculations as well as you

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can. Now it's next to leading order We are
reaching a level of accuracy that

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typically goes in the range of 10 to 15,
sometimes 20% residual us concerned from

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missing high orders and for many of these,
the error bars especially at the higher

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multiplicities are still large enough that
you can that you can live with a theory of

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uncertainty at the level of 10 to 15%.
However, for benchmark cross action so

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much with the process this is not enough
and this has motivated quite a fraction of

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the community to embark on to next to next
to building our calculations of first of

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all more inclusive process like eggs and
vegetables on production. And then and

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then my differential process a lot of the
revenue today two reactions are now

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computed to next to next to living our
currency and in the community. We say I

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have I think a healthy competition between
different groups also between different

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techniques, I mean calculations all these
calculations require quite sophisticated,

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sophisticated methodology to combine all
the ingredients you have really ideation,

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your virtual corrections, all this you
want to come by I want to combine really

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on a face to face this point basis which
requires sophisticated subtraction

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techniques to handle infrared
singularities and this there's been quite

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a number of techniques that have been
developed over the years first and

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pioneering was appeared in America
techniques sector become position, which

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was then later accompanied by Qt
subtraction sector and proof methods and

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antenna subtraction in reading and
subtraction projection to one method, all

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these methods, they pursued the same aim.
However, they all use completely different

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company different approaches, completely
different technologies. And what you see

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here is that quite a number of the process
have been covered not with one method, but

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with two methods, sometimes, even with
three methods and they're cross comparison

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between between the different codes is,
has proven to be crucial, really to all of

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the groups to iron out, to iron out bugs,
to iron out approximations, and to get

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better physics predictions wrote out to
the communities now, enough these

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calculations is a walk in the park neither
in terms of performing the calculation of

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implementing it, nor actually running it
runtimes for many of these calculations,

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amount to hundreds of thousands of CPU
hours to get distributions for one set of

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additional cuts out so this very quickly
gets very expensive and also most of these

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codes are still proper it to the office
since they have so many whistles and

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tweaks that only few people are actually
using them safely. Up to now public codes

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have been made available only for closing
that process. And the two main players on

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the market there are MCF M and matrix. And
so any of these calculations here would by

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itself warrant a warrant a large plenary
talk to really explain all the details is

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not what I'm going to do. But instead, I
will focus on kind of the simplest process

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you can think about, which is the Dre
intersection and there make the case for

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why we need all these ionic calculations
to really get the most physics out of out

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of this measurement and crayon is very
simple. It's a lot simpler. It's a lot

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simpler than many of the process that we
just had. In the list of accomplished next

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next to the tomato calculations, it's
definitely a lot simpler and Tiki Bar lots

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of gadgets. Still it contains a lot of the
lot of the physics a lot of information

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that you really draw from the higher order
corrections. Now, first of all, for the

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dragon itself was one of the very first
precision observatories or the hadron

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colliders. Stan what a theory is very well
understood we have next to the model

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electroweak we have next to next leading
order QED the total cross sections so

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without any cuts is even understood two to
one or higher and for transfers momentum

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distributions, we even have three
summation to highlight words we got. Now

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all these calculations they went into
precision tools, which brought us also by

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experimental this most of these codes are
available to a to a larger public. Now,

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what we are going to look at is the triple
differential rayon cross section. Triple

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differential means differential in the
mass of the dialect on payers who are not

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focusing us on the Z resonance, but where
differential in the in the rapidity of the

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electron pair and in the in the leptons
scattering angle in the in the center of

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mass French it's really to to process
proton proton going to die electrons plus

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anything and then of course, you can, you
can go to a to a specific frame and then

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look into the scattering angle and also
into the inclination between the left hand

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plane and on prey plane in the collider
framework. And there we are now focusing

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on the Atlas measurement which has, which
has measured this in a huge number of bins

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in total.

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And 650 bins in different ranges in these
variables what they are distinguishing is

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central Central. So both leptons seen
centrally and central father, one electron

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in central region, one leptons
morphometry. And this already kind of

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trouble starts because what's measured is
not the inclusive cross sections

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differential in these bins, but it is
fiducial cross sections with fiducial

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events, election cuts, and those are in
contrast to these cuts here, which are all

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cuts on the left on pairs. These are cuts
on individual laptops, so minimum

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requirements on individual laptops and
these fiducial cuts. They influence the

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acceptances in triple differential bids.
And in order to see this, let us look here

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just at the leading otter kinematics. So
even order is true and they are all the

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different bins in a fixed slice of
invariant mods. They are they are outlined

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here for the central Central and central
arbitrating. So, we are in dialect or

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ability and in scattering Angular and what
we see here is that this region is fully

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allowed or a leading order, then you have
here in red this cat which delimits the

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end of the meeting on a face face. So, a
lot of the bins where this is crossing

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addressed, addressed cut in half by the
leading American Medical restrictions, and

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then out here out here we have leading
order forbidden bits gets even more

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complicated in central arbitration because
there you treat two lectins differently

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and you actually only have one single beam
out all the central fava beans, which is

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fully allowed most of them are actually
allowed one corner is completely

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forbidden. Now at leading order forbidden
Of course it as soon as You allow for your

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triangle to recall again some extra
radiation, it gets a finer transverse

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momentum. And this immediately implies
that you ease these restrictions so what's

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leading on a forbidden is no longer
forbidden when you allow the dielectric

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required because then your relationship
between single electron transfers momenta

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and the electron kinematics they are east
and for symmetric leptons here, you can

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translate this in the same plots into
minimal transfers more into that you need

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to have in order to attain a certain
region, you see that this very quickly

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goes up to macroscopic values. So here
it's up to you need sometimes to go up to

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50 gV of pair transverse momentum here in
the central format, it's sometimes even

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goes up to TV also and this then turns
insights on bins into transfers momentum,

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this Now, transverse momentum was not part
of our triple differential variables here,

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but somehow we get it transfers momentum
depends in to our calculation from the

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interplay of fiducial cuts and
differential variables and this then in

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the end translates into an acceptance for
individual wins and you see some of the

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bins, especially in central Central,
central central in the in the region have

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a large scattering hangers. So, where you
basically scatter at 90 degrees, they have

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full acceptance. So all the events that
are that are clustered on all the events

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that would be their inclusive cross
sectional as usual cuts but some of the

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other bits especially at low scattering
angle, have very, very low acceptances And

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here, we are computing this next And
excluding Ireland QC, but next to next to

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leading order in the photogram process.
So, this is auto fair square. And this

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means that if we want to have a final
transfers momentum, we are already losing

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one perturbative order and this is
reflected here in this theory to data

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ratios. We see especially in the forbidden
bins in red, that there's fairly poor

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agreement with data and large fury
uncertainties. And this is where auto

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calculations come in not forbidden vintage
leading order they require minimal

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transverse momentum. So, they have very
similar kinematics to transduce momentum

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or faster distribution of electron pairs.
And for these ones, the orifice cube

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correction which would amount to dread Eon
and cube Hello can be obtained from a

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vegetables and plus jet calculation and
next to next to the offer and there's

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quite a few of this on the market. So,
what you then do is to replace the jet

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requirement by a small transfers momentum
cut and this depends on the bin which you

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are sitting in. And then you can correct
these forbidden bins to one order one

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order higher. Now you need to make sure
that your coach still on safely and that

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is by actually comparing his predictions
to risk summation. And after you've

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convinced yourself that your code is doing
what he expected to do, you can actually

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include one other high in the forbidden
bins. What you also need to include the

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next two leading electric corrections and
these two features taped together they

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considerably improve the care uncertainty
I mean, all these large uncertainties

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which you saw in red, they're basically
all gone much more moderated out of these.

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We see You're much better agreement with
data and what can also be done is to

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construct derived quantities like Angular
coefficients of our packet symmetries in

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this data set to aim free from the trip of
differential measurements for measurement

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of the mixing. Now, this was much of an
excursion which was more sought to

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illustrate to you the power of these
higher order calculations. And in the

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precision to city, we have several
directions and challenges. One of them is

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to go to higher multiplicity so beyond two
to two so far, the only genuine two three

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process is three photon production that is
known next next to leading order and their

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limiting factors are multiple its virtual
amplitudes that are lacking methods for

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handling infrared similarities that become
unpractical and we will see kind of recent

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progress has been made. has been made in
this field. And also you would like to

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come to similar level of sophistication as
was attained at next to leading order,

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namely matching to pattern showers
matching to the summation. And for some of

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these reactions, like fixed cross sections
are very cross section read to get to full

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mq below prediction in order to really
come to present level occurs. And let's

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see where we stand in these directions.
And one of the most active areas for in

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recent times has been computation of loop
amplitudes. Now one loop amplitudes, you

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can compute them for arbitrary process.
They are inside your automated tools,

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mighty loop amplitudes. And even more so
much integrals are only known for special

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cases. And there's two main types of
techniques. One is using differential

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equations for these integrals. And either
two In order to reconstruct the analytic

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structure of the integrals potentially
then solving them numerically numerically,

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so solving these differential equations
numerically in order to get okay

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integrals, or a purely numerical technique
sector decomposition, which is divide and

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conquer approach on the face of low
momentum. And very often most of the

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research results were obtained with a
mixture of analytical and numerical

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techniques and they're for master's
propagators. We kind of are now in at a

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level that we that we have many of
irrelevant two to three integrals. And

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then as soon as you go up with number of
loops, the number of legs on the integrals

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goes down and current limits are at three
to level 20 grants are known and followed

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level four Factor vertex integrals are
known. So, one to one or one to two

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integrals and there is a long list of
people that have recently contributed to

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this. And I'm pretty sure I even have
forgotten forgotten some of the main

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contributions. Now, this is all for
masters propagates into his master's

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propagates, we understand a lot of the
analytical structure. So, we kind of know

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00:20:24,720 --> 00:20:30,210
fairly often what function space we
should, we should find our answers and

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with massive propagators this is far from
being the case. So, there actually we have

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results only at a kind of lower low, lower
low and leg level. And, again, their risk

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a lot has been obtained, combining
analytical and numerical techniques. And

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of course, once you have the integrals,
you still don't have the amplitudes

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because what you need is to Determine the
integral coefficients. So, with what

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multiplicity integral appears in, appears
in give low amplitude. So, this reduction

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to master integrals, this has been in the
past performed

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performed purely symbolically and the
spiritual techniques they are also

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hitting, hitting their limits in terms of
size and complexity and a very, very

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important development in the present
taking off in the past two to three years

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or so called finite fields reconstruction.
So, you evaluate such multi loop

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amplitudes a large number of times
hundreds of thousands of times for

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kinematics variables set to set to
different prime now, and then over this

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large finite field of prime numbers, you
you get numerically variations in terms of

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rationale Rational coefficients and then
out of knowing these hundreds of thousands

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of variations, you can actually then
reconstruct the full radical form of these

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of these integral coefficients. And a lot
a lot of the research results for

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instance, in fact, pattern process of
vegetables before patterns, they have been

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thriving really on these on these finite
field reconstruction methods, a point

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where mighty amplitudes changing might
play a key role is whenever you have

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processes that are forbidden at Bond level
and the emblematic example for this is the

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top Quark top loop contribution to Higgs
production there in directs production and

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his project production actually have four
point functions for to four point

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functions with massive propagators.
Already at the next two leading artists

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You're leading order one level process is
at one. Now for all these, all these

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amplitudes. The main here you do have
results that are evaluated for 1.2 phase

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space. However, if you want to evaluate
them multiple times, it's very quickly

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becomes extremely challenging in terms of
stability and CBOT some lots of room for

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improvement. This is not only not only not
the only bottleneck the second bottleneck

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if we want to go to higher multiplicities
is another issue with the matrix elements

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namely next to next to leading order. We
also have one new type contributions that

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are evaluated in unresolved limits you
will have next next leading order. You

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have one new matrix elements were one of
the patterns get soft or collinear because

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you have one order that you eat up in the
loop and another order that you stay left

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free for reader ideation. And there,
especially the auto generate amplitudes

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are not really made for being used in
these areas of limits. So fairly often,

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there's quite a bit of work still to be
done to make them work where you would

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like to work. And then the next step is
the whole set of real radiation

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contributions also, real radiation is a
tree level and they are all the methods

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that have been using various that we have
been using successfully so far. They scale

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very, very poorly with much bliss in terms
of complexity, in terms of computation

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efficiency, and failing often as soon as
you go to too high level of multiplicity,

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you discover that you still need some new
ingredients because not everything is

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available. And they are what people have
been doing is either pragmatic approaches

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or more more clever ideas in search for
generic methods oh so much about fixed

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order next next to leading order at high
multiplicities. We would also like to

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00:25:13,769 --> 00:25:17,849
there have been too sorry, you hear me?

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I'm warning because the time is over right
okay.

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00:25:23,190 --> 00:25:26,790
Then give me one minute I did not get your
three minute warning sorry,

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thank you

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okay. So, combination was pattern showers,
this is now advancing to higher

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00:25:33,269 --> 00:25:41,909
multiplicity also matching on to matching
onto re summation. Matching on to literary

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00:25:41,909 --> 00:25:49,319
summation is really taking, thinking
advances now and we have seen Higgs boson

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00:25:49,619 --> 00:25:54,299
and dialect compare transfers momentum
distributions, where you see that the

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00:25:54,329 --> 00:26:00,659
summation is actually needed to to match
data especially at low transports. Mental

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or at low opening angles now, as a last
point, ultimate precision in Cuba okay

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collations we have them for quite a few
process in terms of inclusive coefficient

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functions. And most recent developments
are aiming to extend these calculations to

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differential observers really to fiducial
cross sections and their projection to

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bond method and Qt subtraction have both
been pioneered until you see an

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application to a simpler process than what
you have at the LFC stret production deep

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elastic scattering where by now one can
actually from knowing inclusive

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coefficient functions and combining this
with a projection to bond method bring the

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theoretical level of the of the
calculation to encompass all which really

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comes down to percent level. The curious
now time is over. So I just flashed this

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Where do we need to go? I think I covered
the motivations and illustrate to you what

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recent advances have been made. Thank you
very much.

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Thank you very much for this very
comprehensive talk. We have a few minutes

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for questions and I see one.

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Joy.

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Can you hear me? Yes. Okay. Thanks for the
very nice talk. Thomas. I had a comment

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and a question. First, the comment. As you
know, that when you're doing next to next

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quarter calculations involving jets,
oftentimes you can end up with scale

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uncertainties that are artificially low
for smaller jets with are being 0.4. So

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just just for people who are doing
comparisons, a copy That you have to take

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that into account, you know, for something
like z plus jet or inclusive jet

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production for Oracle 0.4. The uncertainty
that you get from the calculation might be

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a factor of two less than what a more
realistic estimate of the uncertainty

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might be. And again, that's just due to
some accidental cancellations that take

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place. And then my question is regarding
the dissemination of the results, as you

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00:28:30,840 --> 00:28:38,760
said, it takes an incredible number of CPU
hours to to run the predictions and the

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00:28:38,790 --> 00:28:45,990
programs are so complex that it's very
difficult to hand it off to you know, any

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users even if they had the available CPU
hours. There are programs such as you

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00:28:51,300 --> 00:28:56,850
know, fast and anello or Apple grid, to
try to disseminate these results but they

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00:28:56,850 --> 00:29:03,510
seem to have you know, also A great deal
of complexity as far as you know,

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00:29:03,750 --> 00:29:09,900
providing finished products. So, do you
see key factors just being the optimal way

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of transmitting these results for the
foreseeable future? Or do you think there

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00:29:14,340 --> 00:29:19,050
will be a breakthrough in something like
fast in a lower Apple grant

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00:29:20,580 --> 00:29:27,990
I mean for the dissemination of the
results in a form that you are able to use

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00:29:28,170 --> 00:29:34,710
say in parameter extractions say PDF fits
or as measurements are so, they are the

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00:29:34,710 --> 00:29:43,950
way to go is really is really through
things like Apple grit, and together with

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00:29:45,210 --> 00:29:51,810
with people from from Apple grit and fast
and oh, we have started we have started

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00:29:51,810 --> 00:29:59,280
the generation of grids for for various
types of process. At next an extra leading

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00:29:59,280 --> 00:30:05,700
order and pay The the the infrastructure
front end to the user can be made

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00:30:05,700 --> 00:30:14,460
sufficiently simple that actually you can
aim for a info broad usage, we are still

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00:30:14,460 --> 00:30:23,070
envisaging public releases of the of the
codes, but you formulate it very nice if

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these codes are complex. I think the main
issue is that these codes are quite

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fragile and fairly easily by changing a
few of the settings or just putting in new

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00:30:37,080 --> 00:30:43,320
types of fiducial cuts you may actually
end up very quickly into generating

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00:30:43,320 --> 00:30:50,880
nonsense nonsense predictions. So,
therefore, therefore, most of the authors

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00:30:50,880 --> 00:30:57,150
have been have been still holding back. I
mean I can see on a reasonable timeline

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00:30:57,150 --> 00:31:03,390
that we will see we will see Public code
releases, at least for the lower

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00:31:03,390 --> 00:31:08,970
multiplicity benchmark process, the
cutting edge will always be, we will

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00:31:08,970 --> 00:31:16,110
always be propriety proprietary codes,
because they are, you're just happy to

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00:31:16,110 --> 00:31:22,290
have treated so much in order to get out
result. But this is not necessarily

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00:31:22,320 --> 00:31:28,470
reproducible by somebody else using the
same code. Really, the way to go is the

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00:31:28,470 --> 00:31:33,270
way to go is through the scripts that
you're basically for each given

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00:31:33,270 --> 00:31:38,520
measurement you are tabulating. So you're
making the large investment of CPU time

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00:31:38,520 --> 00:31:45,510
once for once per measurement once per set
of fiducial cuts. And once this is done,

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00:31:45,990 --> 00:31:51,090
it is it is good, efficient functions that
are reasonably easy to use.

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00:31:52,170 --> 00:31:55,770
Thank you. Thank you for raising this
important point in a very comprehensive

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00:31:56,310 --> 00:32:03,030
answer. I think our time is very title And
since I don't see any other