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Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC

G. Bozzi, S. Catani, D. de Florian, M. Grazzini

TL;DR

The paper develops a comprehensive transverse-momentum resummation framework in $b$-space to predict the $q_T$ spectrum of high-mass systems, notably the SM Higgs boson at the LHC. It achieves NNLL resummation for small $q_T$ and matches to fixed-order calculations (NLO or NNLO) to cover the entire $q_T$ range, enforcing a perturbative unitarity constraint that reproduces total cross sections upon integration. Applying this to gluon-fusion Higgs production, the authors demonstrate a stable, accurate prediction with reduced scale uncertainties and quantifiable non-perturbative effects. The results are implemented in the HqT code and provide a robust tool for precise Higgs phenomenology and for similar high-mass processes at hadron colliders.

Abstract

We consider the transverse-momentum (q_T) distribution of generic high-mass systems (lepton pairs, vector bosons, Higgs particles, ....) produced in hadron collisions. At small q_T, we concentrate on the all-order resummation of the logarithmically-enhanced contributions in QCD perturbation theory. We elaborate on the $b$-space resummation formalism and introduce some novel features: the large logarithmic contributions are systematically exponentiated in a process-independent form and, after integration over q_T, they are constrained by perturbative unitarity to give a vanishing contribution to the total cross section. At intermediate and large q_T, resummation is consistently combined with fixed-order perturbative results, to obtain predictions with uniform theoretical accuracy over the entire range of transverse momenta. The formalism is applied to Standard Model Higgs boson production at LHC energies. We combine the most advanced perturbative information available at present for this process: resummation up to next-to-next-to-leading logarithmic accuracy and fixed-order perturbation theory up to next-to-leading order. The results show a high stability with respect to perturbative QCD uncertainties.

Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC

TL;DR

The paper develops a comprehensive transverse-momentum resummation framework in -space to predict the spectrum of high-mass systems, notably the SM Higgs boson at the LHC. It achieves NNLL resummation for small and matches to fixed-order calculations (NLO or NNLO) to cover the entire range, enforcing a perturbative unitarity constraint that reproduces total cross sections upon integration. Applying this to gluon-fusion Higgs production, the authors demonstrate a stable, accurate prediction with reduced scale uncertainties and quantifiable non-perturbative effects. The results are implemented in the HqT code and provide a robust tool for precise Higgs phenomenology and for similar high-mass processes at hadron colliders.

Abstract

We consider the transverse-momentum (q_T) distribution of generic high-mass systems (lepton pairs, vector bosons, Higgs particles, ....) produced in hadron collisions. At small q_T, we concentrate on the all-order resummation of the logarithmically-enhanced contributions in QCD perturbation theory. We elaborate on the -space resummation formalism and introduce some novel features: the large logarithmic contributions are systematically exponentiated in a process-independent form and, after integration over q_T, they are constrained by perturbative unitarity to give a vanishing contribution to the total cross section. At intermediate and large q_T, resummation is consistently combined with fixed-order perturbative results, to obtain predictions with uniform theoretical accuracy over the entire range of transverse momenta. The formalism is applied to Standard Model Higgs boson production at LHC energies. We combine the most advanced perturbative information available at present for this process: resummation up to next-to-next-to-leading logarithmic accuracy and fixed-order perturbation theory up to next-to-leading order. The results show a high stability with respect to perturbative QCD uncertainties.

Paper Structure

This paper contains 11 sections, 133 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Transverse-momentum resummation
  3. The resummation formalism: from small to large values of $q_T$
  4. The resummed component
  5. Sudakov form factor, universal form factor and perturbative coefficients
  6. The finite component
  7. The $q_T$ spectrum of the Higgs boson at the LHC
  8. Numerical results at the LHC
  9. Conclusions
  10. Appendix: Exponentiation in the multiflavour case
  11. Appendix: Bessel transformation of logarithmic contributions

Figures (11)

  • Figure 1: The $q_T$ spectrum at the LHC with $M_H=125$ GeV: ( left) setting $\mu_R=\mu_F=Q=M_H$, the results at NLL+LO accuracy are compared with the LO spectrum and the finite component of the LO spectrum; ( right) the uncertainty band from variations of the scales $\mu_R$ and $\mu_F$ at NLL+LO accuracy.
  • Figure 2: The $q_T$ spectrum at the LHC with $M_H=125$ GeV: ( left) setting $\mu_R=\mu_F=Q=M_H$, the results at NNLL+NLO accuracy are compared with the NLO spectrum and the finite component of the NLO spectrum; ( right) the uncertainty band from variations of the scales $\mu_R$ and $\mu_F$ at NNLL+NLO accuracy.
  • Figure 3: Scale dependence of the LHC cross section for Higgs boson production ($M_H=125$ GeV) at $q_T=50$ GeV. Results at a) (upper) LO, NLL+LO and b) (lower) NLO, NNLL+NLO accuracy.
  • Figure 4: Scale dependence of the LHC cross section for Higgs boson production ($M_H=125$ GeV) at $q_T=15$ GeV. Results at a) (upper) LO, NLL+LO and b) (lower) NLO, NNLL+NLO accuracy.
  • Figure 5: Comparison of the NLL+LO and NNLL+NLO bands ($M_H=125$ GeV). The inset plot shows the NNLL+NLO band normalized to the central value of the NLL+LO result.
  • ...and 6 more figures