Gaps and critical temperature for color superconductivity

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 61, Issue 5, 2000, Pages

  Rischke, Dirk H ^b  

^a BROOKHAVEN NATIONAL LABORATORY   (United States)

^b RIKEN BNL RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750554098     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.61.051501     Document Type: Article

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27. The interaction between two quarks contains two pieces, which are symmetric or antisymmetric in the color indices of the fundamental representation. The antisymmetric representation is attractive to lowest order in g; for an (Formula presented) gauge theory, the coefficient in Eq. (4) is (Formula presented) 7. When (Formula presented), the antisymmetric representation is the color (Formula presented) representation, the symmetric the color (Formula presented). Fermi statistics for a (Formula presented) gap imposes constraints which require the number of massless flavors, (Formula presented) 4. The form of the quark propagator in Eq. (2) is only valid when (Formula presented), and the (Formula presented) representation is (Formula presented) 4. When (Formula presented), the (Formula presented) representation mixes with the (Formula presented) 4. This mixing only affects the gap equation to higher order (Formula presented), which is negligible in weak coupling.
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29. Due to infrared singular factors, the effective action for the condensate is (Formula presented), so that the (true) gluon mass from color superconductivity is not (Formula presented), as one would naively expect, but much larger, (Formula presented). (We thank T. Schäfer for discussions on this point.) To the order at which we work, this is irrelevant for the gap equation because the dominant momenta are (Formula presented), and on that scale, corrections from the condensate are small, (Formula presented) at large (Formula presented).
30. From Eq. (6) the imaginary part of (Formula presented) arises from the cut in the logarithm for (Formula presented) (Formula presented) (Formula presented). Taking (Formula presented), momenta exponentially close to the Fermi surface occur when (Formula presented). In this region, the imaginary part of the gap function, (Formula presented), is down by g relative to the real part, (Formula presented). Away from the Fermi surface, (Formula presented), so (Formula presented), and (Formula presented) is strongly damped, with the real and imaginary parts of comparable magnitude, (Formula presented).
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