Hadron spectra of finite-density QC${}_2$D

Abstract

We investigate the chemical-potential dependence of hadron spectra in two-color QCD using first-principles lattice simulations. We compute two-point correlation functions for all allowed hadronic operators by newly including the contributions from disconnected diagrams, and extract the corresponding effective masses. In the meson sector, the mass hierarchy in the hadronic phase (normal vacuum) is found to be $m_{\pi }\lesssim m_{\eta }<m_{\sigma }(\mathrm{noisy})<m_{\rho }\sim m_{\omega }\ll m_{a_1}$, which is similar to that in three-color QCD. In the superfluid phase, this hierarchy is modified, and with increasing density it changes to $m_{\sigma }(\mathrm{noisy})<m_{a_1}<m_{\rho }<m_{\pi }\sim m_{\eta }(\mathrm{noisy})\ll m_{\omega }(\mathrm{noisy})$. In the diquark sector, the ordering remains as $m_{NG}\lesssim m_{I=0,S}<m_{I=1,AV}<m_{I=0,PS}\lesssim m_{I=0,V}$ in both phases, and the Nambu--Goldstone mode associated with spontaneous breaking of $U(1{)}_B$ is confirmed to be nearly massless. Furthermore, by comparing correlators for chiral partners, we find indications of chiral symmetry restoration at high density.

Comments: 42pages, 30figures; (ver2) Minor improvements; correlation-function data made publicly available on Zenodo (Ref.[66])