Differential Top Quark Pair Production at the LHC: Challenges for PDF Fits

TL;DR

The paper investigates incorporating differential ttbar production data into MMHT PDFs, focusing on ATLAS and CMS 8 TeV measurements across multiple channels and kinematic variables. It finds that full simultaneous fits to ATLAS lepton+jets data are severely hampered by cross-distribution correlations of dominant two-point MC systematics, and that decorrelating these errors can dramatically improve fit quality but shifts the inferred high-x gluon uncertainty. The dilepton channel shows cleaner fits and consistent gluon pulls, while CMS data's constraining power is highly sensitive to correlation treatment. Overall, the study emphasizes that error correlations can dominate gluon PDF constraints and advocates for careful handling of systematic correlations or alternative observables in PDF determinations.

Abstract

We present the results of a PDF fit to differential top quark production within the MMHT framework. We in particular consider ATLAS data in the lepton + jet and dilepton channels and CMS data in the lepton + jet channel, at 8 TeV. While the fit quality to the ATLAS dilepton data is good, for the CMS case we see some issues in achieving a good fit quality for certain distributions. However, we focus on the ATLAS lepton + jet data, for which correlations of the statistical and systematic errors are provided across the four relevant distributions for PDF determination, namely $p_T^t$, $M_{tt}$, $y_t$ and $y_{tt}$. We find severe difficulties in fitting these distributions simultaneously, with particular sensitivity to the precise degree of correlation taken between the dominant two--point MC uncertainties in the data. We investigate the effect of some reasonable decorrelation of these uncertainties, finding the impact on the fit quality to be significant and the resultant gluon not negligible. This is in particular found to be larger than the effect of including NNLO QCD and NLO EW corrections in the top quark pair production cross section on the fit, motivating a closer understanding of the physics underlying these errors sources and in particular the uncertainty on the degree of correlation in them.

Figures (12)

• Figure 1: Impact of the ATLAS 8 TeV lepton + jet data on the gluon PDF. Results for fits to individual distributions as well as the combined $p_T+M_{tt}$ case are shown, while the result from a combined fit to all four distributions is shown for comparison in all cases.
• Figure 2: The tension between shifts for the ATLAS 8 TeV lepton + jet data, between the individual distributions. This is calculated as $(1/6)\sum_{j=1}^{4}\sum_{l>j}^{4}(\lambda_{i,j}-\lambda_{i,l})$ where $\lambda_{i,j}$ is the $i^\text{th}$ nuisance parameter calculated when fitting the $j^\text{th}$ distribution.
• Figure 3: Impact of the ATLAS 8 TeV lepton + jet data on the gluon PDF. The result of the default to the combined dataset is shown, as well as decorrelating the parton shower systematic uncertainty between the four distributions.
• Figure 4: As in Fig. \ref{['pdf 1']}, for fits to different distributions taken in the literature: $y_t$ and $p_T+M_{tt}$ (with decorrelation of the parton shower systematic error), as well as the combined fit.
• Figure 5: Values for individual shift parameters ($\lambda_i$ in Eq. \ref{['chi2 1']}) for the parton shower error when fitting the $y_{tt}$ distribution of the ATLAS 8 TeV lepton + jet data, while decorrelating the error between each data point.