Abstract
The prediction of differential cross-sections in hadron-hadron scattering processes is typically performed in a scheme where the heavy-flavour quarks (c, b, tc,b,t) are treated either as massless or massive partons. In this work, a method to describe the production of colour-singlet processes which combines these two approaches is presented. The core idea is that the contribution from power corrections involving the heavy-quark mass can be numerically isolated from the rest of the massive computation. These power corrections can then be combined with a massless computation (where they are absent), enabling the construction of differential cross-section predictions in a massive variable flavour number scheme. As an example, the procedure is applied to the low-mass Drell-Yan process within the LHCb fiducial region, where predictions for the rapidity and transverse-momentum distributions of the lepton pair are provided. To validate the procedure, it is shown how the n_fnf-dependent coefficient of a massless computation can be recovered from the massless limit of the massive one. This feature is also used to differentially extract the massless N^3LON3LO coefficient of the Drell-Yan process in the gluon-fusion channel.
Highlights
The prediction of high-energy scattering processes which involve initial-state hadrons is crucial for understanding the physics of hadron collisions in both controlled environments as well as a range of naturally occurring scattering processes
A,b dξA dξB fa/A(ξA, μ) fb/B(ξB, μ) × dσab xA, xB, Q; αs(μ), μ. This theorem separates the full scattering process into a partonic scattering process involving the scattering of the hadron constituents a, b, and a set of parton distribution functions (PDFs) f (x, Q) which describe the probability distribution of the internal content of the hadron as a function of hadron momentum-fraction and virtuality carried by the constituent particle
The main goal of this work is to provide a deeper theoretical understanding of the treatment and role of massive quarks in predicting hadron-hadron scattering processes. This has been achieved by studying the general structure of calculations which involve a single massive quark, and presenting a formalism to construct differential cross-section predictions in a massive variable flavour number scheme
Summary
The prediction of high-energy scattering processes which involve initial-state hadrons is crucial for understanding the physics of hadron collisions in both controlled environments (such as the LHC) as well as a range of naturally occurring scattering processes (such as those involving cosmic rays). Provided that QCD inclusive and/or infrared- and collinear-safe observables are considered, the logarithmic dependence of the massive crosssection on the heavy-quark mass m is of collinear origin This behaviour is universal, and it can be described with knowledge of a set of decoupling relations which describe how parameters (e.g. αs and PDFs) in a theory with a massive quark are mapped (at fixed-order accuracy) into an effective theory where that quark is treated as massless. This can be achieved if both massive and logarithmic calculations are known at the desired perturbative order, by performing a fit to the constant difference dσM − dσln[m] in the limit m → 0 Once this constant is known, the power corrections can be extracted at the physical value of the heavy-quark mass. Notice that when this conversion is applied to equal powers of αs and the gluon PDF, the dependence on m vanishes and a logarithm of the ratio μF /μR remains
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