Systematic improvement of parton showers with effective theory

Abstract

We carry out a systematic classification and computation of next-to-leading order kinematic power corrections to the fully differential cross section in the parton shower. To do this we devise a map between ingredients in a parton shower and operators in a traditional effective field theory framework using a chain of soft-collinear effective theories. Our approach overcomes several difficulties including avoiding double counting and distinguishing approximations that are coordinate choices from true power corrections. Branching corrections can be classified as hard-scattering, that occur near the top of the shower, and jet-structure, that can occur at any point inside it. Hard-scattering corrections include matrix elements with additional hard partons, as well as power suppressed contributions to the branching for the leading jet. Jet-structure corrections require simultaneous consideration of potential 1 → 2 and 1 → 3 branchings. The interference structure induced by collinear terms with subleading powers remains localized in the shower. * Electronic address:

Factorization and resummation for dijet invariant mass spectra

“…The virtuality of the csoft modes is 19) which is the intermediate soft scale we already encountered. Hence, the main feature of SCET + is that its soft sector contains two separate degrees of freedom, a csoft mode with virtuality m 4 /t, and a usoft mode with virtuality m 4 /Q 2 .…”

“…Note that for the hard matching coefficient, the kinematic situation of t ≪ s ij has been addressed before [17][18][19] using a two-step matching procedure similar to our matching step at the scale √ t. It was shown through an explicit one-loop calculation that this matching separates the two scales Q 2 and t in the hard function from one another. In App.…”

“…The jet functions satisfy the RGE 18) with the anomalous dimensions 19) where Γ cusp [α s ] is the universal cusp anomalous dimension [32] given in Eq. (C8), and the non-cusp terms are given in Eq.…”

“…The Lagrangians for csoft quarks and gluons are simply scaled down versions of the original n t collinear quark and gluon Lagrangians, L 19) where the csoft covariant derivatives are defined exactly as in Eq. (3.12) but in terms of csoft gluons.…”

Jet quenching from QCD evolution

“…These are well-known and reproduced using the SCET collinear Lagrangian [15,70]. The real emission contribution of the splitting kernels are calculated from the tree level diagrams of 1 → 2 splitting.…”