Parton distribution functions in the context of parton showers

Abstract

When the initial state evolution of a parton shower is organized according to the standard "backward evolution" prescription, ratios of parton distribution functions appear in the splitting probabilities. The shower thus organized evolves from a hard scale to a soft cutoff scale. At the end of the shower, one expects that only the parton distributions at the soft scale should affect the results. The other effects of the parton distributions should have cancelled. This means that the kernels for parton evolution should be related to the shower splitting functions. If the initial state partons can have non-zero masses, this requires that the evolution kernels cannot be the usual MS kernels. We work out what the parton evolution kernels should be to match the shower evolution contained in the parton shower event generator Deductor, in which the b and c quarks have non-zero masses.

Collinear and TMD quark and gluon densities from parton branching solution of QCD evolution equations

“…Charge conjugation and SU(N f ) flavor symmetries imply that the splitting functions P ab obey the following relations to all orders, 10) where the superscripts N S and S stand respectively for non-singlet and singlet. Therefore, P ab has three independent quark-gluon or gluon-gluon components (P qg , P gq and P gg ) and four independent quark-quark components (the N S components P N S qq , P N S qq and the S components P S qq , P S qq ).…”

“…While great progress has been achieved in the last decade on matching and merging methods [5][6][7] to combine parton showers with perturbative calculations through next-to-leading order (NLO), important open questions still remain, both conceptual and technical, on the appropriate use of parton distribution functions in parton showers (see e.g. [8][9][10][11]) and on the treatment of the shower's transverse momentum kinematics (see e.g. [12][13][14]).…”

Ordering variable for parton showers

“…[1]. One of these features is that the algorithm uses non-zero masses for initial state partons, which requires modified evolution equations for the parton distribution functions, as described in a separate companion paper [7]. The second feature is the choice of shower evolution variable, which is the subject of this paper.…”

“…(We discuss this in some detail in ref. [7].) Of course, if what we want is a calculation using a parton shower of a single observable with a very large scale Q 2 , we do not need to choose V 2 much smaller than Q 2 .…”

“…(3.31) includes all four diagrams for emission from either parton l or parton k in the amplitude and the conjugate amplitude, calculated in the limitp g = λP g with λ → 0. We introduce a partitioning function A lk with the properties that A lk > 0 and A lk + A kl = 1 as follows 7 …”