Jets in e+A SIDIS and Denominator Regularization

Abstract

We compute the in-medium jet broadening to leading order in energy in the opacity expansion. At leading order in αs the elastic energy loss gives a jet broadening that grows with ln E. The next-to-leading order in αs result is a jet narrowing, due to destructive LPM interference effects, that grows with ln2 E. We find that in the opacity expansion the jet broadening asymptotics are— unlike for the mean energy loss—extremely sensitive to the correct treatment of the finite kinematics of the problem; integrating over all emitted gluon transverse momenta leads to a prediction of jet broadening rather than narrowing. We compare the asymptotics from the opacity expansion to a recent twist-4 derivation and find a qualitative disagreement: the twist-4 derivation predicts a jet broadening rather than a narrowing. Comparison with current jet measurements cannot distinguish between the broadening or narrowing predictions. We comment on the origin of the difference between the opacity expansion and twist-4 results.We also introduce a novel regularization scheme in quantum field theory, denominator regularization (den reg). Den reg is as simple to apply as the usual dimensional regularization, works simply with a minimal subtraction scheme, and manifestly 1) maintains Lorentz invariance, 2) maintains gauge invariance, 3) maintains supersymmetry, 4) correctly predicts the axial anomaly, and 5) yields Green functions that satisfy the Callan-Symanzik equation. Den reg also naturally enables regularization in asymmetric spacetimes, finite spacetimes, curved spacetimes, and in thermal field theory.