Neutrino magnetic moment in a magnetized plasma N.Mikheev, - PowerPoint PPT Presentation

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma Neutrino magnetic moment in a magnetized plasma N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Quarks’ 2010 N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma Contents Introduction 1 N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma Contents Introduction 1 Additional energy and magnetic moment of neutrino 2 N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma Contents Introduction 1 Additional energy and magnetic moment of neutrino 2 Magnetic moment of neutrino in a magnetized plasma 3 N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma Contents Introduction 1 Additional energy and magnetic moment of neutrino 2 Magnetic moment of neutrino in a magnetized plasma 3 Conclusions 4 N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma Introduction Investigations of the influence of an active medium on neutrino dispersion are based on calculations of the neutrino self-energy operator Σ( p ) M ( ν → ν ) = − ¯ U ( p ) Σ( p ) U ( p ) , where M ( ν → ν ) is the amplitude of the neutrino forward scattering. N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma The operator Σ( p ) was studied in the previous literature, for example: J.C. D’Olivo, J.F.Nieves, and P.B.Pal, Phys.Rev. D40 , 3679, (1989). V.B. Semikoz and J.W.F.Valle, Nucl.Phys. B425 , 651, (1994); 485 , 545 (Erratum), (1997). G. G. Raffelt, Phys. Rep. 198 , 1 (1990). P. Elmfors, D. Grasso and G.Raffelt, Nucl.Phys. B479 , 3, (1996). E. Elizalde, E.J.Ferrer, V. de la Incera, Phys. Rev. D70 , 043012, (2004). N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma The additional interest to the Σ( p ) is caused by the possibility of extraction from one the data on neutrino magnetic moment. V. Ch. Zhukovskii, T. L. Shoniya, and P. A. Aminov, Zh. Eksp. Teor. Fiz. 104 (4), 3269 (1993) [JETP 77 (4), 539 (1993)]. under physical conditions E ν ≪ m 2 W µ N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma 2 eB > µ 2 − m 2 in the strong magnetic field limit, e , ∆ µ ν = 16 π 3 n e ( E ν − q 3 ) 3 eG F µ ( 0 ) µ ( 0 ) √ ν , = 2 π 2 m ν . ν m 2 W m 2 3 8 ν N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma 2 eB > µ 2 − m 2 in the strong magnetic field limit, e , ∆ µ ν = 16 π 3 n e ( E ν − q 3 ) 3 eG F µ ( 0 ) µ ( 0 ) √ ν , = 2 π 2 m ν . ν m 2 W m 2 3 8 ν 2 eB ≪ µ 2 − m 2 in the weak magnetic field limit, e , ( 3 π 2 n e ) 1 / 3 3 eG F ∆ µ ν = − 8 µ ( 0 ) µ ( 0 ) ν , = √ 2 π 2 m ν . ν 3 ( E ν + q 3 ) m ν 8 N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma 2 eB > µ 2 − m 2 in the strong magnetic field limit, e , ∆ µ ν = 16 π 3 n e ( E ν − q 3 ) 3 eG F µ ( 0 ) µ ( 0 ) √ ν , = 2 π 2 m ν . ν m 2 W m 2 3 8 ν 2 eB ≪ µ 2 − m 2 in the weak magnetic field limit, e , ( 3 π 2 n e ) 1 / 3 3 eG F ∆ µ ν = − 8 µ ( 0 ) µ ( 0 ) ν , = √ 2 π 2 m ν . ν 3 ( E ν + q 3 ) m ν 8 P. Elmfors, D. Grasso and G.Raffelt, Nucl.Phys. B479, 3, (1996) : ” The use of an “effective magnetic dipole moment” to describe the neutrino energy shift in a magnetized medium is somewhat misleading... “ N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma Additional energy and magnetic moment of neutrino In the general case in a magnetized plasma [ A L ( p γ ) + B L ( u γ ) + C L ( p ˜ Σ( p ) = F γ )] γ L + [ A R ( p γ ) + B R ( u γ ) + C R ( p ˜ + F γ )] γ R + m ν [ K 1 + iK 2 ( γ F γ )] , where u µ is the 4-vector of medium velocity, p µ is the neutrino 4-momentum, γ L , R = ( 1 ± γ 5 ) / 2 , A R , B R , C R , A L , B L , C L , K 1 , K 2 are the numerical coefficients, F µν and ˜ F µν are the tensor and dual tensor of the electro-magnetic field. N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma A change of the neutrino energy caused by its forward scattering in a medium can be expressed via the neutrino self-energy operator as follows 1 ∆ E ν = Sp { (( p γ ) + m ν ) ( 1 + ( s γ ) γ 5 ) Σ( p ) } , 4 E ν taking into account the general expression for Σ( p ) we can rewrite ∆ E ν in the form N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma 1 − ( � 1 + ( � m 2 ξ · � v ) ξ · � v ) ν ∆ E ν = ( A L + A R + 2 K 1 ) + B L + B R 2 E ν 2 2 m ν B t ) + m ν 2 ( C L − C R + 4 K 2 ) [( � ξ · � E ( � ξ · � − B l )] , where E ν is the neutrino energy in a vacuum, � ξ is the double average neutrino spin vector, � B l and � B t are the longitudinal and transverse magnetic field components relative to the direction of neutrino propagation respectively, � v is the neutrino velocity vector. N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma The change of neutrino energy due to presence of magnetic moment µ ν could be found from lagrangian. int = i µ ν ∆ L ( µ ) 2 ( ¯ Ψ σ µν Ψ ) F µν , where σ µν = ( γ µ γ ν − γ ν γ µ ) / 2 . � dV < ∆ L ( µ ) ∆ E ( µ ) = − int > ν N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma The contribution to neutrino energy caused by µ ν B t ) + m ν ∆ E ( µ ) = − µ ν [( � ξ · � E ( � ξ · � B l )] . ν The neutrino additional energy 1 − ( � 1 + ( � m 2 ξ · � v ) ξ · � v ) ν ∆ E ν = ( A L + A R + 2 K 1 ) + B L + B R 2 E ν 2 2 m ν B t ) + m ν 2 ( C L − C R + 4 K 2 ) [( � ξ · � E ( � ξ · � − B l )] , N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma The contribution to neutrino energy caused by µ ν B t ) + m ν ∆ E ( µ ) = − µ ν [( � ξ · � E ( � ξ · � B l )] . ν The neutrino additional energy 1 − ( � 1 + ( � m 2 ξ · � v ) ξ · � v ) ν ∆ E ν = ( A L + A R + 2 K 1 ) + B L + B R 2 E ν 2 2 m ν B t ) + m ν 2 ( C L − C R + 4 K 2 ) [( � ξ · � E ( � ξ · � − B l )] , N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma

Introduction Additional energy and magnetic moment of neutrino Magnetic moment of neutrino in a magnetized plasma The contribution to neutrino energy caused by µ ν B t ) + m ν ∆ E ( µ ) = − µ ν [( � ξ · � E ( � ξ · � B l )] . ν The neutrino additional energy 1 − ( � 1 + ( � m 2 ξ · � v ) ξ · � v ) ν ∆ E ν = ( A L + A R + 2 K 1 ) + B L + B R 2 E ν 2 2 m ν B t ) + m ν 2 ( C L − C R + 4 K 2 ) [( � ξ · � E ( � ξ · � − B l )] , N.Mikheev, E.Narynskaya Yaroslavl State University, Russia Neutrino magnetic moment in a magnetized plasma