Factorization for radiative heavy quarkonium decays into scalar Glueball

Abstract

We establish the factorization formula for scalar Glueball production through radiative decays of vector states of heavy quarkonia, e.g. J/ψ, ψ(2S) and Υ(nS), where the Glueball mass is much less than the parent heavy quarkonium mass. The factorization is demonstrated explicitly at one-loop level through the next-to-leading order (NLO) corrections to the hard kernel, the non-relativistic QCD (NRQCD) long-distance matrix elements (LDMEs) of the heavy quarkonium, and the light-cone distribution amplitude (LCDA) of scalar Glueball. The factorization provides a comprehensive theoretical approach to investigate Glueball production in the radiative decays of vector states of heavy quarkonia and determine the physic nature of Glueball. We discuss the scale evolution equation of LCDA for scalar Glueball. In the end, we extract the value of the decay constant of Scalar Glueball from Lattice QCD calculation and analyze the mixing effect among f 0 (1370), f 0 (1500) and f 0 (1710).

Study of ϒ(1S) radiative decays to γπ+Lees1, Poireau2, Tisserand3 et al. 2018Phys. Rev. D9230View full textAdd to dashboardCite

“…The status of f 0 ð1370Þ is controversial [34] as this state could just be an effect related to the broad f 0 ð500Þ. Reference [10] estimates for f 0 ð1370Þ a branching fraction of Bðϒð1SÞ → γf 0 ð1370ÞÞ ¼ 3.2 þ1.8 −0.8 × 10 −5 , in the range of our measurement of the branching fraction of Bðϒð1SÞ → γðππS-waveÞÞ.…”

“…For this latter state, in the gluonium hypothesis, Ref. [10] computes a branching fraction of Bðϒð1SÞ → γf 0 ð1710Þ ¼ 0.96 þ0.55 −0.23 × 10 −4 . Taking into account the presence of additional, not well measured, f 0 ð1710Þ decay modes, our result is consistent with this predicted branching fraction as well as with the dominance of an ss decay mode.…”

“…Recently, detailed calculations have been performed on the production rates of the scalar glueball in the process Vð1 −− Þ → γG, where G indicates the scalar glueball and Vð1 −− Þ indicates charmonium or bottomonium vector mesons such as J=ψ, ψð2SÞ, or ϒð1SÞ [10][11][12][13].…”

Form factors for semileptonic Bc decays into η , η′ and glueballs

“…On the other hand, the axial U (1) anomaly will lead to a large mass difference between the η and η , which can not be ignored [19][20][21][22][23]. Besides, the flavor singlet and octet contents, even then the gluonium state will be mixed with each other with the identical J P C and form the physical η ( ) states [19][20][21][22][23][24]. The η meson is viewed as the mixing state between flavor singlet and octet contents, and the gluonium content is usually suppressed.…”

Fully-heavy tetraquark spectra and production at hadron colliders

“…Using the LDMEs of S-wave charmonium, bottomonium, and B c meson in Refs. [68,[71][72][73], the fully heavy tetraquark hadroproduction cross section can be obtained as…”