Renormalisation of heavy-light light ray operators

Abstract

We calculate the renormalisation of different light ray operators with one light degree of freedom and a static heavy quark. Both $2\to 2$- and $2\to 3$-kernels are considered. A comparison with the light-light case suggests that the mixing with three-particle operators is solely governed by the light degrees of freedom. Additionally we show that conformal symmetry is already broken at the level of the one loop counterterms due to the additional UV-renormalisation of a cusp in the two contributing Wilson-lines. This general feature can be used to fix the $2\to 2$-renormalisation kernels up to a constant. Some examples for applications of our results are given.

23 pages, 5 figures; v2: changed some wording, added a few references and one appendix concerning some subtleties related to gauge fixing and ghost terms; v3: clarified calculation in section 3.2., added an explicit calculation in section 5.2, corrected a few typos and one figure, added a few comments, results unchanged, except for typesetting matches version to appear in JHEP

References in corpus (8)

• Form Factors from Light-Cone Sum Rules with B-Meson Distribution Amplitudes
• Modelling light-cone distribution amplitudes from non-relativistic bound states
• Baryon Operators of Higher Twist in QCD and Nucleon Distribution Amplitudes
• Distribution Amplitudes of the Lambda_b Baryon in QCD
• Renormalization of Twist-Four Operators in QCD
• Three-particle contributions to the renormalisation of B-meson light-cone distribution amplitudes
• Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space
• Heavy Meson Distribution Amplitudes of Definite Geometric Twist with Contribution of 3-Particle Distribution Amplitudes

Cited by in corpus (15)

• Light-Cone Distribution Amplitudes for Heavy-Quark Hadrons
• Form Factors for Lambda_b -> Lambda Transitions in SCET
• QCD corrections to $B\to \pi$ form factors from light-cone sum rules
• Perturbative Corrections to ${\Lambda }_b\to \Lambda$ Form Factors from QCD Light-Cone Sum Rules
• Higher-twist B-meson Distribution Amplitudes in HQET
• Light-Cone Sum Rules for $B\to K\pi$ Form Factors and Applications to Rare Decays
• B-Meson Light-Cone Distribution Amplitude: Perturbative Constraints and Asymptotic Behaviour in Dual Space
• The NLO twist-3 contributions to $B\to \pi$ form factors in $k_T$ factorization
• Two-loop evolution equation for the B-meson distribution amplitude
• Conformal symmetry of the Lange-Neubert evolution equation
• Integrability of the evolution equations for heavy-light baryon distribution amplitudes
• Evolution equation for the higher-twist B-meson distribution amplitude
• Renormalization of twist-four operators in light-cone gauge
• Integrability in heavy quark effective theory
• Scale-dependence of the $B$-meson LCDA beyond leading order from conformal symmetry