publication . Preprint . Article . 2012

Banks-Casher-type relation for the BCS gap at high density

Takuya Kanazawa; Tilo Wettig; Naoki Yamamoto;
Open Access English
  • Published: 22 Nov 2012
We derive a new Banks-Casher-type relation which relates the density of complex Dirac eigenvalues at the origin to the BCS gap of quarks at high density. Our relation is applicable to QCD and QCD-like theories without a sign problem, such as two-color QCD and adjoint QCD with baryon chemical potential, and QCD with isospin chemical potential. It provides us with a method to measure the BCS gap through the Dirac spectrum on the lattice.
arXiv: High Energy Physics::LatticeHigh Energy Physics::PhenomenologyHigh Energy Physics::Experiment
free text keywords: High Energy Physics - Lattice, High Energy Physics - Phenomenology, High Energy Physics - Theory, Nuclear and High Energy Physics, Quantum chromodynamics, Isospin, Physics, Atomic physics, Hadron, Dirac operator, symbols.namesake, symbols, Baryon, Quark, Dirac spectrum, Particle physics, Dirac (video compression format), Mathematical physics
Related Organizations
61 references, page 1 of 5

1. T. Banks and A. Casher, Chiral Symmetry Breaking in Con ning Theories, Nucl. Phys. B169 (1980) 103.

2. S. J. Hands and M. Teper, On the value and origin of the chiral condensate in quenched SU(2) lattice gauge theory, Nucl. Phys. B347 (1990) 819.

3. M. Berbenni-Bitsch, A. Jackson, S. Meyer, A. Schafer, J. Verbaarschot, and T. Wettig, Random matrix universality in the small eigenvalue spectrum of the lattice Dirac operator, Nucl.Phys.Proc.Suppl. 63 (1998) 820 [hep-lat/9709102].

4. L. Giusti and M. Luscher, Chiral symmetry breaking and the Banks-Casher relation in lattice QCD with Wilson quarks, JHEP 0903 (2009) 013 [arXiv:0812.3638].

5. Z. Lin, The QCD Phase Transition Region with Domain Wall Quarks, AIP Conf.Proc. 1441 (2012) 904 [arXiv:1110.6870].

6. H. Ohno, U. Heller, F. Karsch, and S. Mukherjee, Eigenvalue distribution of the Dirac operator at nite temperature with (2+1)- avor dynamical quarks using the HISQ action, PoS LATTICE2011 (2011) 210 [arXiv:1111.1939].

7. G. Cossu, S. Aoki, S. Hashimoto, T. Kaneko, H. Matsufuru, et. al., Topological susceptibility and axial symmetry at nite temperature, PoS LATTICE2011 (2011) 188 [arXiv:1204.4519].

8. H. Leutwyler and A. V. Smilga, Spectrum of Dirac operator and role of winding number in QCD, Phys. Rev. D46 (1992) 5607. [OpenAIRE]

9. A. V. Smilga and J. J. M. Verbaarschot, Spectral sum rules and nite volume partition function in gauge theories with real and pseudoreal fermions, Phys. Rev. D51 (1995) 829 [hep-th/9404031]. [OpenAIRE]

10. J. B. Kogut, M. A. Stephanov, D. Toublan, J. J. M. Verbaarschot, and A. Zhitnitsky, QCD-like theories at nite baryon density, Nucl. Phys. B582 (2000) 477 [hep-ph/0001171]. [OpenAIRE]

11. K. Fukushima and T. Hatsuda, The phase diagram of dense QCD, Rept. Prog. Phys. 74 (2011) 014001 [arXiv:1005.4814].

12. L. von Smekal, Universal Aspects of QCD-like Theories, Nucl.Phys.Proc.Suppl. 228 (2012) 179 [arXiv:1205.4205]. [OpenAIRE]

13. M. G. Alford, A. Schmitt, K. Rajagopal, and T. Schafer, Color superconductivity in dense quark matter, Rev. Mod. Phys. 80 (2008) 1455 [arXiv:0709.4635].

14. N. Yamamoto and T. Kanazawa, Dense QCD in a Finite Volume, Phys. Rev. Lett. 103 (2009) 032001 [arXiv:0902.4533].

15. T. Kanazawa, T. Wettig, and N. Yamamoto, Chiral Lagrangian and spectral sum rules for dense two-color QCD, JHEP 08 (2009) 003 [arXiv:0906.3579]. [OpenAIRE]

61 references, page 1 of 5
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Preprint . Article . 2012

Banks-Casher-type relation for the BCS gap at high density

Takuya Kanazawa; Tilo Wettig; Naoki Yamamoto;