No. Yeah, we hear you, sir audio. Okay, excellent. Good. Okay, well, thank you
very much for inviting me all the way to Paris, the trip was a lot easier than I
anticipated. I've crammed quite a lot in here. So we'll go with something of speed.
I do have a meeting setup at the end to discuss in more detail with anyone who has
questions. You know, as theorists, we can talk forever. So feel free to come with
detailed questions, I'll be happy to discuss them. This first half of the talk
follows the title that was given, which is a bit before the column and also follows
this article here, which is a little bit aged, but such as life sometimes just a
little bit on where we're coming from and why we're going to use effective field
theory to parameterize what we should expect from any new physics. And this is
the exact same thing we did when we talked about Fermi's for fermion interaction for
weak decay. We actually still use even that effective theory today, it's really
good for capturing physics in a particular energy regime where you're talking about
processes at a much lower energy than the mass scale of the new physics. In this
case, energy over and w is counting that you do. And the key point is that you need
to be able to systematically improve your theory predictions, at least in principle,
in order for the FT to be useful. The goal is to give you a new expansion that allows
you to control your calculations in a new way that you couldn't do in the full UV
theory. So when you apply these tools to the standard model, you get a nice long
list of operators, which I'm sure any expert has already seen, but I'll let you
stare at them for a little bit just to get nervous if nothing else, and then
furthermore, I'll move on to the next slide full of more operators to be nervous
about. And in principle, what we would really like to do in this model is the
standard model EFT is to construct The coefficients of all of these operators,
these are all the operators at dimension six. And if we knew where we have to land
in coupling space at dimension six, we could then have whatever region it is map
that into every UV level of interest, and get constraints on UV models for
relatively zero work. That would be awfully nice. Now, why am I going to start
by telling you about loops of things? Well, it's because we go and make all
these electroweak measurements we've been hearing about for the rest of the session
with just ridiculous exquisite precision.
So this is just left data here.
And all these measurements are ridiculous. And we're working to improve on these in
various ways. I like this one step on all of the right hand column, our to loop
calculations in the standard model, because that's the level of calculation
you you need in order to really actually test the standard model with data this
precise If you did a tree level fit to the experimental boundary, you would conclude
this general model is unquestionably wrong. But we know that's not the case. It
turns out those loop corrections are really important to understand what the
theory is telling you. And the same thing is true. If you predict new physics
contributions to anything precisely measured like this, you need to make sure
that your theory prediction is as accurate as the boundary you're trying to enforce.
Otherwise, you're going to come to the wrong conclusions. So what is the theory
later on our tree level EFT effects? Well, if we imagine that we have a loop that
looks like a 1% defect. And actually, we have an additional source of 1% defects
here as well, from extensions in the Higgs back over the new physics scale, and that
if we're lucky, and there's new physics that we actually have a chance of finding
evidence of at some point is order 1% as well. The numerical coefficients that show
up in front of these two things are not known a priori. The sum after
normalization has been done now has been rejected multiple different ways. You
could do RG improvement to capture the the leading log effect. If we have sort of Lh
C scale or just trans Elysee scale in physics, running from here to here, stops
being as impressive as an effect as it is and say supersymmetry, where the upper
here is almost a POC scale. When we're running just from here's where the new
physics is, and now we're in the FT we're going one or one and a half or two decades
in energy to get down to the electroweak scale, those laws stop being as huge as
they normally are. And purifying that effects can be comparable. So we really
need the full loop result. If we want to say that we have things at the level of
accuracy that we're used to thinking about. Now I'm going to present your
results that happen in a particular limit where I've only turned on two couplings
that UCD coupling compares. But that's a lot of work. These two are easy. So that's
what we decided to do. It turns out that doing anything with higher order gauge
corrections in the presence of these dimensions, six operators gives you
additional subtleties in fixing and doing your age fixing and your calculation
becomes a lot more painful need to be extra careful. Here, if you don't allow
additional gauge couplings, then your gauge independence is a trivial statement.
This is a decent first step toward a full analog treatment to the problem. And what
I'm looking at here in particular is z production. Okay, so z goes on couplings.
Now, from all those operators, you can identify classes that end up contributing
at this order. You're going to find that all of them have tops internal to the loop
or Hicks's internal to the loop. And that's because it's only tough Because in
The Hague self coupling that we've turned on, there's nothing deep about that. So
for fermion operators that include the top will give us corrections to those on
couplings to other types of fermions scalar thermionic. Current operators do
two things. One, they change at the simple tree level from the insertion of Higgs
Bez, the Z coupling to fermions. And they also give rise to new interactions that
include both a scalar and a fermion current. Both of these effects are
important to get our one loop calculation and cdks, right. And you also get effects
from mixings that sort of correct your Weinberg in your weak mixing angle. So one
thing that can happen is you can have an operator that talks to W and B and mixes
them together with the Higgs loop, or anything of dipoles. They give you access
To a mixing of W and D again.
One other place where you might not think you need to worry so much is in
calculating all of your input parameters. It turns out, this actually becomes a
pretty subtle problem already a tree level in the Standard Model EFT. And it only
gets worse at loop level, you need to choose what inputs you're using to define
your theory parameters. So for instance, when I talk about the top Yukon, or the
Higgs valve, those are theory parameters, we have not measured those things.
Instead, we've measured things like the top mass, or the Higgs mass, or G Fermi is
actually where we get the Higgs bed from generically. And if you want to measure g
for me, but the Standard Model EFT is turned on, it's possible that what you
thought was the Higgs there is some combination of the Higgs verb and the new
Wilson coefficient. So you need to work hard to extract That would be standard
model Hicks from the new EFT contribution. And once you start calculating at one
loop, you need to do that mapping that one little border as well. So there's a
certain amount of work that goes into this. We treated all of our listening
coefficients as though they were input parameters as well, to try to get a hold
of something where we could start making predictions. And when you run all of these
calculations through and you have three different people do them and you all argue
about who's wrong until you decide everyone was wrong. And here's the right
answer. and convince yourself that you have it right, you get results that look
like this. Now, this is meant mostly to be a scare slide. These are all the different
contributions to the left on cars, rb. Okay, there's a massive quantity of them
is the point that first line, the easy ish looking line, that's the three level and
the other two equations have to be something to do. together to give you a
group level vfg contribution to delta delta RCP. Now, why am I showing you this?
Well, at the end of the day, you don't need to know all these coefficients to get
the main point. The main point I'm trying to make to you is count the number of
listen coefficients that you need. Our analog corrections have introduced
dependence on a whole spate of operators. And at this level of precision, we can
measure only five or six if you want to turn on a forward backward. I still worry
a little bit about getting getting things kicked around. But I've been told by
experts including irises here, that I should be able to turn that on and not
worry too much. So the moral of the story there is obviously I can't constrain all
those rules and coefficients with that small number of observables. In fact, at
tree level, there already were flat directions in the Z polar observables. And
we were able to constrain those albeit very weakly With the left triple gauge
coupling measurements with this increase in the number of parameters, all of our
electroweak precision data is not enough to constrain the EFT to live in some
closed region of the relevant parameter space, there will always be directions
that you could travel arbitrarily far and not in any way affect these observables.
So the lesson here is that once you get to precisions, where you think loops matter,
which from those Numerix that I showed you is really sort of an order 10% correction
to the naive tree level prediction, then you can't constrain things stronger than
that by electronic precision data alone. So you should never be imagining from your
precision measurements, that you have something that you could effectively turn
off because of the vision that it lifts. That can't be an issue. While they did not
measure one listen coefficient for separately, that's not possible
generically, in EFT. So we cannot turn off different operators. And they're going to
give us different effects that led them they did it left. So there'll be separable
there, we hope. This is one example of potential theory errors. Having calculated
a one loop correction to something that we had done at tree level, it gives us a
handle on how big our theory errors were at tree level.
And just to give a little motivation, about theory errors more generally, we
oftentimes don't care very much about uncertainties in our signals, at least I
don't because I was trained as a VSM phenomenologist. So we tend to turn on the
arm physics model and say, Oh, yes, I know exactly what this new physics will do. It
will give me a bump over there and that distribution, you guys should go and look
for it. And the basic idea behind that was that we can go back and clean things up in
our VSM theory, once you found the particle, then we can start saying, Oh,
well, that bump was actually off from where I thought it would be five, five gv.
And I can explain that at one or two loop order, that's fine. But if you're in the
business of precision measurements, which is where we find ourselves now, in this
electroweak seminar, but also in the life, the life cycle of the LFC, generally, I
would say, we're now in the business of making precision standard level
measurements to a large extent and trying to find small deviations there. ignoring
your errors is never a good idea, even if their signal errors. And here's the basic
motivation for why we should not do that. Just because historically. Sorry, you say
five minute warning. Okay. Historically, it's been the case that when we do EFT
analyses, if you do them ignoring these errors, Then model builders like Bhaskar
here, who I use as a guinea pig, I really like that start. This is a very honest
statement from him about the history of DFT analyses, he can build a model that
violates the bounds that I have without violating the data I got the bound from is
the claim of Unix. And this is generically true. So we need to fight back against
that somehow. So for this little bit of the talk, I want to pick based on these
two articles, that 226 used to tell the plus or minus one but now I've become more
confident, so I took the robot off. So how do we go about building a collider search?
We try to run things through Monte Carlo tools and constrain what comes out. There
are nice tools for this in standard model, EFT, there's a package that you can plug
in directly into Minecraft and get out your results. The greatest challenge to
these searches is the concern about whether the DFT is actually consistent Or
not. The way to make sure that you are using the FT honestly is to actually
estimate your errors in that new perturbation series though. Ensuring that
this thing is consistent means making a sample of what's going on at the next
order in your perturbation series. And if that's bigger than your signal, which is a
first order, then you know you have a problem. So I'll look at this in the
context of leptons in particular, there are two types of energy contributions to
the electrons from the Standard Model DFT. There are direct for fermion operators,
they give you amplitudes that grow with energy, which is what we're used to
thinking about, but you can actually also shift the z components like I was talking
about earlier. We do a forward backward separation. Everyone here is super
familiar with this, you define forward as more forward in either direction. And you
have here the linear combinations of Wilson coefficients that give you x Tree
level forward and backward contributions of two different types either energy
growing at the top of the slide, or shifts in the Z couplings and proportional
external rates at the bottom of the slide. The way to deal with your uncertainties
from the EFT expansion is to be honest about estimating your theory errors. We
have completely unknown effects from dimension eight operators in the Standard
Model EFT they are in order one overland to the fourth, and our signal function is
at order one over lambda squared. Now, if we want to estimate something and order
one are willing to force that we don't really know we can take something we do
know in order to one overlain before and yes, or just hope that that's a decent
approximation to what happens generically in order whatever line before, so I
calculate the cross section from dimension six squared, which is something that we
get for free inside Smith sim For inside really any Monte Carlo that's doing
Standard Model DFT. And I change its leading coefficient to lock myself up the
effect not only of the dimension six squared piece, but also have some number
of dimension eight operators interfering with the Standard Model amplitude here.
We D correlate this between the bins of our analysis because we don't want to
assume that I mentioned six squared describes the exact shape just gives us
the overall normalization. And we insist that our dimension a Wilson coefficient is
at least the order one, or C six, whichever is larger. And then we sub that
in quadrature, with our other error sources, and doing that we can mock up
expectations of how far we should be able to get. So these three curves, blue,
orange, and green are showing us 100 303,000 inverse femto bonds of data
and what we can learn There are four directions in this parameter space that
are interesting. We can with a large amount of data close an ellipse in this
pure forward and backward, which is to say energy growing contributions to forward
and backward distributions. The tight constraint in this space is the total
cross section direction which is almost horizontal but not quite backward, it
turns out as weaker than forward from this left. And perpendicular to that here is
the forward backward asymmetry direction. Here you get some more interesting stuff
with shifts, it turns out they're still a direction you can run forever, your
forward and backward asymmetry is more or less this way. And you can see out here
that at some point when you turn your Wilson coefficients up way too high, and
this is comically high for a listen coefficient must be said. You lose your
constraint again, because your theory and errors become so large that you can't
meaningfully constrain this distribution. There's two other slices you can Easily
taking the space as well. Both of the forward directions, both of the backward
directions energy growing and shrinking perspective. So this is the kind of thing
you can do if you're taking your EFT seriously. And the nice thing is that
these bounds once you've included that theory, or should actually hold for UV
models, which is to say they should be useful to someone, our previous sort of
EFT bounds gave us nice things that we could constrain colliders. But ultimately,
those constraints simply weren't interesting to what should be our biggest
consumers, which is the model builders, who should be able to take our precision
measurements and say, Do these constrain my model or not in a relatively
straightforward way without having to do a complete recast of the analysis. So the
moral of the story is that with all of the excellent data that we have available, and
all of the much, much more that we're going to make, we really need to respect
That data and do our new physics predictions with as much precision as we
can. The z poll data cannot close all of the parameters that enter it at one loop
order that this is a completely unavoidable consequence of field theory.
So, we need to go beyond that we need to use a total real global analysis to
properly constrain the Standard Model EFT without making up assumptions. developing
more observables that can be consistently constrained in this way is a important
future path here digests and die leptons are basically done other directions are
being worked on but there's an awful lot to do this technology to to do these
errors is 100% mad graph a minimal so this could be picked up and done in house by
experiments and actually it should, for one important reason. If you take a look
at the digest stuff in this in the backup there information, you'll find that that
analysis actually draws its constraining power from a very different region of
phase space than you guess if you don't include theory errors. So I would
recommend checking that out. It really changes your search design significantly
once you include these theory errors, this is not just a trivial rescaling of your
bound.
The basic takeaway message from this talk should be that setting shifts in
electroweak observables to zero or even worse setting operators that shift
electroweak observables to zero for the purpose of further searches, breaks model
independence, it does not give you real results. Neglecting theory errors in these
EFT interpretations gets they're ignored by model builders who really are meant to
be the customers for this. So we must stop ignoring those theory errors. We need to
make results that they cannot evade by using an honest theory error estimate. We
need to then produce a sales pitch to them that says, Look, this actually is better.
And we need to push back against any Cavalier claims that new models can always
be built that vft results once we are taking our error seriously. We need to go
out there and say no, that's what it used to be true. I understand where you're
coming from. But we have fixed that problem in our EFT now actually tells us
something useful about whether your model is there or not. In short, we need to make
sure that best our ends up being wrong about this in our new EFT interpretations,
because otherwise, the CFT interpretations simply are not very useful. Thank you very
much for your attention, and I hope you'll come and visit with me in the coffee
break.
Thanks a lot for the really illuminating talk.
Can I ask people to raise hands if they have questions?
Si RS has a question to go ahead.
Yeah. Thanks. Could you walk me once more through the plots you show that the end so
so with the different colored curves? How do I see the theory hours here?
So one place where you can feel the theory errors, they're not explicitly present in
these plots, because these are just constrained plots, but you can feel them
happening at very large Wilson coefficients. So this between these two
green curves, for instance, is a region that we will be able to constrain at large
luminosity that's our 3% of our constraint. So zeros you're not
constrained because the standard model is what we assumed as our signal. Sure, but
very large Wilson coefficients also are not constrained because the theory error
has started to grow quadratically in
that Wilson coefficient Oh, sure. I mean, I understand it extremely Legion, but for
for the Legion dead descended on zero. Do you have any plots where you can compare
the curves, whether you include those dimension athili, Atlas or not.
So on this curve, you can see the effect of the theory errors very clearly in the
in the non three inverse data markers. We don't actually have a plot where I have
ignored them. But you never get a behavior like this where your urbane actually
grows, as you get further away from the standard model. If you don't include a
theory, you will get a normal ellipse and it will just be bigger. And so why does
this Why me when theory error, because eventually we do actually managed to get
enough in a symmetry there. This is actually still not an ellipse that has
some whitening behavior out here. This is not a perfect ellipse that you would get
from just a linear fit. But we ultimately get enough statistics that we can use the
forward backward symmetry to close that to some extent, if I assumed this plot
layout, there's also an opening of green down here again, Just like you see here at
extreme regions. Thanks.
Are there any further questions?
If not, I propose that we thank William again. And we can also thank all of our
speakers. And again, I realized that with the current setup, I can't ask everyone to
unmute and give a round of applause. But I'm sure that everyone is extremely
grateful for the fantastic talks we've heard today from all our speakers. So
thank you very much.
Sure, I speak for the other speakers as well. When I say please do join the zoom
rooms we made. If you have any more detailed questions that you'd like to
spend time on. We'll be happy to discuss them.
Yes, please, please do
join in chat during the coffee
break. And I'll just note that our next Parallel session meeting is on Wednesday.
So we look forward to