On the imaginary part of the next-to-leading-order static gluon self-energy in an anisotropic plasma

Details On the imaginary part of the next-to-leading-order static gluon self-energy in an anisotropic plasma On the imaginary part of the next-to-leading-order static gluon self-energy in an anisotropic plasma

2009-06-29

arxiv.org/abs/0906.5220v2

Phys.Rev.80:065035,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

REVTEX, 15 pages, 4 figures. v2: slightly shortened title, shorter appendix B

Scientific paper

10.1103/PhysRevD.80.065035

Using hard-loop (HL) effective theory for an anisotropic non-Abelian plasma, which even in the static limit involves nonvanishing HL vertices, we calculate the imaginary part of the static next-to-leading-order gluon self energy in the limit of a small anisotropy and with external momentum parallel to the anisotropy direction. At leading order, the static propagator has space-like poles corresponding to plasma instabilities. On the basis of a calculation using bare vertices, it has been conjectured that, at next-to-leading order, the static gluon self energy acquires an imaginary part which regulates these space-like poles. We find that the one-loop resummed expression taken over naively from the imaginary-time formalism does yield a nonvanishing imaginary part even after including all HL vertices. However, this result is not correct. Starting from the real-time formalism, which is required in a non-equilibrium situation, we construct a resummed retarded HL propagator with correct causality properties and show that the static limit of the retarded one-loop-resummed gluon self-energy is real. This result is also required for the time-ordered propagator to exist at next-to-leading order.

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