Abstract
We present a formalism that sums up both soft-virtual (SV) and next to SV (NSV) contributions to all orders in perturbative QCD for the rapidity distribution of any colorless particle produced in hadron colliders. We have exploited the factorization properties and the renormalisation group (RG) invariance of the differential cross-section to achieve this. Using the state-of-the-art multiloop and multileg results, we determine the complete NSV contributions to third order in strong coupling constant for the rapidity distributions for a pair of leptons in Drell-Yan and also for Higgs boson in gluon fusion as well as bottom quark annihilation. Using the integral representation of our all order $z$ space result, we show how the NSV contributions can be resummed in two-dimensional Mellin space.
Highlights
Accurate measurements of observables at the Large Hadron Collider (LHC) and their precise theoretical predictions provide an opportunity to test the Standard Model (SM) with unprecedented accuracy, thereby constraining beyond-the-SM (BSM) scenarios
Measurements [2,3,4] of inclusive and differential rates of DY production are used as a standard candle to calibrate the detectors and fit the nonperturbative parton distribution functions (PDFs) [5,6,7,8,9]
Finite partonic processes contain soft and collinear divergences associated with the soft gluons and collinear partons, beyond leading order in perturbation theory, which can be removed by summing over degenerate final states and by mass factorization
Summary
Accurate measurements of observables at the Large Hadron Collider (LHC) and their precise theoretical predictions provide an opportunity to test the Standard Model (SM) with unprecedented accuracy, thereby constraining beyond-the-SM (BSM) scenarios. The ongoing measurements of inclusive and differential cross sections [12,13], along with the theoretical predictions [14] on strong and electroweak radiative corrections, help us to probe the symmetrybreaking mechanism and the coupling of the Higgs boson with other SM particles. Differential ones get large contributions from logarithms from phase-space boundaries of the final-state particles, spoiling the reliability of the fixed-order predictions These large logarithms can be summed up to all orders in perturbation theory. In a series of articles [50,51], we studied a variety of inclusive reactions to understand these subleading logarithms and found a systematic way to sum them up to all orders in z as well as in Mellin N spaces The latter provides a resummed prediction in N space for subleading logarithms similar to that of threshold ones. In the present paper, using factorization properties of physical observables and RG invariance, we complete the task of organizing the subleading logarithms in a systematic fashion that is suitable for summing them up to all orders in perturbation theory, in both zl and Nl spaces
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