Next to soft corrections to Drell-Yan and Higgs boson productions

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 the Drell-Yan process and of the 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)-1ln' (1 - z))+ resulting from soft plus virtual (SV) and the logarithms ln'(1 - z) from next-to-SV contributions. We use collinear factorization and renormalization group invariance to achieve this. The former allows one to define a soft-collinear (SC) function that encapsulates soft and collinear dynamics of the perturbative results to all orders in the strong coupling constant. The logarithmic structure of these results is governed by universal infrared anomalous dimensions and process-dependent functions of the Sudakov differential equation that the SC satisfies. The solution to the differential equation is obtained by proposing an all-order ansatz in dimensional regularization, 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, the tower of logarithms ans /N alpha ln2n-alpha (N); ans /N alpha ln2n-1-alpha (N) center dot center dot center dot for alpha = 0, 1 is summed to all orders in a(s).

Automated summary

This study presents a framework for resumming threshold enhanced large logarithms to all orders in perturbation theory for the production of a pair of leptons in the Drell-Yan process and of the Higgs boson in gluon fusion as well as in bottom quark annihilation. The use of collinear factorization and renormalization group invariance allows for the calculation of soft and collinear dynamics to all orders.