Astrophysical neutrino oscillations accounting for neutrino charge radii

Abstract

We derive for the first time an effective neutrino evolution Hamiltonian accounting for neutrino interactions with external magnetic field due to neutrino charge radii and anapole moment. The results are interesting for possible applications in astrophysics.

Full text

aa r X i v : . [ h e p - ph ] F e b Astrophysical neutrino oscillations accounting forneutrino charge radii

Konstantin Kouzakov, 𝑎 Fedor Lazarev, 𝑎 Vadim Shakhov, 𝑎 Konstantin Stankevich 𝑎, ∗ and Alexander Studenikin 𝑎,𝑏 𝑎 Faculty of Physics, Lomonosov Moscow State University,Moscow 119991, Russia 𝑏 Joint Institute for Nuclear Research,Dubna 141980, Moscow Region, Russia

E-mail: kl.stankevich@physics.msu.ru, studenik@srd.sinp.msu.ru

We derive for the first time an effective neutrino evolution Hamiltonian accounting for neutrinointeractions with external magnetic field due to neutrino charge radii and anapole moment. Theresults are interesting for possible applications in astrophysics. ∗ Speaker © Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ strophysical neutrino oscillations accounting for neutrino charge radii

Konstantin StankevichIt is well known that neutrino electromagnetic interactions [1] are important for neutrinoevolution and oscillations in different astrophysical environments (see, for example, [2–4]). Weconsider for the first time neutrino flavour, spin and spin-flavour oscillations engendered by neutrinointeractions with an external magnetic field due to neutrino charge radii and anapole moment. Note,that in this case only the toroidal and poloidal magnetic fields matters. We perform similarcalculations that were performed for derivations of the neutrino effective evolution Hamiltonians inthe presence of magnetic fields and moving matter [5, 6].The neutrino electromagnetic interactions is described by the effective interaction Hamiltonian[1] 𝐻 𝑖𝑛𝑡 ( 𝑥 ) = 𝑗 ( 𝜈 ) 𝜇 ( 𝑥 ) 𝐴 𝜇 ( 𝑥 ) = Õ 𝑘, 𝑗 ¯ 𝜈 𝑘 ( 𝑥 ) Λ 𝜇𝑘 𝑗 𝜈 𝑗 ( 𝑥 ) 𝐴 𝜇 ( 𝑥 ) , (1)where Λ 𝜇𝑘 𝑗 is the neutrino electromagnetic vertex function. Here below, we are interested only inthe charge radii h 𝑟 i 𝑓 𝐴 in Λ 𝜇𝑘 𝑗 , thus we use Λ 𝜇𝑓 𝑖 ( 𝑞 ) = ( 𝑞 𝛾 𝜇 − 𝑞 𝜇 𝛾 𝜈 𝑞 𝜈 ) " h 𝑟 i 𝑓 𝑖 + 𝑓 𝐴𝑓 𝑖 𝛾 . (2)Within calculations similar to those of [5, 6], we get the following effective interaction Hamiltonianfor the considered case: 𝐻 𝑠𝑠 ′ 𝛼𝛼 ′ = 𝑢 † 𝑠 𝛼 (cid:26) [ curl 𝑩 ] | | (cid:18) h 𝑟 i 𝛼𝛼 ′ + 𝑓 𝐴𝛼𝛼 ′ 𝜎 (cid:19) + [ curl 𝑩 ] ⊥ (cid:18) 𝛾 − 𝛼𝛼 ′ 𝑓 𝐴𝛼𝛼 ′ 𝜎 − 𝑖 ˜ 𝛾 − 𝛼𝛼 ′ h 𝑟 i 𝛼𝛼 ′ 𝜎 (cid:19) (cid:27) 𝑢 𝑠 ′ 𝛼 ′ , (3)where [ curl 𝑩 ] | | is the component of the curl of the magnetic field parallel to the neutrino propagationand [ curl 𝑩 ] ⊥ is the perpendicular component, 𝑢 𝑠 𝛼 is the neutrino spinor. The gamma factors aregiven by 𝛾 − 𝛼 = 𝑚 𝛼 𝐸 𝛼 , 𝛾 − 𝛼𝛽 = (cid:16) 𝛾 − 𝛼 + 𝛾 − 𝛽 (cid:17) , ˜ 𝛾 − 𝛼𝛽 = (cid:16) 𝛾 − 𝛼 − 𝛾 − 𝛽 (cid:17) . One can see that [ curl 𝑩 ] | | is responsible for the flavour oscillations and [ curl 𝑩 ] ⊥ is responsiblefor the spin and spin-flavour oscillations. Note, the spin and spin-flavour oscillations are suppressedby gamma factors. In the flavour basis 𝜈 𝑓 = ( 𝜈 𝐿𝑒 , 𝜈 𝐿𝑥 , 𝜈 𝑅𝑒 , 𝜈 𝑅𝑥 ) the evolution Hamiltonian can bedecomposed into two parts 𝐻 𝑓 = [ curl 𝑩 ] | | 𝐻 𝑓 + [ curl 𝑩 ] ⊥ 𝐻 𝑓 , (4)where 𝐻 𝑓 = © « h 𝑟 i 𝑒𝑒 + 𝑓 𝐴𝑒𝑒 h 𝑟 i 𝑒𝑥 + 𝑓 𝐴𝑒𝑥 h 𝑟 i 𝑒𝑥 + 𝑓 𝐴𝑒𝑥 h 𝑟 i 𝑥𝑥 + 𝑓 𝐴𝑥𝑥 h 𝑟 i 𝑒𝑒 − 𝑓 𝐴𝑒𝑒 h 𝑟 i 𝑒𝑥 − 𝑓 𝐴𝑒𝑥 h 𝑟 i 𝑒𝑥 − 𝑓 𝐴𝑒𝑥 h 𝑟 i 𝑥𝑥 − 𝑓 𝐴𝑥𝑥 ª®®®®®¬ , (5)2 strophysical neutrino oscillations accounting for neutrino charge radii Konstantin Stankevich 𝐻 𝑓 = © « (cid:16) h 𝑟 i 𝛾 (cid:17) 𝑒𝑒 + (cid:16) 𝑓 𝐴 𝛾 (cid:17) 𝑒𝑒 (cid:16) h 𝑟 i 𝛾 (cid:17) 𝑒𝑥 + (cid:16) 𝑓 𝐴 𝛾 (cid:17) 𝑒𝑥 (cid:16) h 𝑟 i 𝛾 (cid:17) 𝑒𝜇 + (cid:16) 𝑓 𝐴 𝛾 (cid:17) 𝑒𝜇 (cid:16) h 𝑟 i 𝛾 (cid:17) 𝑥𝑥 + (cid:16) 𝑓 𝐴 𝛾 (cid:17) 𝑥𝑥 (cid:16) 𝑓 𝐴 𝛾 (cid:17) 𝑒𝑒 − (cid:16) h 𝑟 i 𝛾 (cid:17) 𝑒𝑒 (cid:16) 𝑓 𝐴 𝛾 (cid:17) 𝑒𝑥 − (cid:16) h 𝑟 i 𝛾 (cid:17) 𝑒𝑥 (cid:16) 𝑓 𝐴 𝛾 (cid:17) 𝑒𝑥 − (cid:16) h 𝑟 i 𝛾 (cid:17) 𝑒𝑥 (cid:16) 𝑓 𝐴 𝛾 (cid:17) 𝑥𝑥 − (cid:16) h 𝑟 i 𝛾 (cid:17) 𝑥𝑥 ª®®®®®®®®¬ . (6)The form factors in the flavour basis are defined as h 𝑟 i 𝑒𝑒 = h 𝑟 i cos 𝜃 + h 𝑟 i sin 𝜃 + h 𝑟 i sin 2 𝜃, 𝑓 𝐴𝑒𝑒 = 𝑓 𝐴 cos 𝜃 + 𝑓 𝐴 sin 𝜃 + 𝑓 𝐴 sin 2 𝜃, h 𝑟 i 𝑥𝑥 = h 𝑟 i sin 𝜃 + h 𝑟 i cos 𝜃 − h 𝑟 i sin 2 𝜃, 𝑓 𝐴𝑥𝑥 = 𝑓 𝐴 sin 𝜃 + 𝑓 𝐴 cos 𝜃 − 𝑓 𝐴 sin 2 𝜃, h 𝑟 i 𝑒𝑥 = h 𝑟 i cos 2 𝜃 + (cid:16) h 𝑟 i − h 𝑟 i (cid:17) sin 2 𝜃, 𝑓 𝐴𝑒𝑥 = 𝑓 𝐴 cos 2 𝜃 + (cid:16) 𝑓 𝐴 − 𝑓 𝐴 (cid:17) sin 2 𝜃, (7)and (cid:18) 𝑓 𝐴 𝛾 (cid:19) 𝑒𝑒 = 𝑓 𝐴 𝛾 cos 𝜃 + 𝑓 𝐴 𝛾 sin 𝜃 + 𝑓 𝐴 𝛾 sin 2 𝜃, (cid:18) h 𝑟 i 𝛾 (cid:19) 𝑒𝑒 = ˜ 𝛾 − h 𝑟 i 𝜃, (cid:18) 𝑓 𝐴 𝛾 (cid:19) 𝑥𝑥 = 𝑓 𝐴 𝛾 sin 𝜃 + 𝑓 𝐴 𝛾 cos 𝜃 − 𝑓 𝐴 𝛾 sin 2 𝜃, (cid:18) h 𝑟 i 𝛾 (cid:19) 𝑥𝑥 = − ˜ 𝛾 − h 𝑟 i 𝜃, (cid:18) 𝑓 𝐴 𝛾 (cid:19) 𝑒𝑥 = 𝑓 𝐴 𝛾 cos 2 𝜃 + 𝑓 𝐴 𝛾 − 𝑓 𝐴 𝛾 ! sin 2 𝜃, (cid:18) h 𝑟 i 𝛾 (cid:19) 𝑒𝑥 = ˜ 𝛾 − h 𝑟 i 𝜃. (8)The obtained evolution Hamiltonian can be used for the analysis of the flavour, spin and spin-flavouroscillations and corresponding resonances due to the neutrino electromagnetic interactions with theexternal magnetic field engendered by neutrino charge radii and anapole moment. This work wassupported by the Russian Foundation for Basic Research under Grant No. 20-52-53022-GFEN-a.The work of KS was also supported by the Russian Foundation for Basic Research under Grant No.20-32-90107. References [1] C. Giunti and A. Studenikin, Rev. Mod. Phys. (2015), 531.[2] A. de Gouvea and S. Shalgar, JCAP (2012), 027.[3] A. de Gouvea and S. Shalgar, JCAP (2013), 018.[4] S. Abbar, Phys. Rev. D (2020) no.10, 103032.[5] R. Fabbricatore, A. Grigoriev and A. Studenikin, J. Phys. Conf. Ser. (2016) no.6, 062058[6] P. Pustoshny and A. Studenikin, Phys. Rev. D98