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Kinematical Limits on Higgs Boson Production via Gluon Fusion in Association with Jets

V. Del Duca, W. Kilgore, C. Oleari, C. R. Schmidt, D. Zeppenfeld

TL;DR

The paper analyzes Higgs production in association with jets in the high-energy limit, focusing on gluon-gluon fusion and two distinct kinematic regimes where Higgs production factorizes into impact factors or coefficient functions connected by t-channel gluon exchange. It derives full top-mass dependent results for Higgs production from off-shell gluons and for Higgs production with gluon or quark jets, and demonstrates that the high-energy factorization framework remains valid when combined with the large-$M_t$ limit, with the two limits commuting. By providing exact LO amplitudes for $qQ o qQH$ and $qg o qgH$, the work enables the explicit construction of the high-energy vertices and cross-checks against the massless effective theory. The study also applies these results to Higgs+2-jet production, showing good agreement between exact, large-$M_t$, and high-energy approximations in regions with large rapidity separation, reinforcing the practical relevance for Higgs coupling measurements and background suppression at the LHC.

Abstract

In this paper, we analyze the high-energy limits for Higgs boson plus two jet production. We consider two high-energy limits, corresponding to two different kinematic regions: a) the Higgs boson is centrally located in rapidity between the two jets, and very far from either jet; b) the Higgs boson is close to one jet in rapidity, and both of these are very far from the other jet. In both cases the amplitudes factorize into impact factors or coefficient functions connected by gluons exchanged in the t channel. Accordingly, we compute the coefficient function for the production of a Higgs boson from two off-shell gluons, and the impact factors for the production of a Higgs boson in association with a gluon or a quark jet. We include the full top quark mass dependence and compare this with the result obtained in the large top-mass limit.

Kinematical Limits on Higgs Boson Production via Gluon Fusion in Association with Jets

TL;DR

The paper analyzes Higgs production in association with jets in the high-energy limit, focusing on gluon-gluon fusion and two distinct kinematic regimes where Higgs production factorizes into impact factors or coefficient functions connected by t-channel gluon exchange. It derives full top-mass dependent results for Higgs production from off-shell gluons and for Higgs production with gluon or quark jets, and demonstrates that the high-energy factorization framework remains valid when combined with the large- limit, with the two limits commuting. By providing exact LO amplitudes for and , the work enables the explicit construction of the high-energy vertices and cross-checks against the massless effective theory. The study also applies these results to Higgs+2-jet production, showing good agreement between exact, large-, and high-energy approximations in regions with large rapidity separation, reinforcing the practical relevance for Higgs coupling measurements and background suppression at the LHC.

Abstract

In this paper, we analyze the high-energy limits for Higgs boson plus two jet production. We consider two high-energy limits, corresponding to two different kinematic regions: a) the Higgs boson is centrally located in rapidity between the two jets, and very far from either jet; b) the Higgs boson is close to one jet in rapidity, and both of these are very far from the other jet. In both cases the amplitudes factorize into impact factors or coefficient functions connected by gluons exchanged in the t channel. Accordingly, we compute the coefficient function for the production of a Higgs boson from two off-shell gluons, and the impact factors for the production of a Higgs boson in association with a gluon or a quark jet. We include the full top quark mass dependence and compare this with the result obtained in the large top-mass limit.

Paper Structure

This paper contains 24 sections, 93 equations, 1 figure.

Table of Contents

  1. Introduction
  2. High-energy factorization of Higgs + one jet
  3. The high-energy limit for Higgs + one jet
  4. The combined high-energy limit and large top-mass limit
  5. The production rate for Higgs + one jet
  6. Exact amplitudes for Higgs + two jets
  7. The amplitude for $\boldsymbol{q\,Q\to q\,Q\,H}$ scattering
  8. The amplitude for $\boldsymbol{q\,g\to q\,g\,H}$ scattering
  9. High-energy factorization of Higgs + two jets
  10. The high-energy limit $\boldsymbol{s_{j_1j_2} \gg s_{j_1 {\rm H}},\, s_{j_2 {\rm H}}\gg M_{ {\rm H}}^2}$
  11. The combined high-energy limit and large top-mass limit
  12. The high-energy limit $\boldsymbol{s_{j_1j_2},\, s_{j_2 {\rm H}}\gg s_{j_1 {\rm H}},\, M_{ {\rm H}}^2}$
  13. The combined high-energy limit and large top-mass limit
  14. The production rate for Higgs + 2 jets
  15. Conclusions
  16. ...and 9 more sections

Figures (1)

  • Figure 1: Transverse momentum distribution of the Higgs boson (and of the jet) in $H$ + one jet production in $pp$ collisions at the LHC energy $\sqrt{s}=14$ TeV. The rapidity difference between the jet and the Higgs is taken to be $\Delta y = 3$. The Higgs mass has been fixed to $M_{ {\rm H}} = 120$ GeV in the left panel, and to $M_{ {\rm H}} = 480$ GeV in the right panel. The curves show the leading order amplitudes computed exactly (solid line) with top mass $M_{t} = 175$ GeV, in the $M_{t}\,\to\,\infty$ limit (dotted line) and in the high-energy limit (dashed line).