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Analytic Results for Higgs Production in Bottom Fusion

Kemal J. Ozeren

TL;DR

The work delivers an analytic NLO calculation for Higgs production in bottom-quark fusion with an associated jet, detailing the partonic cross sections and their small-$p_T$ behavior. By computing the $G^{(2)}_{ij}$ coefficient functions and performing a careful small-$p_T$ resummation, the authors extract the universal and process-dependent Sudakov coefficients, including the first direct determination of $B^{(2)}$ for this process and verifying consistency with established resummation frameworks. Their results agree with existing numerical implementations and provide a solid foundation for NNLO differential predictions in bottom-fusion–driven Higgs scenarios. The analysis enhances precision Higgs phenomenology in models with enhanced $Hb\bar{b}$ couplings and supplies techniques applicable to other quark-initiated processes.

Abstract

We evaluate analytically the cross section for Higgs production plus one jet through bottom quark fusion. By considering the small pT limit we derive expressions for the resummation coefficients governing the structure of large logarithms, and compare these expressions with those available in the literature.

Analytic Results for Higgs Production in Bottom Fusion

TL;DR

The work delivers an analytic NLO calculation for Higgs production in bottom-quark fusion with an associated jet, detailing the partonic cross sections and their small- behavior. By computing the coefficient functions and performing a careful small- resummation, the authors extract the universal and process-dependent Sudakov coefficients, including the first direct determination of for this process and verifying consistency with established resummation frameworks. Their results agree with existing numerical implementations and provide a solid foundation for NNLO differential predictions in bottom-fusion–driven Higgs scenarios. The analysis enhances precision Higgs phenomenology in models with enhanced couplings and supplies techniques applicable to other quark-initiated processes.

Abstract

We evaluate analytically the cross section for Higgs production plus one jet through bottom quark fusion. By considering the small pT limit we derive expressions for the resummation coefficients governing the structure of large logarithms, and compare these expressions with those available in the literature.

Paper Structure

This paper contains 11 sections, 33 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Notation
  3. .9 NLO Corrections
  4. Real Radiation
  5. Results
  6. Checks
  7. Small $p_T$ limit
  8. Fixed Order Expansion of the Resummed Formula
  9. Extracting the Resummation Coefficients
  10. Conclusion
  11. Acknowledgments

Figures (4)

  • Figure 1: Diagrams for Higgs production through bottom fusion in the (a) four and (b) five flavour schemes.
  • Figure 2: Examples of one loop diagrams at .9 NLO
  • Figure 3: Examples of real emission diagrams at .9 NLO. The initial state lines are bottom quarks, but the final state quarks can be of any flavour.
  • Figure 4: Diagram controlling the process-dependent part of the .9 NNLL resummation coefficient $B^{(2)}$, as described in Ref. deFlorian:2001zd.