科研之友
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摘要
The P-wave charmonium decays h(c) -> gamma eta(()'()) are revisited by taking into account relativistic corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, in which the involved one-loop integrals are evaluated analytically. Intriguingly, from both the quark-antiquark content and the gluonic content of eta(()'()), the relativistic corrections make significant contributions to the decay rates of h(c) -> gamma eta(()'()). By comparison with the leading-order contributions from the quark-antiquark content (one-loop level), the ones from the gluonic content (tree level) are also important, which is compatible with the conclusion obtained without relativistic corrections. Usually, for the eta production processes, the predicted branching ratios are sensitive to the angle of eta-eta' mixing. As an illustration, using the Feldmann-Kroll-Stech result about the mixing angle phi = 39.3 degrees +/- 1.0 degrees as input, we find that the predicted ratio R-hc = B(h(c) -> gamma eta)/B(h(c) -> gamma eta') is much smaller than the experiment measurement, while, with phi = 33.5 degrees +/- 0.9 degrees extracted from the asymptotic limit of the gamma*gamma - eta' transition form factor, we obtain R-hc = 30.3%, consistent with R-hc(exp) = (30.7 +/- 11.3 +/- 8.7)%. As a cross-check, the mixing angle phi = 33.8 degrees +/- 2.5 degrees is extracted by employing the ratio R-hc, and a brief discussion on the difference in the determinations of phi is given.
