Pseudo Goldstone spectrum of 2-colorQCDat finite density

We examine the spectrum of two-color lattice QCD with one staggered quark field (four flavors) at a finite chemical potential $\left(\mu \right)$ for quark number, on a ${12}^3\times 24$ lattice. First we present evidence that the system undergoes a transition to a state with a diquark condensate, which spontaneously breaks quark number at $\mu {=m}_{\pi }/2,$ and that this transition is mean field in nature. We then examine the three states that would be Goldstone bosons at $\mu =0\mathrm{}$ for zero Dirac and Majorana quark masses. The predictions of chiral effective Lagrangians give a good description of the behavior of these masses for $\mu <m_{\pi }/2.\mathrm{}$ Except for the heaviest of these states, these predictions diverge from our measurements, once $\mu$ is significantly greater than $m_{\pi }/2.\mathrm{}$ However, the qualitative behavior of these masses indicates that the physics is very similar to that predicted by these effective Lagrangians, and there is some indication that at least part of these discrepancies is due to saturation, a lattice artifact.