TY - JOUR
T1 - Complete basis for power suppressed collinear-ultrasoft operators
AU - Pirjol, Dan
AU - Stewart, Iain W.
PY - 2003
Y1 - 2003
N2 - We construct operators that describe power corrections in mixed collinear-ultrasoft processes in QCD. We treat the ultrasoft-collinear Lagrangian to [Formula Presented] and heavy-to-light currents involving collinear quarks to [Formula Presented] including new three body currents. A complete gauge invariant basis is derived which has a full reduction in Dirac structures and is valid for matching at any order in [Formula Presented] The full set of reparametrization invariance (RPI) constraints is included, and is found to restrict the number of parameters appearing in Wilson coefficients and to rule out some classes of operators. The QCD ultrasoft-collinear Lagrangian has two [Formula Presented] operators in its gauge invariant form. For the [Formula Presented] heavy-to-light currents there are [Formula Presented] subleading (scalar, pseudoscalar, vector, axial-vector, tensor) currents, where [Formula Presented] have coefficients that are not determined by RPI. In a frame where [Formula Presented] and [Formula Presented] the total number of currents reduces to [Formula Presented] but the number of undetermined coefficients is the same. The role of these operators and universality of jet functions in the factorization theorem for heavy-to-light form factors is discussed.
AB - We construct operators that describe power corrections in mixed collinear-ultrasoft processes in QCD. We treat the ultrasoft-collinear Lagrangian to [Formula Presented] and heavy-to-light currents involving collinear quarks to [Formula Presented] including new three body currents. A complete gauge invariant basis is derived which has a full reduction in Dirac structures and is valid for matching at any order in [Formula Presented] The full set of reparametrization invariance (RPI) constraints is included, and is found to restrict the number of parameters appearing in Wilson coefficients and to rule out some classes of operators. The QCD ultrasoft-collinear Lagrangian has two [Formula Presented] operators in its gauge invariant form. For the [Formula Presented] heavy-to-light currents there are [Formula Presented] subleading (scalar, pseudoscalar, vector, axial-vector, tensor) currents, where [Formula Presented] have coefficients that are not determined by RPI. In a frame where [Formula Presented] and [Formula Presented] the total number of currents reduces to [Formula Presented] but the number of undetermined coefficients is the same. The role of these operators and universality of jet functions in the factorization theorem for heavy-to-light form factors is discussed.
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U2 - 10.1103/PhysRevD.67.094005
DO - 10.1103/PhysRevD.67.094005
M3 - Article
AN - SCOPUS:0038575176
SN - 1550-7998
VL - 67
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 9
ER -