Abstract
We investigate color superconductivity on the lattice using the gap equation for the Cooper pair condensate. The weak coupling analysis is justified by choosing the physical size of the lattice to be smaller than the QCD scale, while keeping the aspect ratio of the lattice small enough to suppress thermal excitations. In the vicinity of the critical coupling constant that separates the superconducting phase and the normal phase, the gap equation can be linearized, and by solving the corresponding eigenvalue problem, we obtain the critical point and the Cooper pair condensate without assuming its explicit form. The momentum components of the condensate suggest spatially isotropic s-wave superconductivity with Cooper pairs formed by quarks near the Fermi surface. The chiral symmetry in the massless limit is spontaneously broken by the Cooper pair condensate, which turns out to be dominated by the scalar and the pseudo-scalar components. Our results provide useful predictions, in particular, for future lattice simulations based on methods to overcome the sign problem such as the complex Langevin method.
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Acknowledgments
We thank Y. Asano, E. Itou, K. Miura and A. Ohnishi for valuable discussions. T. Y. was supported by the RIKEN Special Postdoctoral Researchers Program. J. N. was supported in part by JSPS KAKENHI Grant Numbers JP16H03988, JP22H01224. Y. N. was supported by JSPS KAKENHI Grant Number JP21K03553. S. T. was supported by the RIKEN Special Postdoctoral Researchers Program. Computations were carried out using computational resources of the Oakbridge-CX provided by the Information Technology Center at the University of Tokyo through the HPCI System Research project (Project ID:hp200079, hp210078, hp220094). Computations were also carried out by using the computers in the Yukawa Institute Computer Facility.
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Yokota, T., Ito, Y., Matsufuru, H. et al. Color superconductivity on the lattice — analytic predictions from QCD in a small box. J. High Energ. Phys. 2023, 61 (2023). https://doi.org/10.1007/JHEP06(2023)061
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DOI: https://doi.org/10.1007/JHEP06(2023)061