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Higgs boson production at hadron colliders in NNLO QCD

Charalampos Anastasiou, Kirill Melnikov

TL;DR

This work computes the total hadronic cross-section for direct Higgs boson production at NNLO in perturbative QCD, focusing on gluon-fusion in the heavy-top limit. It introduces an automated, unified framework that combines Cutkosky phase-space cutting with IBP reduction and differential equations to evaluate all virtual and real contributions through master integrals, yielding full analytic NNLO partonic cross-sections. Numerical results, convolved with MRST 2002 NNLO PDFs, show large NNLO corrections but significantly reduced scale dependence, with $K$-factors near $2$ for the LHC and $\sim 3$ for the Tevatron, underscoring improved precision over NLO. The methodology is general and facilitates extensions to differential distributions and other inclusive processes, offering a path toward even more precise predictions and potential connections to threshold-resummed calculations.

Abstract

We compute the total cross-section for direct Higgs boson production in hadron collisions at NNLO in perturbative QCD. A new technique which allows us to perform an algorithmic evaluation of inclusive phase-space integrals is introduced, based on the Cutkosky rules, integration by parts and the differential equation method for computing master integrals. Finally, we discuss the numerical impact of the O(alpha_s^2) QCD corrections to the Higgs boson production cross-section at the LHC and the Tevatron.

Higgs boson production at hadron colliders in NNLO QCD

TL;DR

This work computes the total hadronic cross-section for direct Higgs boson production at NNLO in perturbative QCD, focusing on gluon-fusion in the heavy-top limit. It introduces an automated, unified framework that combines Cutkosky phase-space cutting with IBP reduction and differential equations to evaluate all virtual and real contributions through master integrals, yielding full analytic NNLO partonic cross-sections. Numerical results, convolved with MRST 2002 NNLO PDFs, show large NNLO corrections but significantly reduced scale dependence, with -factors near for the LHC and for the Tevatron, underscoring improved precision over NLO. The methodology is general and facilitates extensions to differential distributions and other inclusive processes, offering a path toward even more precise predictions and potential connections to threshold-resummed calculations.

Abstract

We compute the total cross-section for direct Higgs boson production in hadron collisions at NNLO in perturbative QCD. A new technique which allows us to perform an algorithmic evaluation of inclusive phase-space integrals is introduced, based on the Cutkosky rules, integration by parts and the differential equation method for computing master integrals. Finally, we discuss the numerical impact of the O(alpha_s^2) QCD corrections to the Higgs boson production cross-section at the LHC and the Tevatron.

Paper Structure

This paper contains 14 sections, 95 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Effective Lagrangian
  3. Method
  4. Virtual corrections
  5. Reduction of phase-space integrals
  6. Evaluation of phase-space master integrals
  7. Partonic cross-sections
  8. Numerical results
  9. Conclusions
  10. Splitting functions
  11. Master Integrals
  12. Double-Virtual
  13. Real-Virtual
  14. Double-Real

Figures (3)

  • Figure 1: The Higgs boson production cross-section at the LHC at leading (dotted), next-to-leading (dashed-dotted) and next-to-next-to-leading (solid) order. The two curves for each case correspond to $\mu_r = \mu_f = m_H/2$ (upper) and $\mu_r = \mu_f = 2 m_H$ (lower).
  • Figure 2: The Higgs boson production cross-section at the Tevatron at leading (dotted), next-to-leading (dashed-dotted) and next-to-next-to-leading (solid) order. The two curves for each case correspond to $\mu_r = \mu_f = m_H/2$ (upper) and $\mu_r = \mu_f = 2 m_H$ (lower).
  • Figure 3: The Higgs boson production cross-section at the LHC at leading (dotted), next-to-leading (dashed-dotted) and next-to-next-to-leading (solid) order as the function of factorization and renormalization scale $\mu$. The mass of the Higgs boson is $115~{\rm GeV}$ for the left and $275~{\rm GeV}$ for the right plot.