Effective Lagrangian for two-photon and two-gluon decays of P-wave heavy quarkonium {chi}{sub c0,2} and {chi}{sub b0,2} states

Journal Article · Fri May 01 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.094016· OSTI ID:21308420

Lansberg, J P ^[1]; Pham, T N ^[2]

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1. SLAC National Accelerator Laboratory, Theoretical Physics, Stanford University, Menlo Park, California 94025 (United States)
2. Centre de Physique Theorique, CNRS, Ecole Polytechnique, 91128 Palaiseau, Cedex (France)

In the traditional nonrelativistic bound state calculation, the two-photon decay amplitudes of the P-wave {chi}{sub c0,2} and {chi}{sub b0,2} states depend on the derivative of the wave function at the origin, which can only be obtained from potential models. However, by neglecting the relative quark momenta, the decay amplitude can be written as the matrix element of a local heavy quark field operator which could be obtained from other processes or computed with the QCD sum rules technique or lattice simulation. Following the same lines as in recent work for the two-photon decays of the S-wave {eta}{sub c} and {eta}{sub b} quarkonia, we show that the effective Lagrangian for the two-photon decays of the P-wave {chi}{sub c0,2} and {chi}{sub b0,2} states is given by the heavy quark energy-momentum tensor local operator or its trace, the QQ scalar density, and that the expression for {chi}{sub c0} two-photon and two-gluon decay rates is given by the f{sub {chi}{sub c}{sub 0}} decay constant and is similar to that of {eta}{sub c} which is given by f{sub {eta}{sub c}}. From the existing QCD sum rules value for f{sub {chi}{sub c}{sub 0}}, we get 5 keV for the {chi}{sub c0} two-photon width, somewhat larger than the measurements, but possibly with large uncertainties.

• OSTI ID: 21308420
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 9 Vol. 79; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
B QUARKS
BOUND STATE
C QUARKS
COMPUTERIZED SIMULATION
DECAY AMPLITUDES
ENERGY-MOMENTUM TENSOR
FIELD OPERATORS
GLUONS
LAGRANGIAN FUNCTION
LATTICE FIELD THEORY
MATRIX ELEMENTS
P WAVES
PARTICLE DECAY
PHOTONS
QUANTUM CHROMODYNAMICS
QUARKONIUM
S WAVES
SUM RULES
T QUARKS
WAVE FUNCTIONS