On next to soft corrections to Drell-Yan and Higgs Boson productions

Abstract

We present a framework that resums threshold enhanced large logarithms to all orders in perturbation theory for the production of a pair of leptons in Drell-Yan process and of Higgs boson in gluon fusion as well as in bottom quark annihilation. We restrict ourselves to contributions from diagonal partonic channels. These logarithms include the distributions $((1-z{)}^{-1}{\ln }^i(1-z){)}_{+}$ resulting from soft plus virtual (SV) and the logarithms ${\ln }^i(1-z)$ from next-to-SV (NSV) contributions. We use collinear factorisation and renormalisation group invariance to achieve this. The former allows one to define a Soft-Collinear (SC) function which encapsulates soft and collinear dynamics of the perturbative results to all orders in strong coupling constant. The logarithmic structure of these results are governed by universal infrared anomalous dimensions and process dependent functions of Sudakov differential equation that the SC satisfies. The solution to the differential equation is obtained by proposing an all-order ansatz in dimensional regularisation, owing to several state-of-the-art perturbative results available to third order. The $z$ space solutions thus obtained provide an integral representation to sum up large logarithms originating from both soft and collinear configurations, conveniently in Mellin $N$ space. We show that in $N$ space, tower of logarithms $a_s^n/N^{\alpha }{\ln }^{2n-\alpha }(N),a_s^n/N^{\alpha }{\ln }^{2n-1-\alpha }(N)\cdots$ etc for $\alpha =0,1$ are summed to all orders in $a_s$.

55 Pages, 3 Tables

References in corpus (34)

• Higgs boson gluon-fusion production in N3LO QCD
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• The five-loop beta function of Yang-Mills theory with fermions
• Quark and gluon form factors to three loops
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• Higher-Order threshold effects to inclusive processes in QCD
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• The Drell-Yan cross section to third order in the strong coupling constant
• The five-loop Beta function for a general gauge group and anomalous dimensions beyond Feynman gauge
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• The method of regions and next-to-soft corrections in Drell-Yan production
• Threshold resummation at N${}^3$LL accuracy and soft-virtual cross sections at N${}^3$LO
• Drell-Yan Production at Threshold to Third Order in QCD
• On next-to-eikonal corrections to threshold resummation for the Drell-Yan and DIS cross sections
• Five-loop renormalisation of QCD in covariant gauges
• Resummed Higgs cross section at N${}^3$LL
• Approximate N^3LO Higgs-boson production cross section using physical-kernel constraints
• N${}^3$LO Higgs and Drell-Yan production at threshold: the one-loop two-emission contribution
• Matter dependence of the four-loop cusp anomalous dimension
• Universality of next-to-leading power threshold effects for colourless final states in hadronic collisions
• Threshold factorization of the Drell-Yan process at next-to-leading power
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• Leading-logarithmic threshold resummation of Higgs production in gluon fusion at next-to-leading power
• A next-to-next-to-leading order calculation of soft-virtual cross sections
• The $Hb\bar{b}$ form factor to three loops in QCD
• Updated Higgs cross section at approximate N${}^3$LO
• Approximate four-loop QCD corrections to the Higgs-boson production cross section
• Higgs boson production through $b\bar{b}$ annihilation at threshold in N${}^3$LO QCD
• On threshold resummation beyond leading 1-x order
• The three loop soft function for N${}^3$LL${}^{\prime }$ gluon fusion Higgs production in SCET
• Associated production of Higgs boson with vector boson at threshold N${}^3$LO in QCD
• QCD threshold corrections to Higgs decay and to hadroproduction in $l^{+}{l}^{-}$ annihilation
• Three loop form factors of a massive spin-2 particle with nonuniversal coupling
• On next-to-eikonal exponentiation

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