Non equilibrium dynamics of mixing, oscillations, and equilibration: A model study

Journal Article · Fri Dec 22 00:00:00 EST 2006 · Physical Review D

OSTI ID:934708

Ho, Chiu Man; Boyanovsky, D; Ho, C M

The non-equilibrium dynamics of mixing, oscillations and equilibration is studied in a field theory of flavored neutral mesons that effectively models two flavors of mixed neutrinos, in interaction with other mesons that represent a thermal bath of hadrons or quarks and charged leptons. This model describes the general features of neutrino mixing and relaxation via charged currents in a medium. The reduced density matrix and the non-equilibrium effective action that describes the propagation of neutrinos is obtained by integrating out the bath degrees of freedom. We obtain the dispersion relations, mixing angles and relaxation rates of ``neutrino'' quasiparticles. The dispersion relations and mixing angles are of the same form as those of neutrinos in the medium, and the relaxation rates are given by $$\Gamma_1(k) = \Gamma_{ee}(k) \cos^2\theta_m(k)+\Gamma_{\mu\mu}(k)\sin^2\theta_m(k); \Gamma_2(k)= \Gamma_{\mu\mu}(k) \cos^2\theta_m(k)+\Gamma_{ee}(k)\sin^2\theta_m(k) $$ where $$\Gamma_{\alpha\alpha}(k)$$ are the relaxation rates of the flavor fields in \emph{absence} of mixing, and $$\theta_m(k)$$ is the mixing angle in the medium. A Weisskopf-Wigner approximation that describes the asymptotic time evolution in terms of a non-hermitian Hamiltonian is derived. At long time $$>>\Gamma^{-1}_{1,2}$$ ``neutrinos'' equilibrate with the bath. The equilibrium density matrix is nearly diagonal in the basis of eigenstates of an \emph{effective Hamiltonian that includes self-energy corrections in the medium}. The equilibration of ``sterile neutrinos'' via active-sterile mixing is discussed.

• Research Organization: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: Physics Division
• DOE Contract Number: DE-AC02-05CH11231
• OSTI ID: 934708
• Report Number(s): LBNL-416E; TRN: US0803840
• Journal Information: Physical Review D, Vol. 75; Related Information: Journal Publication Date: 12 April 2007
• Country of Publication: United States
• Language: English

Related Subjects

72
APPROXIMATIONS
CHARGED CURRENTS
DEGREES OF FREEDOM
DENSITY MATRIX
DISPERSION RELATIONS
EIGENSTATES
HADRONS
HAMILTONIANS
LEPTONS
MESONS
NEUTRINOS
OSCILLATIONS
QUARKS
RELAXATION
SELF-ENERGY
neutrino
mixing angle
neutrino
oscillation
meson
interaction
charged current
density matrix
reduced
effective action
dispersion relations
neutrino
quasiparticle
neutrino
width
effective Hamiltonian
Langevin equation
solution
correlation function