Mass Effects in the Quark–gluon Decays of Heavy Paraquarkonia

Abstract

Quark-gluon decays of heavy paraquarkonia 1 S 0 (QQ) →qqg are investigated with account of the masses of final quarks. The decay widths and the energy distributions of the final quarks and gluons are calculated in dependence on the relative quark masses. The strong collinear enhancement of the gluon energy distribution at the end of the spectrum is shown to take place in all such decays of η c and η b mesons except the decay η b →ccg. The total decay width is shown to have an essential dependence on the final quark masses. The corresponding branching ratios of η c and η b mesons are numerically estimated with a good agreement of Br(η c →ssg) with experimental data on η c decays.Mod. Phys. Lett., 1998, V. A13, No. 23, P. * E-mail: asmirnov@univ.uniyar.ac.ru Many-partical decays of heavy quarkonia such as 1 S 0 (QQ) → 3g,qqg, 3 S 1 (QQ) → 4g,qqgg depend on the 3g-andqqg-interactions of the final quarks and gluons and can give the useful information about these interactions. In particular, these interactions give rise to the specific thrust [1,2] and invariant masses [3,4] distributions, to the acomplanarity of the fourparticle decays [5], to the collinearization effect of final gluons [6], etc. It should be noted, however, that such effects can be essentially affected by masses of final quarks. For example, the four-particle quark-gluon decays of the orthobottomonium with the production ofūu-,dd-orss-pairs exhibit a collinear enhancement whereas this effect in such decays with the production ofcc-pair is absent because of the relatively large mass of c-quark [7]. Hence, the effect of the final quark masses can be essential in the decays of heavy quarkonia with production ofqq-pairs and it should be taken into account in investigations of such decays.In this letter the quark-gluon decay of heavy paraquarkonium 1 S 0 (QQ) → qqg is investigated taking account of the masses of final quarks. The differential and total decay widths are calculated in tree approximation in dependence on the final quark masses and are discussed in comparison with the experimental data on η c decays. The branching ratios of η b decay are also predicted and discussed.The decay of a heavy paraquarkonium into a quark-antiquark pair and a gluon 1 S 0 (QQ) →qqg is described by two graphs shown in Fig. 1. The amplitude of this process in the limit of static quarks in the quarkonium can be presented in the form:where t a are the generators of the color group SU(N c ), a = 1, 2, . . . , N 2 c − 1 and α, β = 1, 2, . . . , N c are the color indices, g s is the strong charge, ψ(r) is the nonrelativistic wave function of a paraquarkonium in the coordinate space, ω, ε 1 and ε 2 are the energies of the gluon, quark and antiquark respectively, (σ , e a µ and k µ are the polarization and wave vectors of the gluon, p = p 1 + p 2 , p 1µ and p 2µ are four-momenta of the final quark and antiquark, P µ ≃ (2m, 0) is the four-momentum of a paraquarkonium in its rest frame, and m is the mass of the heavy quark in the quarkonium. 2The differential pr...

Observation prospects of leptonic and Dalitz decays of pseudoscalar quarkonia

“…The analytic expressions for the energy distributions of the gluon, quark and the integrated decay rate, has been presented in Ref. [25]. In the following, we will independently derive the corresponding energy spectra of the photon, lepton and the integrated decay rate for the η Q Dalitz decay process.…”

“…( 4), ( 5), (6) in Ref. [25]. The process η b → ccg has also been studied numerically in [15,26,27].…”

“…Note that the quark energy distributions in various η Q → q qg processes, have not been correctly displayed in Fig.3of[25], due to some input mistakes.…”