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A two-loop application of the threshold expansion: the bottom quark mass from $b\bar{b}$ production

M. Beneke, A. Signer, V. A. Smirnov

TL;DR

The paper presents a NNLO determination of the bottom quark mass from near-threshold bb̄ production using threshold expansion and non-relativistic effective field theory. By factorizing scales into hard, soft, potential, and ultrasoft modes and employing potential NRQCD, the authors resum velocity-enhanced terms and compute the bb̄ cross section to NNLO, using dispersion relations to connect theory with experimental moments. A key methodological advance is the use of the potential-subtracted mass to reduce infrared sensitivity and improve convergence, followed by conversion to the MSbar mass. The resulting MSbar bottom mass is mb(mb) = 4.26 ± 0.12 GeV, with uncertainties dominated by residual scale dependence; the work demonstrates a consistent, high-precision NNLO framework that aligns with other NNLO determinations and clarifies the role of resummation and short-distance effects in heavy-quark mass extractions.

Abstract

We use the threshold expansion and non-relativistic effective theory to determine the bottom quark mass from moments of the $b\bar{b}$ production cross section at next-to-next-to-leading order in the (resummed) perturbative expansion, and including a summation of logarithms. For the $\bar{\rm MS}$ mass $\bar{m}_b$, we find $\bar{m}_b(\bar{m}_b)=(4.26\pm 0.12)$ GeV.

A two-loop application of the threshold expansion: the bottom quark mass from $b\bar{b}$ production

TL;DR

The paper presents a NNLO determination of the bottom quark mass from near-threshold bb̄ production using threshold expansion and non-relativistic effective field theory. By factorizing scales into hard, soft, potential, and ultrasoft modes and employing potential NRQCD, the authors resum velocity-enhanced terms and compute the bb̄ cross section to NNLO, using dispersion relations to connect theory with experimental moments. A key methodological advance is the use of the potential-subtracted mass to reduce infrared sensitivity and improve convergence, followed by conversion to the MSbar mass. The resulting MSbar bottom mass is mb(mb) = 4.26 ± 0.12 GeV, with uncertainties dominated by residual scale dependence; the work demonstrates a consistent, high-precision NNLO framework that aligns with other NNLO determinations and clarifies the role of resummation and short-distance effects in heavy-quark mass extractions.

Abstract

We use the threshold expansion and non-relativistic effective theory to determine the bottom quark mass from moments of the production cross section at next-to-next-to-leading order in the (resummed) perturbative expansion, and including a summation of logarithms. For the mass , we find GeV.

Paper Structure

This paper contains 8 sections, 16 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Heavy quark production cross section near threshold
  3. Classification of momentum regions
  4. Relativistic corrections
  5. Instantaneous interactions
  6. Perturbation theory with potential NRQCD
  7. Potential subtracted quark mass
  8. Results and discussion

Figures (1)

  • Figure 1: The 8th moment (in GeV$^{-16}$) as function of the bottom quark pole mass (in GeV) (upper figure) and the bottom quark PS mass (lower figure) at $\mu_f=2\,$GeV. The solid curve is for the scale $\hat{\mu}=2 m_b/\sqrt{8}$, the outer (dash-dotted) curves show the result, when the scale is varied by a factor of 2 in both directions. The inner (dotted) curves correspond to $2\hat{\mu}/3$ and $3\hat{\mu}/2$. The experimental moment is given by the grey bar.