Tensor Glueball Photoproduction and Decay

Using vector meson dominance (VMD), tensor glueball photoproduction cross sections, asymmetries and widths are calculated. The predicted hadronic V V ′ decays are comparable for different vector meson (V = ρ, ω and φ) channels with the ωφ width the largest but the radiative ωγ and φγ decays are suppressed relative to ργ by over a factor of 2. This decay profile is distinct from typical meson branching rates and may be a useful glueball detection signature. Results are compared to a previous VMD scalar glueball study. Documenting hadron states with predominantly gluonic degrees of freedom, i.e. glueballs, has been a challenging and somewhat elusive pursuit. Even though such states are consistent with quantum chromodynamics (QCD) and predicted by both lattice simulations [1,2,3,4] and gluonic models [5,6], clear experimental evidence is lacking. The purpose of this letter is to motivate additional experimental investigations by providing estimates, based upon VMD, of tensor glueball photoproduction observables and also to detail a possible decay signature for hadronic states with a significant gluonic component. The latter entails comparable V V ′ hadronic widths, with the largest branch to ωφ that promptly goes to 3πKK̄, and somewhat suppressed ωγ and φγ radiative decays relative to ργ. As discussed below, this decay signature is not expected for hadrons with a predominantly quark structure. These results are essentially model-independent since they follow directly from the general principles Preprint submitted to Elsevier Science 9 February 2008 of VMD, which has been found to agree with more fundamental QCD based meson radiative calculations [7], and the flavor independence of quark-gluonic couplings. Consider the radiative decay f2 → V (k)γ(k) of a neutral tensor hadron with arbitrary quark, gluon structure and mass Mf . Here k, k ′ are the momenta of the photon and vector meson with mass MV (k ′2 = M V ). The most general, gauge invariant f2V γ vertex is [8,9] < γ(k)V (k′)|f2 >= ǫǫfAκλμν(k, k) , (1) Aκλμν(k, k )= 4 g1 M f Bκλμν + 2 g2 M f Cκλμν , (2) Bκλμν(k, k )= (gκλk · k − k κkλ)kμkν , (3) Cκλμν(k, k )= 2gκλkμkν + gλμk ′ κkν + gλνk ′ κkμ − gκμkλkν − gκνkλkμ − k · k′(gκμgλν + gκνgλμ) , (4) where ǫ, ǫ and f are the photon, vector meson and f2 polarization vectors and tensor, respectively. Note that there are two possible coupling constants, g1 and g2, which in VMD (also tensor meson dominance) are given by [8] g1 = 0, g2 = egf2V γ = e ∑ V ′ gf2V V ′ fV ′ , (5) with gf2V V ′ the f2V V ′ hadronic coupling constant, fV ′ the V ′ leptonic decay constant and the sum is over all vector meson contributions consistent with isospin conservation for the f2V V ′ vertex. The radiative decay widths are Γf2→V γ = 2 5 αeg 2 f2V γMf2(1− x) [1 + x 2 + x 6 ] , (6) and αe = e /4π = 1/137.036, x = M V /M 2 f2 . Focusing upon isoscalar tensor hadrons (If2 = 0) yields the radiative couplings gf2ργ = gf2ρρ fρ , f2 → ργ , (7) gf2ωγ = gf2ωω fω + gf2ωφ fφ , f2 → ωγ , (8) gf2φγ = gf2φφ fφ + gf2φω fω , f2 → φγ . (9) Since the ρ and ω masses are almost equal (Mρ0 = 775.8 MeV, Mω = 782.59