Mixing of scalar glueballs and flavour-singlet scalar mesons

TL;DR

The paper tackles how scalar glueballs mix with flavour-singlet scalar mesons in lattice QCD. It develops and applies a variational framework and mixing-formalism to extract the mixing strength $x_{00}$ in quenched QCD and then directly measures the mixed spectrum in full QCD with two dynamical flavours, uncovering a notably light flavour-singlet scalar state. The results indicate significant mixing effects that shift scalar masses, highlighting the importance of lattice spacing and discretization choices. Overall, the work demonstrates both the feasibility of extracting hadronic mixing strengths on the lattice and the physical impact of mixing on the scalar meson spectrum, while providing practical variance-reduction techniques for challenging disconnected diagrams.

Abstract

We discuss in detail the extraction of hadronic mixing strengths from lattice studies. We apply this to the mixing of a scalar glueball and a scalar meson in the quenched approximation. We also measure correlations appropriate for flavour-singlet scalar mesons using dynamical quark configurations from UKQCD. This enables us to compare the results from the quenched study of the mixing with the direct determination of the mixed spectrum. Improved methods of evaluating the disconnected quark diagrams are also presented.

Figures (5)

• Figure 1: We illustrate correlations among scalar glueballs (created by a closed Wilson loop) and scalar mesons made from quark-antiquark. Clockwise from the top left: the disconnected fermionic correlation ($D^{ss}$), the cross correlation of a fermion loop with a Wilson loop ($C^{ms}$ or $H$), the correlation of Wilson loops ($C^{mm}$) and the connected fermionic correlation (${\cal C}^{ss}$).
• Figure 2: Quenched scalar correlations with quark masses approximately strange. Here HH is the connected mesonic correlation (${\cal C}^{ss}$), GG is the glueball correlation ($C^{mm}$), DD is the disconnected mesonic correlation ($D$) and GD is the cross correlation between glueball and meson operators ($H$). Lattice results are illustrated for one glueball operator and one (local) meson operator. The curves are a simple mixing model, as described in the text.
• Figure 3: The mixing coefficient $x_{00}$ is determined in lattice units with $a^{-1} \approx 1$ GeV, at each $t$ value, from quenched scalar correlations with quark masses approximately strange: DD is the disconnected mesonic correlation ($D$) and GD is the cross correlation between glueball and meson operators ($H$).
• Figure 4: As fig. \ref{['mixing_ratio']} but with quenched scalar correlations with quark masses approximately twice strange.
• Figure 5: The scalar mass versus $a^2$. The quenched results DForcmtukqcdggf11 are for the scalar glueball and are shown by boxes. The results from $N_f=2$ flavours of sea quark are from glueballs SESAM (crosses from SESAM) and the lightest flavour singlet scalar we find here (circles).