Soft-collinear effective theory and heavy-to-light currents beyond leading power

Abstract

An important unresolved question in strong interaction physics concerns the parameterization of power-suppressed long-distance effects to hard processes that do not admit an operator product expansion (OPE). Recently Bauer et al. have developed an effective field theory framework that allows one to formulate the problem of soft-collinear factorization in terms of fields and operators. We extend the formulation of soft-collinear effective theory, previously worked out to leading order, to second order in a power series in the inverse of the hard scale. We give the effective Lagrangian and the expansion of "currents" that produce collinear particles in heavy quark decay. This is the first step towards a theory of power corrections to hard processes where the OPE cannot be used. We apply this framework to heavy-to-light meson transition form factors at large recoil energy.

Heavy-to-light currents at NNLO in SCET and semi-inclusive decay

“…A generic heavy-to-light currentq Γ i b is represented in SCET by a set of non-local "twobody" and "three-body" [3][4][5][6] …”

“…The matrix elements of the currents, usually parameterized by several transition form factors, are also important inputs to the factorization formulae for non-leptonic B decays [1]. In the kinematic region where the hadronic final state has small invariant mass but large energy, softcollinear effective theory (SCET) [2,3] is the appropriate theoretical framework, with which transparent factorization formulae for the heavy-to-light form factors have been derived [4] (see also [5,6]). Thus, the accurate representation of the heavy-to-light currents in SCET is of particular interest.…”

Four-fermion production near the W pair-production threshold

“…The interactions of the collinear modes are given by soft-collinear effective theory [22][23][24]. There is nothing specifically new related to collinear modes in pair production, and we refer to [13] for further details.…”

Three-particle contributions to the renormalisation ofB-meson light-cone distribution amplitudes

“…This has been progressively achieved within the frameworks of QCD factorisation [1][2][3] and Soft-Collinear Effective Theory [4][5][6][7][8]. The hadronic input collecting soft physics are not only the form factors, but also the light-cone distribution amplitudes, defined generally as the matrix element of a non-local operator along a light-like direction.…”