TY - JOUR

T1 - Resonances driven by a neutrino gyroscope and collective neutrino oscillations in supernovae

AU - Wu, Meng Ru

AU - Qian, Yong Zhong

PY - 2011/8/5

Y1 - 2011/8/5

N2 - We show that flavor evolution of a system of neutrinos with continuous energy spectra as in supernovae can be understood in terms of the response of individual neutrino flavor-isospins (NFIS's) to the mean field. In the case of a system initially consisting of νe and ν̄e with the same energy spectrum but different number densities, the mean field is very well approximated by the total angular momentum of a neutrino gyroscope. Assuming that NFIS evolution is independent of the initial neutrino emission angle, the so-called single-angle approximation, we find that the evolution is governed by two types of resonances driven by precession and nutation of the gyroscope, respectively. The net flavor transformation crucially depends on the adiabaticity of evolution through these resonances. We show that the results for the system of two initial neutrino species can be extended to a system of four species with the initial number densities of νe and ν̄e significantly larger than those of νx and ν̄x. Further, we find that when the dependence on the initial neutrino emission angle is taken into account in the multiangle approximation, nutation of the mean field is quickly damped out and can be neglected. In contrast, precession-driven resonances still govern the evolution of NFIS's with different energy and emission angles just as in the single-angle approximation. Our pedagogical and analytic study of collective neutrino oscillations in supernovae provides some insights into these seemingly complicated yet fascinating phenomena.

AB - We show that flavor evolution of a system of neutrinos with continuous energy spectra as in supernovae can be understood in terms of the response of individual neutrino flavor-isospins (NFIS's) to the mean field. In the case of a system initially consisting of νe and ν̄e with the same energy spectrum but different number densities, the mean field is very well approximated by the total angular momentum of a neutrino gyroscope. Assuming that NFIS evolution is independent of the initial neutrino emission angle, the so-called single-angle approximation, we find that the evolution is governed by two types of resonances driven by precession and nutation of the gyroscope, respectively. The net flavor transformation crucially depends on the adiabaticity of evolution through these resonances. We show that the results for the system of two initial neutrino species can be extended to a system of four species with the initial number densities of νe and ν̄e significantly larger than those of νx and ν̄x. Further, we find that when the dependence on the initial neutrino emission angle is taken into account in the multiangle approximation, nutation of the mean field is quickly damped out and can be neglected. In contrast, precession-driven resonances still govern the evolution of NFIS's with different energy and emission angles just as in the single-angle approximation. Our pedagogical and analytic study of collective neutrino oscillations in supernovae provides some insights into these seemingly complicated yet fascinating phenomena.

UR - http://www.scopus.com/inward/record.url?scp=80052837519&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052837519&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.84.045009

DO - 10.1103/PhysRevD.84.045009

M3 - Article

AN - SCOPUS:80052837519

VL - 84

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 4

M1 - 045009

ER -