Charmonium-Glueball spectroscopy with improved hadron creation operators

Abstract

Construction of creation operators which can properly sample the underlying energy eigenstates remains a fundamental first step in lattice QCD spectroscopy calculations, particularly when the spectrum includes states with different composition such as mesons, glueballs, multi-particle states, etc. We tackle this issue in the study of the scalar glueball and charmonium mixing, where we use improved operators for both types of states to resolve the low-lying spectrum and identify the dominant composition of each state in a mass regime where the glueball is stable. We include derivative-based meson operators combined with distillation profiles, as well as glueball operators built from the chromo-magnetic field and its derivatives which retain angular momentum information from their continuum counterparts. We comment on the advantages of these operators, particularly on the construction and implementation of the glueball ones, thanks to which we identify the lightest iso-scalar state as glueball-dominated $0^{++}$.

Figures (12)

• Figure 1: Link variables involved in the calculation of $D^2_k B_i(\vec{x},t)$ for a fixed spatial derivative direction $\hat{k}$ and all components $i$. The red dot marks the spatial position $\vec{x}$ and the blue links indicate the links used for the derivative.
• Figure 2: Ground state effective masses coming from separate GEVPs. Red points come from a $3\times 3$ GEVP using $\Gamma = \mathbb{I}, \gamma_i \nabla_i, \gamma_0 \gamma_5 \gamma_i \mathbb{B}_i$. The red band is the corresponding plateau average. Blue and green points come from solving a $7\times 7$ GEVP for $\mathbb{I}$ and $\gamma_i \nabla_i$ respectively using distillation profiles. Black points come from building a $21\times 21$ correlation matrix including all three choices of $\Gamma$ and 7 profiles for each one and then pruning it down to an $8\times 8$ matrix to solve the GEVP. The black band is the corresponding plateau average. We omit the results from the $7\times 7$ GEVP using only $\gamma_0 \gamma_5 \gamma_i \mathbb{B}_i$ since the statistical uncertainties are much larger than for the other cases.
• Figure 3: Correlation matrices at $t = 2a$ using three choices of $\Gamma$ with standard distillation (up) and 7 profiles per $\Gamma$ (down).
• Figure 4: Low-lying $A_1^{++}$ iso-vector spectrum determined via different GEVPs. Left: Using $\Gamma = \mathbb{I}, \gamma_i \nabla_i$, $\gamma_0 \gamma_5 \gamma_i \mathbb{B}_i$ with standard distillation. Middle: Using $\Gamma = \mathbb{I}$ with 7 profiles. Right: Using $\Gamma = \mathbb{I}, \gamma_i \nabla_i$, $\gamma_0 \gamma_5 \gamma_i \mathbb{B}_i$ with 7 profiles for each $\Gamma$.
• Figure 5: Normalized correlation matrix taking the absolute value of the entries at $t=a$ using the alternative glueball operators at different levels of APE smearing. The operators $\mathcal{O}_i$ are defined in Eq. \ref{['eqn:GlueballOperators']}.