Hybrid Charmonium at Finite Temperature

TL;DR

This work investigates the finite-temperature fate of the exotic charmonium state with $J^{PC}=1^{-+}$ by applying lattice QCD techniques—specifically distillation with a large operator basis—to a set of anisotropic, $N_f=2+1$ ensembles. It develops and uses symmetry-aware operator construction and the optimal distillation profiles to overcome finite-$T$ challenges in extracting spectra via the GEVP, and employs reconstructed correlators to assess spectral changes without full spectral reconstruction. The main finding is that the $T_1^{-+}$ ground state is more strongly affected by temperature than the $A_1^{-+}$ counterpart, with groundwork laid for future spectral analyses and extensions to Generation 3 ensembles. The work demonstrates a viable path to studying hot QCD hybrids and sets the stage for more detailed spectral investigations and higher-precision finite-temperature spectroscopy.

Abstract

Drawing upon well established zero-temperature techniques, we present, for the first time in a lattice calculation, insight into the fate of the $1^{-+}$ exotic charmonium state at finite temperature. Specifically, using anisotropic FASTSUM ensembles we employ distillation with a wide operator basis which has been extensively used at zero-temperature by the Hadron Spectrum Collaboration to study the charmonium spectrum. The constant contribution to some finite-temperature temporal correlation functions requires particular care with the extended operator basis common to distillation setups and we discuss this effect. As an alternative to derivative based extended operators, we also consider the use of optimal distillation profiles at finite temperature for the first time. Finally, we remark on the temperature dependence of the $1^{-+}$ spectral function by consideration of the reconstructed correlator method.

Figures (3)

• Figure 1: Effective masses of the ground state $T_1^{-+}$$\left( 1^{-+} \right)$ charmonium at $N_\tau = 40$ using different operators labeled by the convention of Dudek-2010. The 8 and 1 mean the operator is either in the group of eight operators with $\{ \Gamma, \gamma_4 \} \neq 0$ or the single operator with $\{ \Gamma, \gamma_4 \} = 0$ as explained in Sec. \ref{['sec:Spectrum']}.
• Figure 2: Left: Effective masses of the ground state $T_1^{-+}$$\left( 1^{-+} \right)$ charmonium across all temperatures included in Table \ref{['table:Gen2']}. Right: Effective masses of the ground state $A_1^{-+}$$\left( 0^{-+} \right)$ charmonium at $N_t = 40$ from two GEVPs: using 3 operators from the available basis and using $\gamma_5$ with 7 different distillation profiles as described in Urrea-2022.
• Figure 3: Ratio of reconstructed correlator (using $N_t=40$ as the zero temperature) to lattice correlator described in Eq. \ref{['eqn:recon:ratio']} for the $A_1^{-+}$ ground state (left) and the $T_1^{-+}$ ground state (right). Note that the temperature dependence as indicated by the deviation from unity is much greater for the $T_1^{-+}$ than for the $A_1^{-+}$.