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Bottom-quark associated Higgs-boson production: reconciling the four- and five-flavour scheme approach

Robert Harlander, Michael Krämer, Markus Schumacher

TL;DR

The paper addresses the discrepancy between four-flavour and five-flavour schemes in predicting bottom-quark associated Higgs production cross sections. It contrasts the 4FS, which treats bottom quarks as massive final-state particles, with the 5FS, which uses bottom PDFs to resum collinear logs, and discusses their respective strengths, limitations, and order-of-accuracy. To reconcile the schemes, the authors propose Santander matching, a pragmatic, weight-based interpolation that blends 4FS and 5FS predictions with a mass-dependent weight w = ln(m_H/m_b) - 2 and linearly combines uncertainties, yielding a central value that transitions from 4FS-dominated at low m_H to 5FS-dominated at high m_H while preserving uncertainty bands. Numerical results at √s = 7 TeV show that the matched cross section closely tracks each scheme in its regime, with explicit weights at m_H = 100, 200, 300, 400, and 500 GeV and uncertainty bands that cover both schemes up to mh ≈ 300 GeV. The approach provides a practical, conservative prediction for LHC phenomenology where both schemes are individually valid but not simultaneously identical at finite order.

Abstract

The main arguments in the discussion of the proper treatment of the total inclusive cross section for bottom-quark associated Higgs-boson production are briefly reviewed. A simple and pragmatic formula for the combination of the so-called four- and five-flavour schemes is suggested, including the treatment of the respective theory error estimates. The numerical effects of this matching formula are discussed.

Bottom-quark associated Higgs-boson production: reconciling the four- and five-flavour scheme approach

TL;DR

The paper addresses the discrepancy between four-flavour and five-flavour schemes in predicting bottom-quark associated Higgs production cross sections. It contrasts the 4FS, which treats bottom quarks as massive final-state particles, with the 5FS, which uses bottom PDFs to resum collinear logs, and discusses their respective strengths, limitations, and order-of-accuracy. To reconcile the schemes, the authors propose Santander matching, a pragmatic, weight-based interpolation that blends 4FS and 5FS predictions with a mass-dependent weight w = ln(m_H/m_b) - 2 and linearly combines uncertainties, yielding a central value that transitions from 4FS-dominated at low m_H to 5FS-dominated at high m_H while preserving uncertainty bands. Numerical results at √s = 7 TeV show that the matched cross section closely tracks each scheme in its regime, with explicit weights at m_H = 100, 200, 300, 400, and 500 GeV and uncertainty bands that cover both schemes up to mh ≈ 300 GeV. The approach provides a practical, conservative prediction for LHC phenomenology where both schemes are individually valid but not simultaneously identical at finite order.

Abstract

The main arguments in the discussion of the proper treatment of the total inclusive cross section for bottom-quark associated Higgs-boson production are briefly reviewed. A simple and pragmatic formula for the combination of the so-called four- and five-flavour schemes is suggested, including the treatment of the respective theory error estimates. The numerical effects of this matching formula are discussed.

Paper Structure

This paper contains 6 sections, 4 equations, 2 figures.

Table of Contents

  1. Two approaches
  2. Discussion
  3. Santander matching
  4. Numerical results
  5. Conclusions
  6. Acknowledgments.

Figures (2)

  • Figure 1: (a) Weight factor $w$, Eq. (\ref{['eq::t']}), as a function of the Higgs-boson mass $m_\text{H}$. The bottom-quark pole mass has been set to $m_\text{b} = 4.75$ GeV. (b) Central values for the total inclusive cross section in the .9 4FS (red, dashed), the .9 5FS (green, dotted), and for the matched cross section (blue, solid). Here and in the following we use the .9 MSTW2008 .9 PDF set Martin:2009iq (.9 NLO for .9 4FS, .9 NNLO for .9 5FS).
  • Figure 2: (a) Theory uncertainty bands for the total inclusive cross section in the .9 4FS (red, dashed), the .9 5FS (green, dotted), and for the matched cross section (blue, solid). (b) Uncertainty bands and central values, relative to the central value of the matched result (same line coding as panel (a)).