On regularizing the infrared singularities in QCD NLO splitting functions with the new Principal Value prescription

Abstract

We propose a modified use of the Principal Value prescription for regularizing the infrared singularities in the light-cone axial gauge by applying it to all singularities in the light-cone plus component of integration momentum. The modification is motivated by and applied to the re-calculation of the QCD NLO splitting functions for the purpose of Monte Carlo implementations. The final results agree with the standard PV prescription whereas contributions from separate graphs get simplified.

Transverse-momentum-dependent quark splitting functions in k T -factorization: real contributions

“…In the following we extend this result by calculating as a start the unintegrated real emissions kernels for quark-to-quark and quark-to-gluon splitting functions. From a technical point of view the determination of TMD splitting kernels is based on a generalization of the high energy factorization approach of Catani and Hautmann [25], which itself is based on the formulation of DGLAP evolution in terms of a two-particleirreducible (2PI) expansion [26] (for overview and recent applications of the method see [27][28][29][30])). To guarantee gauge invariance in presence of off-shell particles we follow the proposal made in [12] and make use of the effective action formulation of the high energy factorization in terms of reggeized quarks and gluons [31,32].…”

Triple collinear emissions in parton showers

“…As fully exclusive, high precision simulations are mandatory in order to perform reliable measurements of Standard Model parameters and/or searches for physics beyond the Standard Model, the extension of parton showers to higher formal accuracy would benefit large parts of the high-energy physics community.The possibility of including next-to-leading order corrections into parton showers has been explored early on [9][10][11][12] and was revisited recently [13,14]. NLO splitting functions have been recomputed using a novel regularization scheme [15,16]. The dependence of NLO matching terms on the parton-shower evolution scheme has been investigated in detail [17].…”

Implementing NLO DGLAP evolution in parton showers

“…How this approach maps onto NLO DGLAP evolution was briefly addressed in [45], which furthermore introduced final-state double-gluon radiation into this formalism. In addition to this, NLO splitting functions have been recomputed using a novel regularization scheme [46,47], with the aim to improve parton-shower simulations. The dependence of NLO matching terms on the parton-shower evolution variable has also been investigated [48].…”