A Determination of the Top Mass from a Global PDF Analysis

Abstract

We present an indirect determination of the top-quark pole mass $m_t$ within a global analysis of parton distribution functions (PDFs), based on the public NNPDF framework. We consider a wide range of measurements, including both single- and double-differential observables, computed at NNLO QCD accuracy with EW corrections, and analyse their individual as well as combined impact on the joint $(α_s, m_t)$ parameter space, while accounting for PDF evolution up to approximate ${\rm N^3LO}$ QCD accuracy with QED corrections. We account for missing higher order QCD uncertainties by default. Unique to our analysis are the inclusion of, first, toponium contributions around the $t\bar{t}$ threshold, second, state-of-the-art constraints on $α_s$ from the lattice, and finally, a detailed sensitivity study of the various ATLAS and CMS differential cross-section measurements at 8 and 13 TeV. We demonstrate explicitly how a combined determination requires the refitting of the PDFs in order to correctly correlate uncertainties. We find $m_t = 172.80 \pm 0.26$ GeV at approximate N$^3$LO QCD including NLO QED, EW and toponium corrections.

Figures (12)

• Figure 3.1: Representative differential distributions of $t\bar{t}$ at 13 TeV by ATLAS and CMS at the top-quark pole mass $m_t = \{170.0, 172.5, 175.0\}$ GeV. From top left to bottom right, we show distributions differential in the invariant mass $m_{t\bar{t}}$, the transverse momentum $p_T^t$, top-quark rapidity $y_t$ and the rapidity $y_{t\bar{t}}$ of the top-quark pair. The shaded bands represent the PDF uncertainties obtained from NNPDF4.0 NNPDF:2021njg
• Figure 3.2: Relative EW corrections when considered on top of the NNLO QCD theory for a representative subset of distributions considered in this work. From top left to bottom right, we display the impact in the $m_{t\bar{t}}$ distribution, the double differential distribution in $(m_{t\bar{t}}, y_{t\bar{t}})$, the $p_T^t$ distribution, and the $y_t$ distribution
• Figure 3.3: Differential distributions in the invariant mass $m_{t\bar{t}}$ (left panel) and top-quark transverse momentum $p_T^t$ (right panel) at LO comparing the toponium signal ($t\bar{t}_{\rm NRQCD}$) modelled with NRQCD following the reweighting from Eq. \ref{['eq:toponium_reweighting']} against the nominal $t\bar{t}$ background at 13 TeV while imposing $m_{t\bar{t}} < 350$ GeV.
• Figure 4.1: A closure test of $\alpha_s(m_Z)$ and $m_t$ generated from 100 $L_1$ instances, each consisting of 100 $L_2$ replicas, at NNLO QCD while including MHOUs with underlying truth $\alpha_s^*=0.118$ and $m_t^*=172.5$ GeV. The weighted average of the $L_1$ instances, indicated by the (blue) ellipse, is compatible with the true values at 68% CL.
• Figure 4.2: 68% C.L. bounds on the top-quark's mass $m_t$ and the strong couplings constant $\alpha_s(m_Z)$, at NNLO QCD with MHOUs. In each case, multiple exclusion contours are shown, each corresponding to a fit performed on the baseline dataset complemented with top-quark data differential in the given observable. Each fit is done with 500 replicas. Ellipses with dashed lines indicate that at least one of the data sets in this measurement has a $\chi^2/n_{\rm dat} > 3.0$