Inclusive Higgs Production at Large Transverse Momentum

TL;DR

This paper derives a factorization formula for high transverse momentum Higgs production, allowing for resummation of large logarithms and providing accurate predictions at future colliders.

Contribution

It introduces a new factorization approach for Higgs production at large P_T, including all leading power terms and leading-order fragmentation functions for key partons.

Findings

The factorization formula accurately predicts Higgs production at P_T > 600 GeV.

Fragmentation functions for top quark, gluon, W, Z, and Higgs are calculated at leading order.

Error in the formula decreases to less than 5% at high P_T for future collider energies.

Abstract

We present a factorization formula for the inclusive production of the Higgs boson at large transverse momentum $P_T$ that includes all terms with the leading power of $1/P_T^2$. The cross section is factorized into convolutions of parton distributions, infrared-safe hard-scattering cross sections for producing a parton, and fragmentation functions that give the distribution of the longitudinal momentum fraction of the Higgs relative to the fragmenting parton. The infrared-safe cross sections and the fragmentation functions are perturbatively calculable. The most important fragmentation functions are those for which the fragmenting parton is the top quark, gluon, $W$, $Z$, and the Higgs itself. We calculate the fragmentation functions at leading order in the Standard Model coupling constants. The factorization formula enables the resummation of large logarithms of $P_T/M_H$ due to final-state radiation by integrating evolution equations for the fragmentation functions. By comparing the cross section for the process $q\bar{q}\to H t\bar t$ from the leading-power factorization formula at leading order in the coupling constants with the complete leading-order cross section, we infer that the error in the factorization formula decreases to less than 5\% for $P_T>600$ GeV at a future $100$ TeV collider.