Scalar quarkonium masses and mixing with the lightest scalar glueball

Abstract

We evaluate the continuum limit of the valence ͑quenched͒ approximation to the mass of the lightest scalar quarkonium state, for a range of different quark masses, and to the mixing energy between these states and the lightest scalar glueball. Our results support the interpretation of f 0 (1710) as composed mainly of the lightest scalar glueball.

Scalar glueball, scalar quarkonia, and their mixing

“…Based on their lattice calculations of the quenched scalar glueball mass at 1625(94) MeV at the infinite volume and continuum limits [13] and the ss meson mass in the connected insertion (no annihilation) at ∼ 1500 MeV, Lee and Weingarten [14,15] considered a mixing scheme where f 0 (1500) is an almost pure ss meson and f 0 (1710) and f 0 (1370) are primarily the glueball and uū + dd meson respectively, but with substantial mixing between the two (∼ 25% for the small component). With the effective chiral Lagrangian approach, Giacosa et al [16] performed a fit to the experimental masses and decay widths of f 0 (1710), f 0 (1500) and f 0 (1370) and found four possible solutions, depending on whether the direct decay of the glueball component is considered.…”

UKQCD's latest results for the static quark potential and light hadron spectrum with O(a) improved dynamical fermions

“…2 Table 2 ground state contributions so that the systematic error on E from this assumption is hard to estimate. The mixing estimated by ref [4] is similar in magnitude at these lattice parameters (E ≈ 0.3 GeV) but they claim that on extrapolation to the continuum limit a much smaller value is obtained. Here we are using clover improvement so order a effects are suppressed.…”

“…Using the glueball mass of 0.97(4) from ref. [4] and scalar qq mass of 1.48(15) from fitting the connected correlations, we are able to fit the disconnected correlation and the hairpin-Wilson loop correlation from t-values of 1 to 3 with a mixing given by Ea = 0.4 assuming N f = 2. This fit (see fig.…”

“…Within the quenched approximation, it is possible to estimate this mixing [4]. We make a preliminary study in the quenched approximation at β = 5.7 of 100 configurations on 12 3 24 lattices with SW-clover valence quarks having κ = 0.14077 with C SW = 1.57 (here a ≈ 1 GeV and the quark mass is close to strange).…”

Lattice Lattice study of “f0 (600) or σ”

“…In quenched QCD, DeTar and Kogut first measured the σ meson screening mass in a lattice simulation [5], Alford and Jaffe discussed the possible light scalar mesons asq 2 q 2 states [6], and masses and mixing of qq states and a glueball have been investigated by Lee and Weingarten [7]. However, as we have already reported in the previous proceedings [8], the connected and disconnected diagrams give almost the same amount of the contributions, indicating that the dynamical quark effect seems to be essential in the calculation.…”