Abstract
We describe an implementation of a subtraction scheme in the nonrelativistic-QCD treatment of heavy-quarkonium production at next-to-leading-order in the strong-coupling constant, covering S- and P-wave bound states. It is based on the dipole subtraction in the massless version by Catani and Seymour and its extension to massive quarks by Phaf and Weinzierl. Important additions include the treatment of heavy-quark bound states, in particular due to the more complicated infrared-divergence structure in the case of P-wave states.
Highlights
In next-to-leading-order (NLO) perturbative calculations in quantum field theory, the phase space integrations of real corrections generally produce infrared (IR) divergences, which have to be regularized
We describe an implementation of a subtraction scheme in the nonrelativisticQCD treatment of heavy-quarkonium production at next-to-leading-order in the strong-coupling constant, covering S- and P -wave bound states
The standard choice for this is dimensional regularization, where the integrations are done in D = 4 − 2ǫ space-time dimensions, so that the IR divergences show up as poles in ǫ, ready to be canceled by other contributions
Summary
In next-to-leading-order (NLO) perturbative calculations in quantum field theory, the phase space integrations of real corrections generally produce infrared (IR) divergences, which have to be regularized. In the vicinity of the IR divergences, both the squared matrix elements and the phase space factorize into simple expressions, the analytic integration in D dimensions is feasible, while the part outside the enclosed region is free from singularities, ready for numerical integration. Both contributions depend on the specific choice of phase space cut, but the sum of both contributions is independent of it. In Appendix A, we collect the expressions through order O(ǫ0) for the integrated Catani-Seymour and Phaf-Weinzierl dipoles needed in our study, in a form that already includes mass factorization counterterms
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