Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space

Journal Article · Tue Jun 01 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.114009· OSTI ID:21407955

Kawamura, Hiroyuki ^[1]; Tanaka, Kazuhiro ^[2]

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1. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 3BX (United Kingdom)
2. Department of Physics, Juntendo University, Inba-gun, Chiba 270-1695 (Japan)

The B-meson distribution amplitude (DA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory, corresponding to a long-distance component in the factorization formula for exclusive B-meson decays. The evolution equation for the B-meson DA is governed by the cusp anomalous dimension as well as the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these anomalous dimensions give the ''quasilocal'' kernel in the coordinate-space representation. We show that this evolution equation can be solved analytically in the coordinate space, accomplishing the relevant Sudakov resummation at the next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite simple form of our solution which determines the B-meson DA with a quark-antiquark light-cone separation t in terms of the DA at a lower renormalization scale {mu} with smaller interquark separations zt (z{<=}1). This formula allows us to present rigorous calculation of the B-meson DA at the factorization scale {approx}{radical}(m{sub b{Lambda}QCD}) for t less than {approx}1 GeV{sup -1}, using the recently obtained operator product expansion of the DA as the input at {mu}{approx}1 GeV. We also derive the master formula, which reexpresses the integrals of the DA at {mu}{approx}{radical}(m{sub b{Lambda}QCD}) for the factorization formula by the compact integrals of the DA at {mu}{approx}1 GeV.

• OSTI ID: 21407955
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 11; Other Information: DOI: 10.1103/PhysRevD.81.114009; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANOMALOUS DIMENSION
B MESONS
B QUARKS
C QUARKS
CUSPED GEOMETRIES
DISTRIBUTION
FACTORIZATION
GEV RANGE 01-10
LIGHT CONE
MATHEMATICAL SOLUTIONS
MATRIX ELEMENTS
OPERATOR PRODUCT EXPANSION
PARTICLE DECAY
QUARK-ANTIQUARK INTERACTIONS
RENORMALIZATION
SIMULATION
T QUARKS
BEAUTY MESONS
BEAUTY PARTICLES
BOSONS
CHARM PARTICLES
DECAY
ELEMENTARY PARTICLES
ENERGY RANGE
FERMIONS
GEV RANGE
HADRONS
INTERACTIONS
MAGNETIC FIELD CONFIGURATIONS
MESONS
OPEN CONFIGURATIONS
PARTICLE INTERACTIONS
POSTULATED PARTICLES
PSEUDOSCALAR MESONS
QUARKS
SCALE DIMENSION
SERIES EXPANSION
SPACE-TIME
TOP PARTICLES