Heavy-flavor hadro-production with heavy-quark masses renormalized in the ${\overline{\rm MS}}$, MSR and on-shell schemes

TL;DR

This work investigates heavy-quark hadro-production at the LHC under three mass renormalization schemes: on-shell (pole), $ar{MS}$, and MSR. It develops and applies implementations in ${\texttt{MCFM}}$ and ${\texttt{xFitter}}$ to compute NLO differential cross-sections in these schemes, explores dynamical mass-renormalization scales, and performs phenomenological fits to extract $m_t$ and constrain PDFs. Key findings include improved perturbative stability with $ar{MS}$ and MSR masses, observable scheme- and scale-dependent differences in differential distributions, and a demonstrable potential to constrain low-$x$ gluon PDFs using charm data (and extrapolated charm data) at NNLO. The results provide a coherent framework for precise top-quark mass determinations and for refining PDFs, with publicly available tools enabling broader adoption.

Abstract

We present predictions for heavy-quark production at the Large Hadron Collider making use of the ${\overline{\rm MS}}$ and MSR renormalization schemes for the heavy-quark mass as alternatives to the widely used on-shell renormalization scheme. We compute single and double differential distributions including QCD corrections at next-to-leading order and investigate the renormalization and factorization scale dependence as well as the perturbative convergence in these mass renormalization schemes. The implementation is based on publicly available programs, ${\texttt{MCFM}}$ and ${\texttt{xFitter}}$, extending their capabilities. Our results are applied to extract the top-quark mass using measurements of the total and differential $t\bar{t}$ production cross-sections and to investigate constraints on parton distribution functions, especially on the gluon distribution at low $x$ values, from available LHC data on heavy-flavor hadro-production.

Figures (21)

• Figure 1: The one-loop evolution of the $\overline{\rm MS}$ charm-, bottom- and top-masses for varying renormalization scales $\mu$ (left). The one-loop evolution of the MSR charm-, bottom- and top-masses for varying scales $R$ (right). The values of $\mu$ and $R$ used in the subsequent calculations and figures of this work are marked with filled dots. The value of $\alpha_S(M_Z)$ is fixed to 0.118 and $\alpha_S$ is evolved at four loops, as in Table \ref{['tab:masses']}.
• Figure 2: The NLO differential cross-sections for charm production at the LHC ($\sqrt{s} = 7$ TeV) with their scale uncertainties as a function of $p_T$ in different intervals of $y$ of the charm-quark with the mass renormalized in the pole, $\overline{\rm MS}$ and MSR schemes. The lower parts of each panel display the theoretical predictions normalized to the central values obtained in the pole mass scheme, including scale uncertainties (upper ratio plot), or just the ratio of central predictions (lower ratio plot) in order to magnify shape differences.
• Figure 3: Same as Fig. \ref{['fig:c-pty-mu']}, but for the charm-mass value $m_{c}(m_{c})\xspace$ = 1.18 GeV (converted to $m_{c}^{\text{MSR}}\xspace$(1 GeV) = 1.21 GeV and $m_{c}^{\mathrm{pole}}\xspace$ = 1.38 GeV), as extracted in the ABMP16 NLO fit.
• Figure 4: Same as Fig. \ref{['fig:c-pty-mu']} for bottom production.
• Figure 5: Same as Fig. \ref{['fig:b-pty-mu']}, but for the bottom-mass value $m_{b}(m_{b})\xspace$ = 3.88 GeV (converted to $m_{b}^{\text{MSR}}\xspace$(3 GeV) = 4.00 GeV and $m_{b}^{\mathrm{pole}}\xspace$ = 4.25 GeV), as extracted in the ABMP16 NLO fit.