Threshold resummation of the rapidity distribution for Higgs production at NNLO+NNLL

Abstract

We present a formalism that resums threshold-enhanced logarithms to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We achieve this by exploiting the factorization properties and K+G equations satisfied by the soft and virtual parts of the cross section. We compute for the first time compact and most general expressions in two-dimensional Mellin space for the resummed coefficients. Using various state-of-the-art multiloop and multileg results, we demonstrate the numerical impact of our resummed results up to next-to-next-to-leading order for the rapidity distribution of the Higgs boson at the LHC. We find that inclusion of these threshold logs through resummation improves the reliability of perturbative predictions.This article is dedicated to the memory of Jack Smith.Introduction.-With the successful running of the LHC at CERN and precise theoretical predictions from various state-of-the-art computations, we can now test the Standard Model (SM) of particle physics with unprecedented accuracy and also severely constrain many physics beyond the SM (BSM) scenarios. The spectacular discovery [1] of a scalar particle and the most precise prediction on its production cross section [2] improved our understanding of the symmetry-breaking mechanism, namely, the Higgs mechanism. The copious production of vector bosons Zs and W ± s and lepton pairs at the LHC through Drell-Yan (DY) process [3], which are used to precisely measure the parton distribution functions (PDFs) [4] are also very important to study.

Threshold resummation in the rapidity distribution for a colorless particle production at the LHC

“…To perform resummation at NNLO+NNLL accuracy, we need resummed coefficients upto g I d,3 and the prefactors upto l I,(2) g 0 and those can be found in [7] 1 . Exponentiation of the coefficients g I d,i resums the terms a s β 0 ln(N 1 N 2 ) systematically to all orders in perturbation theory.…”

“…In Mellin space, the limits z i → 1 translate into N i → ∞ and large logarithms proportional to ln(N i ) are resummed to all orders in perturbation theory. We present numerical results for resummed rapidity distributions for Higgs [7] and DY [8] productions at the LHC.…”

Quark and gluon jet functions at three loops in QCD

“…To achieve this, we exploit the Sudakov (KG) equation that the virtual part (form factor) of the cross section satisfy, renormalization group invariance, factorization theorem and use various three-loop results. We use the framework developed in [16,17,18,19,20] which describes resummation of soft gluons to all orders in QCD perturbation theory. In [17], it was shown that DIS cross section in the threshold limit factorizes into the square of ultraviolet (UV) renormalized form factor, soft plus jet (SJ) function and the mass factorization kernels.…”

Gluon jet function at three loops in QCD

“…We use the framework developed in [16][17][18] which describes resummation of soft gluons to all orders in QCD perturbation theory. For the recent results on the soft gluon resummation of the rapidity distribution of Higgs and lepton pair production in Drell-Yan, see [19,20]. In [17], it was shown that DIS cross section in the threshold limit factorizes into the square of ultraviolet (UV) renormalized form factor, soft plus jet function and the mass factorization kernels.…”