Mass-induced crystalline color superconductivity

We demonstrate that crystalline color superconductivity may arise as a result of pairing between massless quarks and quarks with a nonzero mass $m_s.$ Previous analyses of this phase of cold dense quark matter have all utilized a chemical potential difference $\delta \mu$ to favor crystalline color superconductivity over ordinary BCS pairing. In any context in which crystalline color superconductivity occurs in nature, however, it will be $m_s$ induced. The effect of $m_s$ is qualitatively different from that of $\delta \mu$ in one crucial respect: $m_s$ depresses the value of the BCS gap ${\Delta }_0$ whereas $\delta \mu$ leaves ${\Delta }_0$ unchanged. This effect in the BCS phase must be taken into account before $m_s$-induced and $\delta \mu$-induced crystalline color superconductivity can sensibly be compared.