Gluonic and leptonic decays of heavy quarkonia and the determination of {alpha}{sub {ital s}}({ital m}{sub {ital c}}) and {alpha}{sub {ital s}}({ital m}{sub {ital b}})
- China Center for Advanced Science and Technology (World Laboratory), Beijing 100080 (People`s Republic of China)
- Department of Physics, Peking University, Beijing 100871 (Peoples Republic of China)
The determination of the QCD running coupling constants {alpha}{sub {ital s}}({ital m}{sub {ital c}}) and {alpha}{sub {ital s}}({ital m}{sub {ital b}}) is studied with heavy quarkonia {ital cc{vert_bar}} and {ital bb{vert_bar}} decays. The decay rates of {ital V}{implies}3{ital g} and {ital V}{implies}{ital e}{sup +}{ital e}{sup -} for {ital V}={ital J}/{psi} and {upsilon} are given in terms of the Bethe-Salpeter amplitudes. To the first-order relativistic correction of on-shell quarks, for the leptonic decay, we have {gamma}({ital V}{implies}{ital e}{sup +}{ital e}{sup -}) =(4{pi}{alpha}{sup 2}{ital e}{sub {ital Q}}{sup 2}/{ital m}{sub {ital Q}}{sup 2}){vert_bar}F{ital d}{sup 3}{ital q} [1-(2{ital q}{searrow}{sup 2}/3{ital m}{sub {ital Q}}{sup 2})]{psi}{sub S}{sub c}{sub h}({ital q}{searrow}){vert_bar}{sup 2}, which agrees with the NRQCD result, while for the gluonic decay we find {gamma}({ital V}{implies}3{ital g}) =[40({pi}{sup 2}-9){alpha}{sub {ital s}}{sup 3}({ital m}{sub {ital Q}})/81{ital m}{sub {ital Q}}{sup 2}{vert_bar}F{ital d}{sup 3}{ital q} [1-(2.95{ital q}{searrow}{sup 2}/{ital m}{sub {ital Q}}{sup 2})]{psi}{sub S}{sub c}{sub h}({ital q}{searrow}){vert_bar}{sup 2}. Here {psi}{sub S}{sub c}{sub h}({ital q}{searrow}) is the {ital QQ{vert_bar}} bound state wave function in momentum space, and {ital m}{sub {ital Q}} is the heavy quark mass. This result clearly shows that the relativistic correction (due to the {ital q}{searrow} {sup 2}/{ital m}{sub {ital Q}}{sup 2} term in the decay widths) suppresses the gluonic decay more severely than the leptonic decay {copyright} {ital 1995 The American Physical Society.}
- OSTI ID:
- 254183
- Journal Information:
- Physical Review, D, Vol. 53, Issue 1; Other Information: PBD: Jan 1996
- Country of Publication:
- United States
- Language:
- English
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