S-wave flavor-singlet meson mixing in QCD with light and charm quarks

Abstract

We investigate the mixing between flavor-singlet light meson and charmonium operators in the S-wave channels, i.e. pseudo-scalar and vector channel, at two different pion masses. We measure statistically significant non-zero correlations between operators with different quark content corresponding to off-diagonal entries of a flavor-singlet mixing correlation matrix. By solving a GEVP we extract the low-lying energy spectrum and compare it with the one obtained by the different types of operators separately. We also calculate the overlaps between the states created by different operators and the energy eigenstates of the theory and find that all types of operators contribute to resolve the states of interest.

Figures (22)

• Figure 1: Plateau mass determination for the $\eta_c$ using only quark-connected correlation functions in ensemble A1. The lower left panel shows the result of the constant term in the constant + exponential fit as a function of $t_{low}$. The right panel corresponds to the same but for the constant fit. The points highlighted in the black and red shaded regions of the lower panels correspond to the values we take as the constant terms for these fits.
• Figure 2: Plateau mass determination for the $h_c$ using only quark-connected correlation functions in ensemble A1. The panels are organized as in Fig. \ref{['fig:Fits_etaC_A1']}.
• Figure 3: Selected off-diagonal pseudoscalar correlations between the light meson and charmonium operators in ensemble A1. Indices $0,...,4$ label charmonium operators and $5,...,9$ light meson operators.
• Figure 4: Selected off-diagonal pseudoscalar correlations between the light meson and charmonium operators in ensemble A1-heavy. Indices $0,...,4$ label charmonium operators and $5,...,9$ light meson operators.
• Figure 5: Effective masses for the two lightest pseudoscalar light meson and charmonium states calculated with and without taking into account the mixing between both types of operators in ensemble A1.