Abstract
In the production of the Higgs through a bottom-quark loop, the transverse momentum distribution of the Higgs at large $P_T$ is complicated by its dependence on two other important scales: the bottom quark mass $m_b$ and the Higgs mass $m_H$. A strategy for simplifying the calculation of the cross section at large $P_T$ is to calculate only the leading terms in its expansion in $m_b^2/P_T^2$. In this paper, we consider the bottom-quark-loop contribution to the parton process $q\bar{q}\to H+g$ at leading order in $\alpha_s$. We show that the leading power of $1/P_T^2$ can be expressed in the form of a factorization formula that separates the large scale $P_T$ from the scale of the masses. All the dependence on $m_b$ and $m_H$ can be factorized into a distribution amplitude for $b \bar b$ in the Higgs, a distribution amplitude for $b \bar b$ in a real gluon, and an endpoint contribution. The factorization formula can be used to organize the calculation of the leading terms in the expansion in $m_b^2/P_T^2$ so that every calculation involves at most two scales.
Highlights
The discovery of the Higgs boson in the year 2012 completed the Standard Model (SM) of particle physics [1,2]
In Ref. [42], we showed that the top-quark-loop contribution to the LP form factor for gà → H þ g at leading order (LO) can be expressed in terms of a factorization formula that separates the hard scale Q from the masses mt and mH
We applied factorization methods developed for QCD to the amplitude for Higgs production at large transverse momentum through a bottom-quark loop
Summary
The discovery of the Higgs boson in the year 2012 completed the Standard Model (SM) of particle physics [1,2]. Since the high-lminosity LHC may be able to measure the Higgs PT distribution with a few percent accuracy, it is important to understand the bottom-quark-loop contribution to the same level of precision This requires calculating the process to higher orders in αs and resumming large logarithms to all orders. The mb → 0 limit can be calculated by solving the differential equations for master integrals in this limit [7] This method has been used by Mueller and Öztürk to calculate bottom-quark-loop contributions to the inclusive cross section for Higgs production to NLO [7]. The bottom-quark-loop contribution to the matrix elements for gq → H þ q and gq → H þ qat LO can be expressed in terms of the same function F as the form factor for qq → H þ g but with the positive Mandelstam variable sreplaced by a negative Mandelstam variablet. If the form factor F for qq → H þ g is expressed in terms of the complex variable sþ iε, it can be applied to gq → H þ q and gq → H þ qby analytic continuation
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have