Neutrino helicity and chirality transitions in Schwarzschild spacetime
Abstract
We study the helicity and chirality transitions of a highenergy neutrino propagating in a Schwarzschild spacetime background. Using both traditional Schwarzschild and isotropic spherical coordinates, we derive an ultrarelativistic approximation of the Dirac Hamiltonian to firstorder in the neutrino’s rest mass, via a generalization of the CiniTouschek transformation that incorporates noninertial frame effects due to the noncommutative nature of the momentum states in curvilinear coordinates. Under general conditions, we show that neutrino’s helicity is not a constant of the motion in the massless limit due to spacetime curvature, while the chirality transition rate still retains an overall dependence on mass. We show that the chirality transition rate generally depends on the zerothorder component of the neutrino’s helicity transition rate under the CiniTouschek transformation. It is also shown that the chiral current for highenergy neutrinos is altered by corrections due to curvature and framedependent effects, but should have no significant bearing on the chiral anomaly in curved spacetime. We determine the upper bound for helicity and chirality transitions near the event horizon of a black hole. The special case of a weakfield approximation is also considered, which includes the gravitational analogue of Berry’s phase first proposed by Cai and Papini. Finally, we propose a method for estimating the absolute neutrino mass and the number of righthanded chiral states from the expectation values of the helicity and chirality transition rates in the weakfield limit.
 Publication:

Physical Review D
 Pub Date:
 May 2005
 DOI:
 10.1103/PhysRevD.71.105003
 arXiv:
 arXiv:grqc/0401044
 Bibcode:
 2005PhRvD..71j5003S
 Keywords:

 13.15.+g;
 04.70.Bw;
 14.60.Lm;
 Neutrino interactions;
 Classical black holes;
 Ordinary neutrinos (nuW bosons;
 General Relativity and Quantum Cosmology;
 Astrophysics;
 High Energy Physics  Phenomenology
 EPrint:
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