Abstract
We study the role of the scale of the threshold variable in soft-gluon threshold resummation. We focus on the computation of the resummed total cross section, the final-state invariant-mass distribution, and transverse-momentum distribution of the Higgs boson when produced in association with a top-anti-top quark pair for the Large Hadron Collider operating at 13 TeV. We show that different choices for the scale of the threshold variable result in differences at next-to-leading power, i.e. contributions that are down by one power of the threshold variable. These contributions are noticeable numerically, although their effect on the resummed observables lies within the scale uncertainty of those observables. The average central results, obtained after combining several central- scale choices, agree remarkably well for different choices of the threshold variable. However, different threshold choices do affect the resulting scale uncertainty. To compute our results, we introduce a novel numerical method that we call the deformation method, which aids the stabilization of the inverse Mellin transform in cases where the analytical Mellin transform of the partonic cross section is unknown. We show that this method leads to a factor of 10 less function evaluations, while gaining a factor of 4 − 5 in numerical precision when compared to the standard method.
Highlights
To lie within 20 − 30% of the SM value
We focus on the computation of the resummed total cross section, the final-state invariant-mass distribution, and transverse-momentum distribution of the Higgs boson when produced in association with a top-anti-top quark pair for the Large Hadron Collider operating at 13 TeV
We introduce a novel numerical method that we call the deformation method, which aids the stabilization of the inverse Mellin transform in cases where the analytical Mellin transform of the partonic cross section is unknown
Summary
To set up our notation, we first introduce the tth process at LO. The final state may be created by two partonic processes: gg → tth and qq → tth. One needs to parameterize the three-body phase space in a suitable way to compute the invariant-mass or transverse-momentum distribution. The phase space of the tt-system dΦ2(ptt; pt, pt) may be computed in the CM system of tt This system is denoted by the starred notation (∗), and the direction of travel of the tt-system in the CM system of the incoming particles is used as the z-axis with respect to which the angle θ∗ is defined. The phase space integration of the (tt)h-system dΦ2(p1 + p2; ptt, ph) is evaluated in the partonic CM system, where the four-momenta of the initial-state particles read. Using these definitions, the LO fully differential partonic cross section is written as dσiLjO→tth(s). Having set up our notation, we are ready to turn our attention to the resummation of the tth production process
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
