Magnetized plasma-induced magnetic moment of a neutrino
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ARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Magnetized PlasmaInduced Magnetic Moment of a Neutrino R. A. Anikin, N. V. Mikheev*, and E. N. Narynskaya Yaroslavl State University, Yaroslavl, 150000 Russia *email: [email protected] Received November 17, 2009
Abstract—The influence of magnetized plasma on neutrino dispersion has been studied. The contribution to the neutrino magnetic moment due to the presence of a magnetized plasma is calculated. It is shown that, in contrast to earlier published data, the plasmainduced magnetic moment of a neutrino is, like that in a vac uum, suppressed by its mass. DOI: 10.1134/S1063776110060063
1. INTRODUCTION Experimental solution of the solar neutrino prob lem with the heavywater detector of the Sudbury Neutrino Observatory [1] and the results of experi ments with atmospheric [2] and reactor [3] neutrinos have proved the existence of thew neutrino rest mass and mixing from the chargedlepton sector. In this context, a topical question arises as to whether neu trino dispersion can be influenced by an external active medium, possibly a dense hot plasma and/or magnetic field. Investigations of the influence of an active medium on neutrino dispersion are based on calculations of the neutrino selfenergy operator Σ(p). Such calculations have been performed repeatedly, in particular, the contribution of an external magnetic field to the neu trino selfenergy operator has been studied in [4–9]. Since real astrophysical conditions involve a dense hot plasma in addition to strong magnetic fields, it is expe dient to study neutrino dispersion in an external active medium simultaneously composed of a field and a plasma. The Σ(p) operator in such a magnetized plasma has also been extensively studied (see, e.g., [10–14]). It should be noted that additional interest in calcu lating the neutrino selfenergy operator stems from the possibility of obtaining data on the anomalous mag netic moment of the neutrino. However, there is some doubt concerning the validity of data in the literature so far and on the magnetic moment of the neutrino in a magnetized plasma, since the results imply that the magnetic moment of the neutrino is either indepen dent of its mass mν [15] or exhibits a giant enhance ment by a factor of 1/mν. As was reasonably pointed out [13], these results confuse the situation with the magnetic moment of the neutrino, instead of elucidat ing it.
In the general case, the neutrino selfenergy oper ator in a magnetized plasma can be represented as fol lows: Σ ( p ) = [ A L ( pγ ) + B L ( uγ ) + C L ( pF˜ γ ) ]γ L (1) + [ A ( pγ ) + B ( uγ ) + C ( pF˜ γ ) ]γ R
R
R
R
+ m ν [ K 1 + iK 2 ( γFγ ) ], where is the 4vector of velocity of the medium; pμ is the neutrino 4momentum; γL = (1 + γ5)/2 and γR are the projection operators; AR, BR, CR, AL, BL, CL, K1, μν and K are numerical coefficients; and Fμν and F˜ are uμ
2
the tensor and dual tensor, respectively, of the electro magnetic field. Here and below, the tensor indices of 4vectors and tensors inside pa
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