Soft-Collinear Effective Theory: Recent Results and Applications

Soft-collinear effective theory (SCET) has become a standard tool to study the factorization of shortand long-distance effects in processes involving low-energetic (soft) particles and high-energetic/low-virtuality (collinear) modes. In this contribution I give a brief overview on recent results for inclusive and exclusive B decays and on applications in collider physics. [Contributed to “Quark Confinement and the Hadron Spectrum”, Sep 2008, Mainz, Germany] ar X iv :0 81 1. 45 90 v1 [ he pph ] 2 7 N ov 2 00 8 1 Factorization and SCET Our ability to provide precise theoretical predictions for high-energy processes in particle physics heavily relies on the concept of factorization, i.e. the systematic separation of dynamical effects from short and long distances. Especially for strong interactions – if factorization holds – the effects of heavy particles and/or highly virtual radiative corrections can be calculated in perturbative Quantum Chromodynamics (QCD), while the long-distance physics of light quarks and gluons can be encoded in (process-independent) hadronic matrix element of composite operators, which can be further studied using non-perturbative methods. A general feature of factorization is the appearance of a factorization scale μ that relates the infrared (IR) divergences, appearing in loop corrections to short-distance amplitudes/cross sections, and the ultraviolet (UV) divergences of composite operators defining the long-distance matrix elements, such that the scale dependence cancels to any given order in perturbation theory. A particularly interesting situation arises in processes like, for instance, B → Xsγ, where Xs denotes a hadronic jet containing a light strange quark with energy of order mb/2 and invariant mass of order √ ΛQCDmb. Here, the infrared divergences of the short-distance b → sγ vertex corrections can be identified as coming from quarks and gluons being either soft (|k| ∼ ΛQCD) or collinear to the hadronic jet (k ‖ pμX). The interactions of the b-quark with soft degrees of freedom can be expanded in the small parameter ΛQCD/mb, and the remaining non-analytic dependence on the b-quark mass mb can be calculated within the well-known heavy-quark effective theory (HQET). The presence of additional collinear modes leads to new phenomena [1]: • The b→ s form factors contain Sudakov double logarithms ln2(pX/mb). • The propagation of a collinear quark in the soft background is described by a jet function. • The partial rate depends on the residual momentum of the b-quark, which is encoded in a so-called shape function (SF), i.e. the parton distribution function (PDF) for the B-meson. Again, the expansion in 1/mb can be formalized in terms of an effective theory, SCET [2, 3]. To this end, one includes separate field operators for soft and collinear modes, with soft-collinear vertices being multi-pole expanded according to the power-counting of momenta/wave-lengths in the different light-cone directions [4]. The short-distance coefficient functions and the jet function can be calculated by perturbative matching calculations. The renormalization-group (RG) running in SCET resums the large Sudakov logarithms between the hard scale (mb) and the jet scale (|pX |) [5], where one finally matches onto (non-local) HQET operators that define the b-quark PDF.