Soft-Collinear Mode for Jet Rates in Soft-Collinear Effective Theory

Download or read book Soft-Collinear Mode for Jet Rates in Soft-Collinear Effective Theory written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose the addition of a new "soft-collinear" mode to soft collinear effective theory (SCET) below the usual soft scale to factorize and resum logarithms of jet radii R in jet cross sections. We consider exclusive 2-jet cross sections in e+e- collisions with an energy veto [Lambda] on additional jets. The key observation is that there are actually two pairs of energy scales whose ratio is R: the transverse momentum QR of the energetic particles inside jets and their total energy Q, and the transverse momentum [Lambda]R of soft particles that are cut out of the jet cones and their energy [Lambda]. The soft-collinear mode is necessary to factorize and resum logarithms of the latter hierarchy. We show how this factorization occurs in the jet thrust cross section for cone and kT-type algorithms at O([alpha]s) and using the thrust cone algorithm at O([alpha]$2\atop{s}$). We identify the presence of hard-collinear, in-jet soft, global (veto) soft, and soft-collinear modes in the jet thrust cross section. We also observe here that the in-jet soft modes measured with thrust are actually the "csoft" modes of the theory SCET+. We dub the new theory with both csoft and soft-collinear modes "SCET++". We go on to explain the relation between the "unmeasured" jet function appearing in total exclusive jet cross sections and the hard-collinear and csoft functions in measured jet thrust cross sections. We do not resum logs that are non-global in origin, arising from the ratio of the scales of soft radiation whose thrust is measured at Q${{\tau}}$/R and of the soft-collinear radiation at 2[Lambda]R. Their resummation would require the introduction of additional operators beyond those we consider here. The steps we outline here are a necessary part of summing logs of R that are global in nature and have not been factorized and resummed beyond leading-log level previously.