Open $B$-hadron production at hadron colliders in QCD at next-to-next-to-leading-order and next-to-next-to-leading-logarithmic accuracy

TL;DR

This work extends the FONLL framework to NNLO+NNLL for open heavy-flavor production at hadron colliders, combining a massive cross section in 4-flavor QCD with a massless cross section in 5-flavor QCD via a FONLL-like matching and a $p_T$-dependent suppression. It includes fragmentation and detailed decay modeling, NNLL soft-gluon resummation, and DGLAP evolution via APFEL, with scale choices $\,\mu^2 = m^2 + d^2 p_T^2$. The NNLO+NNLL results exhibit reduced scale uncertainties and improved agreement with LHC data for $B$-hadrons and muons, while $J/\psi$ final states show a tension that may be attributable to the $BR(B\to J/\psi)$. This framework offers a precise tool to constrain heavy-flavor production and decay parameters, impacting LHC $B$-physics analyses and related phenomenology.

Abstract

We report on a calculation of open heavy-flavor production at hadron colliders which extends to next-to-next-to-leading order (NNLO) accuracy the classic NLO-accurate formalism developed almost 30 years ago under the acronym FONLL. The approach retains the exact heavy-flavor mass dependence at low transverse momentum, $p_T$, and resums collinear logarithms through next-to-next-to-leading log (NNLL) at high $p_T$. Provided are predictions for $B$-hadrons as well as $B$-decay products like $J/Ψ$ and muons. The main features of the NNLO+NNLL results are reduced scale dependence and moderate NNLO correction, consistent with perturbative convergence in a wide range of kinematic scales from few GeV up to asymptotically large values of $p_T$. The new calculation significantly improves the agreement with data for $B$-hadrons and muons. We uncover an intriguing discrepancy in $J/Ψ$ final states which may point to a lower value of the $B\to J/Ψ$ decay rate.

Figures (5)

• Figure 1: Fiducial $\bar{b} b$ cross section in LO, NLO and NNLO QCD. The data uncertainty is based on a naive combination of ten separate measurements UA1:1985bnqUA1:1990vvpUA1:1993jokCDF:1992sueCDF:1993faxCDF:1993dogCDF:1994zxdCDF:1996kanD0:1999hayCDF:2007pxr.
• Figure 2: $B^+$$p_T$ spectrum (see supplementary materials SM for more rapidity slices). Shown is our best prediction at NNLO+NNLL (orange) versus the current state of the art NLO+NNLL (purple) versus LHC data. Shown are the ratios w.r.t. the central prediction at NLO+NNLL.
• Figure 3: As in fig. \ref{['fig:B-LHC-2']} but with NNLO (red) instead of NLO+NNLL.
• Figure 4: Muon $p_T$ spectrum at LO+NNLL (light blue), NLO+NNLL (purple) and NNLO+NNLL (orange) compared with LHC data.
• Figure 5: $J/\Psi$$p_T$ spectrum at NNLO+NNLL (orange) compared with LHC data for two rapidity slices (see supplementary materials SM for the other slices). The dotted lines (green) show the uncertainty from $BR(B\to J/\Psi)$.