Analysis Overview

Motivation

In top-quark physics, nowadays, almost all precision measurements are limited by theoretical, systematic and modelling uncertainties. In addition, the interpretation of ttbar data with modern pQCD predictions is also limited by theoretical uncertainties; some of them are even inherent to the data. This is because ttbar data is not accurate to NNLO accuracy, since some contributions have been removed from the data in an uncontrolled way. Also, top-quark pair cross section measurements are of overall moderate quality only, since those have commonly very low acceptance (~10%) or suffer from 'combinatorial' background, which is terrible, or have large QCD background, or two neutrinos.

The lepton+jets final state tries to improve on all of that by measuring the actual final state of events including top-quarks.
  pp -> (tt ->) WWbb -> lvbbqq 
Infact, when measuring pp -> WWbb not necessarily all diagrams must include a top-quark, and also top-quarks in these diagrams can become off-shell.

One theoretical limitation arises from the fact, that higher-order QCD diagrams alter the top-quark decay, lower-order tW diagrams contribute to the signal, and the top-quark can become off-shell.

Presently, many theoreticians work on NLO+PS Monte Carlo, which include a correct treatment of non-resonant mass effects.

The goal of the analysis is to measure cross sections for pp->WWbb production. Of course, in a later stage, one can do a lot of physics with it, like top-quark mass determinations, top-quark width, PDF fits, alpha_s fits, running top-quark studies etc....


The primary goal of the analysis?
I would say, this should be, first of all, a high-quality measurement of differential WWbb cross sections:
W-pT, b-pT, W-eta, b-eta, dR(b,b), dR(l,W), m_W[?]
Maybe double-differential?
This may look a bit shallow at the first view, but it is finally one of the most reasonable and comprehensive (and precise?) Standard Model measurements at the LHC.

The theory community once made a statement at the LHCTopWG-Meeting: "There are too few useful measurements in the top-quark sector". At the same time, the SM community complains that that all present ttbar-measurements exhibit some tensions when used, e.g., in PDF fits.
So, I believe, that WWbb will become a very useful measurement, both for SM and for top-quark physics. And although it appears to be simple, it is the first measurement of its kind and is highly sensitive to all SM parameters: m_top, Γ_t, alpha_s, gluon-PDFs (possibly even m_W). It is sensitive to higher-order QCD, higher-order EW, etc..., but it is free from awkward mismodelling effects, soft-QCD, resummation, interference, QED radiation, etc..., and at a very reasonable renormalization scale. Beautiful!

The sensitivity to interference effects is neat, but I would not give it high priority. Why? In WWbb we accurately measure the actual final state; at the same time the predictions are self-consistent. Why should someone try to fudge ttbar+Wt predictions together to describe these data if already more complete predictions are available? Why should someone subtract Wt-predictions from WWbb data to obtain ttbar data, if our accurate WWbb data themselves are available ?
Though, it is nice to have such studies, and it may be indeed useful for some modelling purposes, and further enhance the usability of our measurement, but I would not try to 'enhance' these effects.

Then, one can extend the measurement further:
+ Either extend the observables towards lvbbqq, where even more non-resonant effects are important, and where NLO-predictions are available.
+ Or combine W+b's. This gives obviously m_lb and m_top. Both observables measured at a time with correlations should provide maximum sensitivity to m_top, with small syst. uncertainties and low modelling uncertainties. Such, it targets to reduce the dominant uncertainties in m_top, but not by reducing these uncertainties, but by circumventing them. It also combines the advantages of di-lepton and l+jets in a single measurement, if done with care. We should see...

Analysis strategy

Lepton triggers
2015@e24_lhmedium_L1EM20VH_OR_e60_lhmedium_OR_e120_lhloose,mu20_iloose_L1MU15_OR_mu50
2016@e26_lhtight_nod0_ivarloose_OR_e60_lhmedium_nod0_OR_e140_lhloose_nod0,mu26_ivarmedium_OR_mu50
2017@e26_lhtight_nod0_ivarloose_OR_e60_lhmedium_nod0_OR_e140_lhloose_nod0,mu26_ivarmedium_OR_mu50
2018@e26_lhtight_nod0_ivarloose_OR_e60_lhmedium_nod0_OR_e140_lhloose_nod0,mu26_ivarmedium_OR_mu50

2015@e24_lhmedium_L1EM20VH_OR_e60_lhmedium_OR_e120_lhloose,mu20_iloose_L1MU15_OR_mu50
2016@e26_lhtight_nod0_ivarloose_OR_e60_lhmedium_nod0_OR_e140_lhloose_nod0,mu26_ivarmedium_OR_mu50
2017@e26_lhtight_nod0_ivarloose_OR_e60_lhmedium_nod0_OR_e140_lhloose_nod0,mu26_ivarmedium_OR_mu50
2018@e26_lhtight_nod0_ivarloose_OR_e60_lhmedium_nod0_OR_e140_lhloose_nod0,mu26_ivarmedium_OR_mu50')

The l+jets analysis is designed such, that one selects events with
  • 1 lepton
  • 1 MET
  • 1 b-jets (or better 2 or more)
  • 1 light jet (or better 2 or more)
Then, one has first large combinatorical background, large QCD background, and low acceptance.
But when then requiring:
  • lepton-pT > 60 GeV
  • MET > 60 MeV
  • b-jet > 60 MeV
then looking for two light jets that fulfill a certain pt--delta-r requirement and have a dijet mass similar to a w-boson, then one has > 80% acceptance. In such a topology, the correct W+b assignment is possible without ambiguity.

Our analysis builts upon Single-top ntuples
These are ~100TB of data, but calibrated and including all systematic uncertainties.

What needs to be done:
We develop a new (fast) code to make the event selection, apply cuts and do the histogramming. Also, we need some unfolding code (TUnfold). Then, the observables need to be defined, the analysis cuts optimised, unfolding, etc...

In later stages, we can incorporate also new NLO MC-generators, which are presently under development by theoreticians.

In later stages, one can do top-quark mass fits, etc...


From the point-of-view of the 'WWbb' analysis, I think, it is reasonable to have symmetric W-pT cuts, so the same for Wlep and Whad.

Because of the ljet.pT, lept.pT and MET cuts that are given by trigger, pile-up and resolution, there is very low acceptance for low W.pT. This is seen as the turn-over of the W.pt-spectra at lower pT.
For a high-quality analysis, the acceptance (with kinematic correlation) should be as large as possible.
Therefore, I think, we need a W.pT cut of at least 50GeV. More reasonable to me appear 70 GeV.
Possibly, we even have to have 100 or 120 GeV !?

a pT-cut of 50GeV sounds also very reasonable.
But, I was more thinking about the two decay products: at 50GeV, the two decay products will unlikely both exceed 25GeV such that they are within our 'pT'-acceptance. So, in this kinematic region large correction factors need to be taken from MC, which I would try to avoid as much as possible.
The other 'W': the efficiency for the reconstruction of the hadronic W is quite low at low-pT. 50GeV would be my dream as well, but likely we run into troubles there. Thus, I suggested to start with a bit higher cut, and once we understand more, we can go down. I hope, that this facilitates the analysis at this stage.

Therefore, I would propose to add a pre-selection of Wlep.pT>70 GeV from now on, and also to impose that cut on Whad.

Of course, you can come to other conclusions and select any different value between 60 and 100 GeV. Though, I would not go to much lower values

This has further the advantage, that the W-tagging becomes much more efficient.
And even further, also the dR(W,b) correlation becomes much cleaner, as you already have shown.

Whether or not to increase the bjet.pT cut needs to be studied/discussed. Maybe, one wants to choose the same pT as for the W's, maybe not...

Choice and cuts on variables

As expected: if one resticts the data to higher scales (higher W-pt), the W+jets background becomes more relevant than at lower scales. Infact, W+jets is more important than DR. Hence, if we would like to draw conclusions about 'interference' the W+jets should be made conisderably smaller than Wt.

From these plots we now see that W+jets is not an irreducible background, but has a distinct structure:
+ The Whad-mass has likely this second peak (probably we have to impose a cut on WHad.M anyhow...)
+ dR(b,b) is small for W+jets, since both b's likely originate from the same gluon and have a common boost
+ dM(b,b) is small for W+jet, since it comes from a massless gluon
+ dR(Whad,b) and dR(lept,b) are both large
I do not yet see a single variable that reduces W+jets with a considerable efficiency and backround/signal ratio.

There are different options:
+ keep the backgroud as it is, or cut on one of the present variables
+ combined several variables to enhance and then cut the background.
(like
R(b,b)<1.6 && R(l,b0)>2 && R(l,b1)>2 && M(b+b)<70) ...
+ Use an MVA

+ find more, and even better, observables.
like
- (b+b).pT / Wlep.pT ?
- R((b+b, l)
- R((b+b, Whad)
- ...
motivated by the fact that the 2-bjet system has a different origin in W+jet than in ttbar.

+ For good control, it would be good to define a 'background enhanced' control region and check if the backround normalisation is well-described. This can be done by defining the control-region 'ontop' of the present preselection (like adding R(b,b)<1.6 && M(b+b)<70 )
Or with a completely different pre-selection (like lept.pT, MET, 2(?)3 jets, (no-bjets?) only. Then plotting n-jet, jet-pt...
-> Possibly there are good examples in previous papers.

I think, I understand the reason for the two lines:
In W+jet one has three processes that produce b-jets:
+ the hard gluon (qq->W+g) decays into two b
+ a soft-gluon (qq-> W+g+g) decays into two b
+ b's from parton shower or hadronisation.

The second and third will likely not yield two high-pT b's, so the high-pT bjets originate from the recoiling gluon. (therefore, I have proposed to plot (b+b).pT/Wlet.pT), which causes the distinct blob at dR~pi.

Since W-pt is somewhat high, (b+b).pT is equally high and thus the two b's are boosted. They originate from a massless gluon and hence they are still 'collinear' after the gluon-decay. Consequently, the two bjets are close together (dR~0.4) and therefore dR to the Wlep is similar, but modulo 0.4--0.6 -> two lines with distance ~0.5?.

From your plot R(b,b) one sees, that W+jets have always R(b,b)<1.5, but mainly R~0.6

Since we need further 1-2 hard light-jets, the b+b are not exactly back-to-back to the W, and R(W,b+b) can be different. This causes the two lines.

So, one key to suppress the W+jets background is R(b,b).

Comparison to other analysis

In the top-sector, there are a number of related measurements. Of course pp->tt->l+jets. Others include associated production tt+Z, tt+gamma, tt+bb, tt+..., and of course the single-top measurements.
Have a look: Top Public Results.
If you select the 'glance' entry, you often find a comprehensive int-note and further details on the analysis.

The ttbar measurements are further divided into 'differential' and 'total' cross section measurements. The later measures only the total cross section.

Our measurement is indeed very (VERY) closely related to ttbar->l+jets. Some may even think, this is the same measurement, but that's not true.

They 'reconstruct' their event using by evaluating a combinatorial kinematic fit, the KLFitter. They assume, that all events arise from a resonant tt-bar process and the final state is lvbbjj. However:
  • there are non-resonant contributions
  • most events have low-pt decay products and the final state is not within the acceptance
  • there are interfernce contribtions from the NLO Wt-process.
You see it from fig. 4c of that publication. The efficiency is only 6-10 % !!
One could say, that 94% of what is published is not data, but just the MC simulation.
In addition (from other plots) these measurements have 'combinatorial' backgroudn that can be as large as 50%. So every second event is wrongly re-combined and such is a huge 'noise'. Furthermore, it is assumed that two top-quarks have been present resonantly, but this is quantum-mechanically not required.

We intend to improve on these aspects. Therefore, we cannot make use of a kinematic fit, but intend to reconstruct the final state products, b, b, W and another W one after the other.
The tricky part is then the hadronic W, which after decay and hadrionsiation may become 1,2 or 3 jets or is not within the acceptance. Importantly, we cannot assume for W-tagging, that the W arises from a resonant top, since we do not measure pp->tt->WWbb->l+jets but pp->WWbb->l+jets.

Therefore, we could not build upon ttbar analysis code, since it completely relies on 2 resonant tops, but that's not our intention.

Flavored Jets

  • TOP2021 Flavored jets in top physics and beyond (M. Czakon)
It emphasizes the need for correctly defined flavored jets in NNLO, explains the problem, and finally proposes a flovor anti-kt algorithm. The conclusion is:
"5.Experimental analyses: please unfold to the new algorithm"

from what I understand, these algorithms are mainly applicable at particle or parton-level. So, in our analysis, we could apply the default algorithms on detector-level, but then unfold to a particle-level using flavor-anti-kt-jets.
I suppose, that the change would be minimal for the cross sections in comparison to our ghost-matched anti-kt jets.

Another thing, since the flavor-matching is mainly important for fixed-order predictions, one can also define the hadronisation-corrections as the ratio of flavor-anti-kt-jets (at parton level) to ghost-matched-jets at particle level.

So, I think, one can find easy and practical solutions to make the theorists happy.

At some point, we will need to define the exact particle-level definition. For that, it might be useful to keep such considerations in mind. Also, we should do the definition in such a way, that it can be implemented in rivet, but as well from scratch by theoreticians.

Skimming idea

If we need small trees.
  • MET > 25 GeV
  • at least 1 lepton with pT > 25 GeV
  • Leading lepton IsTight
  • Lepton |Eta| < 2.5
Then
  • (MET+lepton).pT > 30 GeV (W-leptonic)
  • at least 1 bjet with pT > 25 GeV, dl1r >= 5 (4?)
  • at least two additional light jets with pT > 25 GeV
Then
  • drop all jets with pT<20 GeV

For truth, there are O(2000) 4-vectors, but only O(10) are useful.

Unfolding

unfolding always causes some debate.

There are several unfolding algorithms:
  • TUnfold
  • fully bayesian
  • d'Agostini
  • IDS (Malaescu)
  • SVD
  • Multi-/Omnifold
Good reviews are Refs 71-76 in arXiv:2112.01548 (physics.data-an).

I have a few slides, together with Stefan Schmitt. This tutorial includes a bit of code.

In the top-group (and ATLAS) most people are using the d'Agostini algorithm. The reason (may be), that it's simplest to use and implemented in RooUnfold which was written by ATLAS people from the UK. However, I've personally never seen a fully convincing application when using this algorithm. (it's not Bayesian, nor is the number of iterations a regularisation)

A colleague recently did a brief study and concluded: "I have tried RooUnfold in addition to TUnfold. I found that RooUnfoldBayes gives nonsense output if I use the default initial prior, which is to set it to the true distribution. It basically converges quickly to the true distribution and has tiny unfolding uncertainties for the bins with the worst resolution and the correlation matrix for those bins is all close to 1. If I instead initialize it to a flat prior and run it for MANY iterations (several thousand), it converges to the same output as TUnfold. "

I would therefore recommend to use TUnfold, which is a straight application of frequentists statistics and a long known algorithm. The author is also member of ATLAS and can help. In brief, it is an analytic linear least square fit using a LSQ pseudo-inverse that includes a regularization term. For the regularization, there are some algorithms that can directly be used. There are many advantages of that algorithm and it does the right job!

However, there is one caveat: since TUnfold is essentially a kind of a fit, one has to overconstrain the detector-level w.r.t. to the particle-level distribution. Therefore, one defines more (about 2x more) bins on detector-level. This often destroys the workflow of the analysis, since many codes cannot deal with different binnings at different levels. However, since in our analysis the binning was anyhow not yet fixed, this should not cause a problem.

If you want to be more sophisticated, then use Omnifold, which is the d'Agostini unfolding but unbinned and using a deep-neural network. It's doable as well and also Ben Nachman is in ATLAS and can help.

Hence, I would recommend the following steps:
Implement a single response matrix as a TH2D histogram, for a single observable into the function DoTruthRecoLevel().
Add in addition a particle-level and a reco-level histogram in that function.

Note!!! As a cross-check, implement the particle-level and reco-level histograms also in DoTruthLevel() and DoRecoLevel(), respectively. This is required for sanity.

I started once with a simple code, but got stuck...
What then needs to be done in a tiny code (could be a ROOT macro, a PyROOT macro, or a small program):
1) Read the TH2D and the four TH1Ds.
2) Confirm, that the sanity histos are equivalent to the nominal ones
3) confirm, that the projection of the matrix (TH2D::ProjectionX(), TH2D::ProjectionY()) are equivalent to the respective TH1Ds
4) instantiate TUnfoldSys (or TUnfoldDensity)
5) Set the matrix
6) Set the data
7) Get the result (DoLCurveScan())
8) Make a few plots...

A simple code to start with is tutorials/unfold/testUnfold1.c from the TUnfold package.

Timeline

Possible timetable for Charlie's contributions to the lepton+jets (and di-lepton) analysis

Oct/Nov/Dec 2020:
  • get familiar with analysis codes, and 'singe-top' ntuple format
  • setup analysis environment, copy ntuples to local cluster, etc...

Dec/Jan 21

  • validation of the ongoing di-lepton analysis cutflow
  • preparation of l+jet single-top ntuples (v31) [see link below]

Jan-Apr 21

  • possible (small) contribution to di-lepton analysis (cut-optimization, same-flavor lepton selection, or similar) (this is important for your possible contribution to the di-lepton paper)

Jan-Aug 21 'design' of the lepton+jets analysis.

  • phase space selection
  • analysis 'up-scaling'
  • background studies
  • resolution studies
  • observable reconstruction
  • efficiencies
  • etc...

Sept-Feb 21/22

  • channel combination (e,mu)
  • Unfolding
  • systematic uncertainties
  • Model predictions

Feb-Jun 22

  • Phenomenological interpretation (NLO, NLO+PS, approx. NNLO,
  • optional: possible extension to pp->lvqqbb
  • optional: possibly include 1-bjet, and/or 1-ljet channel (requires new ntuples)

Jun-Aug 22

  • paper preparation, conf note (ICHEP?)

Aug-Jan 22/23

  • extended phenomenological analysis (m_top, \gamma_top, PDF, alpha_s, etc...)
  • paper preparation

Feb-May 23

  • extra-time

Jun-Oct 23

  • Writing thesis.

MC samples

tW samples
  • DR = Diagram Removal
  • DS = Diagram Subtraction

Analysis code

  • WWbbLoop currently used for the di-lepton analysis
  • WWbb intended by Daniel for the l+jets analysis. There are infact two analysis packages included. One by Andrii (neowwbb) and one by Daniel WWbb (libwwbb)

-- KenjiHamano - 2021-09-15

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