We started directly with nobody with the radical review of precision TriCity. Thank
you for giving this talk amasa is on to you. Okay, thank you for the for the nice
introduction. And thanks to the organizers for inviting me for this conference.
Although, I guess I'm expressing the feeling of almost all of the participants
by saying that initially, I was looking forward to a nice week in Paris with
interesting physics, but also be in a very nice city. Now, we still have interesting
physics, perhaps even even more interesting because we really have to
focus and what I think we all have seen so far of this conference is a real success,
which proves that even online we can make our community very, very lively and have
nice Discussions Now, with this, let me delve into precision physics precision
UCD. And I think this audience don't really need to need to motivate why we are
doing precision physics. It's all about on the one hand, testing the Standard Model
finding tiny cracks in the standard model, but also extracting, extracting the most
out for data in terms of fundamental physics parameters in terms of fundamental
information. And at the same time also, using QC D, not only not only to make the
bridge between theory predictions and experimental data, but really as an
analysis tool for inference in data driven background predictions are with new
developments like substructure techniques. So they Huge motivation really to do
precision physics. And much of this motivation is summarized in this in this
cartoon, which shows the an overview on all the star model cross section
measurements that have been performed at the nhc. Now, here, it's a CMS plot. Other
places, it will also be Atlas plots, I try to be more or less, more or less unbiased
towards one or the other experiment. And what we see here and what we will be
focusing on in this talk is especially the entries that are kind of on the upper end
of the staircase, which are, which are those processes that have a relatively low
multiplicity, but at the same time, a quite large, quite large cross section.
And it's in there that we are really striving for the highest level of
precision. Now, state of the art precisely dictions whenever you talk about precise
making precise predictions, you have to talk about using perturbation theory,
making a perturbation serious expansion and go to as high as high order as you
can, given, given your resources and technical capabilities and the current
state of the art the current theory default and this is already a major step
as compared to previous generations of experiments is that we now have a variety
of automated tools at our disposal that not only do leading order but also next to
leading order predictions including next to leading order effects both in Houston V
and the electric theory and this has been made possible to a large extent by an
engineering type of approach that people started 10 years ago to define standard
interfaces between between programs. Such that one could combine infrastructure from
multiple apps event generator programs with one amplitude calculations and really
have an automated tools that that do all these calculations to next to the order
fairly often also combined with pattern showers, which then allow you to get full
event properties at next to leading or accuracy on differential cross sections on
fiducial perception. So whenever we're talking about comparisons with
experimental data, although this does not show, kind of in the in the tiny dots
here, all these are cross sections that are defined for a certain set of fiducial
cuts, so rapidity, acceptances, transfers, momentum acceptances, and so on. You want
to mirror these at the level of your theoretical calculations as well as you
can. Now it's next to leading order We are reaching a level of accuracy that
typically goes in the range of 10 to 15, sometimes 20% residual us concerned from
missing high orders and for many of these, the error bars especially at the higher
multiplicities are still large enough that you can that you can live with a theory of
uncertainty at the level of 10 to 15%. However, for benchmark cross action so
much with the process this is not enough and this has motivated quite a fraction of
the community to embark on to next to next to building our calculations of first of
all more inclusive process like eggs and vegetables on production. And then and
then my differential process a lot of the revenue today two reactions are now
computed to next to next to living our currency and in the community. We say I
have I think a healthy competition between different groups also between different
techniques, I mean calculations all these calculations require quite sophisticated,
sophisticated methodology to combine all the ingredients you have really ideation,
your virtual corrections, all this you want to come by I want to combine really
on a face to face this point basis which requires sophisticated subtraction
techniques to handle infrared singularities and this there's been quite
a number of techniques that have been developed over the years first and
pioneering was appeared in America techniques sector become position, which
was then later accompanied by Qt subtraction sector and proof methods and
antenna subtraction in reading and subtraction projection to one method, all
these methods, they pursued the same aim. However, they all use completely different
company different approaches, completely different technologies. And what you see
here is that quite a number of the process have been covered not with one method, but
with two methods, sometimes, even with three methods and they're cross comparison
between between the different codes is, has proven to be crucial, really to all of
the groups to iron out, to iron out bugs, to iron out approximations, and to get
better physics predictions wrote out to the communities now, enough these
calculations is a walk in the park neither in terms of performing the calculation of
implementing it, nor actually running it runtimes for many of these calculations,
amount to hundreds of thousands of CPU hours to get distributions for one set of
additional cuts out so this very quickly gets very expensive and also most of these
codes are still proper it to the office since they have so many whistles and
tweaks that only few people are actually using them safely. Up to now public codes
have been made available only for closing that process. And the two main players on
the market there are MCF M and matrix. And so any of these calculations here would by
itself warrant a warrant a large plenary talk to really explain all the details is
not what I'm going to do. But instead, I will focus on kind of the simplest process
you can think about, which is the Dre intersection and there make the case for
why we need all these ionic calculations to really get the most physics out of out
of this measurement and crayon is very simple. It's a lot simpler. It's a lot
simpler than many of the process that we just had. In the list of accomplished next
next to the tomato calculations, it's definitely a lot simpler and Tiki Bar lots
of gadgets. Still it contains a lot of the lot of the physics a lot of information
that you really draw from the higher order corrections. Now, first of all, for the
dragon itself was one of the very first precision observatories or the hadron
colliders. Stan what a theory is very well understood we have next to the model
electroweak we have next to next leading order QED the total cross sections so
without any cuts is even understood two to one or higher and for transfers momentum
distributions, we even have three summation to highlight words we got. Now
all these calculations they went into precision tools, which brought us also by
experimental this most of these codes are available to a to a larger public. Now,
what we are going to look at is the triple differential rayon cross section. Triple
differential means differential in the mass of the dialect on payers who are not
focusing us on the Z resonance, but where differential in the in the rapidity of the
electron pair and in the in the leptons scattering angle in the in the center of
mass French it's really to to process proton proton going to die electrons plus
anything and then of course, you can, you can go to a to a specific frame and then
look into the scattering angle and also into the inclination between the left hand
plane and on prey plane in the collider framework. And there we are now focusing
on the Atlas measurement which has, which has measured this in a huge number of bins
in total.
And 650 bins in different ranges in these variables what they are distinguishing is
central Central. So both leptons seen centrally and central father, one electron
in central region, one leptons morphometry. And this already kind of
trouble starts because what's measured is not the inclusive cross sections
differential in these bins, but it is fiducial cross sections with fiducial
events, election cuts, and those are in contrast to these cuts here, which are all
cuts on the left on pairs. These are cuts on individual laptops, so minimum
requirements on individual laptops and these fiducial cuts. They influence the
acceptances in triple differential bids. And in order to see this, let us look here
just at the leading otter kinematics. So even order is true and they are all the
different bins in a fixed slice of invariant mods. They are they are outlined
here for the central Central and central arbitrating. So, we are in dialect or
ability and in scattering Angular and what we see here is that this region is fully
allowed or a leading order, then you have here in red this cat which delimits the
end of the meeting on a face face. So, a lot of the bins where this is crossing
addressed, addressed cut in half by the leading American Medical restrictions, and
then out here out here we have leading order forbidden bits gets even more
complicated in central arbitration because there you treat two lectins differently
and you actually only have one single beam out all the central fava beans, which is
fully allowed most of them are actually allowed one corner is completely
forbidden. Now at leading order forbidden Of course it as soon as You allow for your
triangle to recall again some extra radiation, it gets a finer transverse
momentum. And this immediately implies that you ease these restrictions so what's
leading on a forbidden is no longer forbidden when you allow the dielectric
required because then your relationship between single electron transfers momenta
and the electron kinematics they are east and for symmetric leptons here, you can
translate this in the same plots into minimal transfers more into that you need
to have in order to attain a certain region, you see that this very quickly
goes up to macroscopic values. So here it's up to you need sometimes to go up to
50 gV of pair transverse momentum here in the central format, it's sometimes even
goes up to TV also and this then turns insights on bins into transfers momentum,
this Now, transverse momentum was not part of our triple differential variables here,
but somehow we get it transfers momentum depends in to our calculation from the
interplay of fiducial cuts and differential variables and this then in
the end translates into an acceptance for individual wins and you see some of the
bins, especially in central Central, central central in the in the region have
a large scattering hangers. So, where you basically scatter at 90 degrees, they have
full acceptance. So all the events that are that are clustered on all the events
that would be their inclusive cross sectional as usual cuts but some of the
other bits especially at low scattering angle, have very, very low acceptances And
here, we are computing this next And excluding Ireland QC, but next to next to
leading order in the photogram process. So, this is auto fair square. And this
means that if we want to have a final transfers momentum, we are already losing
one perturbative order and this is reflected here in this theory to data
ratios. We see especially in the forbidden bins in red, that there's fairly poor
agreement with data and large fury uncertainties. And this is where auto
calculations come in not forbidden vintage leading order they require minimal
transverse momentum. So, they have very similar kinematics to transduce momentum
or faster distribution of electron pairs. And for these ones, the orifice cube
correction which would amount to dread Eon and cube Hello can be obtained from a
vegetables and plus jet calculation and next to next to the offer and there's
quite a few of this on the market. So, what you then do is to replace the jet
requirement by a small transfers momentum cut and this depends on the bin which you
are sitting in. And then you can correct these forbidden bins to one order one
order higher. Now you need to make sure that your coach still on safely and that
is by actually comparing his predictions to risk summation. And after you've
convinced yourself that your code is doing what he expected to do, you can actually
include one other high in the forbidden bins. What you also need to include the
next two leading electric corrections and these two features taped together they
considerably improve the care uncertainty I mean, all these large uncertainties
which you saw in red, they're basically all gone much more moderated out of these.
We see You're much better agreement with data and what can also be done is to
construct derived quantities like Angular coefficients of our packet symmetries in
this data set to aim free from the trip of differential measurements for measurement
of the mixing. Now, this was much of an excursion which was more sought to
illustrate to you the power of these higher order calculations. And in the
precision to city, we have several directions and challenges. One of them is
to go to higher multiplicity so beyond two to two so far, the only genuine two three
process is three photon production that is known next next to leading order and their
limiting factors are multiple its virtual amplitudes that are lacking methods for
handling infrared similarities that become unpractical and we will see kind of recent
progress has been made. has been made in this field. And also you would like to
come to similar level of sophistication as was attained at next to leading order,
namely matching to pattern showers matching to the summation. And for some of
these reactions, like fixed cross sections are very cross section read to get to full
mq below prediction in order to really come to present level occurs. And let's
see where we stand in these directions. And one of the most active areas for in
recent times has been computation of loop amplitudes. Now one loop amplitudes, you
can compute them for arbitrary process. They are inside your automated tools,
mighty loop amplitudes. And even more so much integrals are only known for special
cases. And there's two main types of techniques. One is using differential
equations for these integrals. And either two In order to reconstruct the analytic
structure of the integrals potentially then solving them numerically numerically,
so solving these differential equations numerically in order to get okay
integrals, or a purely numerical technique sector decomposition, which is divide and
conquer approach on the face of low momentum. And very often most of the
research results were obtained with a mixture of analytical and numerical
techniques and they're for master's propagators. We kind of are now in at a
level that we that we have many of irrelevant two to three integrals. And
then as soon as you go up with number of loops, the number of legs on the integrals
goes down and current limits are at three to level 20 grants are known and followed
level four Factor vertex integrals are known. So, one to one or one to two
integrals and there is a long list of people that have recently contributed to
this. And I'm pretty sure I even have forgotten forgotten some of the main
contributions. Now, this is all for masters propagates into his master's
propagates, we understand a lot of the analytical structure. So, we kind of know
fairly often what function space we should, we should find our answers and
with massive propagators this is far from being the case. So, there actually we have
results only at a kind of lower low, lower low and leg level. And, again, their risk
a lot has been obtained, combining analytical and numerical techniques. And
of course, once you have the integrals, you still don't have the amplitudes
because what you need is to Determine the integral coefficients. So, with what
multiplicity integral appears in, appears in give low amplitude. So, this reduction
to master integrals, this has been in the past performed
performed purely symbolically and the spiritual techniques they are also
hitting, hitting their limits in terms of size and complexity and a very, very
important development in the present taking off in the past two to three years
or so called finite fields reconstruction. So, you evaluate such multi loop
amplitudes a large number of times hundreds of thousands of times for
kinematics variables set to set to different prime now, and then over this
large finite field of prime numbers, you you get numerically variations in terms of
rationale Rational coefficients and then out of knowing these hundreds of thousands
of variations, you can actually then reconstruct the full radical form of these
of these integral coefficients. And a lot a lot of the research results for
instance, in fact, pattern process of vegetables before patterns, they have been
thriving really on these on these finite field reconstruction methods, a point
where mighty amplitudes changing might play a key role is whenever you have
processes that are forbidden at Bond level and the emblematic example for this is the
top Quark top loop contribution to Higgs production there in directs production and
his project production actually have four point functions for to four point
functions with massive propagators. Already at the next two leading artists
You're leading order one level process is at one. Now for all these, all these
amplitudes. The main here you do have results that are evaluated for 1.2 phase
space. However, if you want to evaluate them multiple times, it's very quickly
becomes extremely challenging in terms of stability and CBOT some lots of room for
improvement. This is not only not only not the only bottleneck the second bottleneck
if we want to go to higher multiplicities is another issue with the matrix elements
namely next to next to leading order. We also have one new type contributions that
are evaluated in unresolved limits you will have next next leading order. You
have one new matrix elements were one of the patterns get soft or collinear because
you have one order that you eat up in the loop and another order that you stay left
free for reader ideation. And there, especially the auto generate amplitudes
are not really made for being used in these areas of limits. So fairly often,
there's quite a bit of work still to be done to make them work where you would
like to work. And then the next step is the whole set of real radiation
contributions also, real radiation is a tree level and they are all the methods
that have been using various that we have been using successfully so far. They scale
very, very poorly with much bliss in terms of complexity, in terms of computation
efficiency, and failing often as soon as you go to too high level of multiplicity,
you discover that you still need some new ingredients because not everything is
available. And they are what people have been doing is either pragmatic approaches
or more more clever ideas in search for generic methods oh so much about fixed
order next next to leading order at high multiplicities. We would also like to
there have been too sorry, you hear me?
I'm warning because the time is over right okay.
Then give me one minute I did not get your three minute warning sorry,
thank you
okay. So, combination was pattern showers, this is now advancing to higher
multiplicity also matching on to matching onto re summation. Matching on to literary
summation is really taking, thinking advances now and we have seen Higgs boson
and dialect compare transfers momentum distributions, where you see that the
summation is actually needed to to match data especially at low transports. Mental
or at low opening angles now, as a last point, ultimate precision in Cuba okay
collations we have them for quite a few process in terms of inclusive coefficient
functions. And most recent developments are aiming to extend these calculations to
differential observers really to fiducial cross sections and their projection to
bond method and Qt subtraction have both been pioneered until you see an
application to a simpler process than what you have at the LFC stret production deep
elastic scattering where by now one can actually from knowing inclusive
coefficient functions and combining this with a projection to bond method bring the
theoretical level of the of the calculation to encompass all which really
comes down to percent level. The curious now time is over. So I just flashed this
Where do we need to go? I think I covered the motivations and illustrate to you what
recent advances have been made. Thank you very much.
Thank you very much for this very comprehensive talk. We have a few minutes
for questions and I see one.
Joy.
Can you hear me? Yes. Okay. Thanks for the very nice talk. Thomas. I had a comment
and a question. First, the comment. As you know, that when you're doing next to next
quarter calculations involving jets, oftentimes you can end up with scale
uncertainties that are artificially low for smaller jets with are being 0.4. So
just just for people who are doing comparisons, a copy That you have to take
that into account, you know, for something like z plus jet or inclusive jet
production for Oracle 0.4. The uncertainty that you get from the calculation might be
a factor of two less than what a more realistic estimate of the uncertainty
might be. And again, that's just due to some accidental cancellations that take
place. And then my question is regarding the dissemination of the results, as you
said, it takes an incredible number of CPU hours to to run the predictions and the
programs are so complex that it's very difficult to hand it off to you know, any
users even if they had the available CPU hours. There are programs such as you
know, fast and anello or Apple grid, to try to disseminate these results but they
seem to have you know, also A great deal of complexity as far as you know,
providing finished products. So, do you see key factors just being the optimal way
of transmitting these results for the foreseeable future? Or do you think there
will be a breakthrough in something like fast in a lower Apple grant
I mean for the dissemination of the results in a form that you are able to use
say in parameter extractions say PDF fits or as measurements are so, they are the
way to go is really is really through things like Apple grit, and together with
with people from from Apple grit and fast and oh, we have started we have started
the generation of grids for for various types of process. At next an extra leading
order and pay The the the infrastructure front end to the user can be made
sufficiently simple that actually you can aim for a info broad usage, we are still
envisaging public releases of the of the codes, but you formulate it very nice if
these codes are complex. I think the main issue is that these codes are quite
fragile and fairly easily by changing a few of the settings or just putting in new
types of fiducial cuts you may actually end up very quickly into generating
nonsense nonsense predictions. So, therefore, therefore, most of the authors
have been have been still holding back. I mean I can see on a reasonable timeline
that we will see we will see Public code releases, at least for the lower
multiplicity benchmark process, the cutting edge will always be, we will
always be propriety proprietary codes, because they are, you're just happy to
have treated so much in order to get out result. But this is not necessarily
reproducible by somebody else using the same code. Really, the way to go is the
way to go is through the scripts that you're basically for each given
measurement you are tabulating. So you're making the large investment of CPU time
once for once per measurement once per set of fiducial cuts. And once this is done,
it is it is good, efficient functions that are reasonably easy to use.
Thank you. Thank you for raising this important point in a very comprehensive
answer. I think our time is very title And since I don't see any other