Astrophysical neutrino oscillations accounting for neutrino charge radii
Konstantin Kouzakov, Fedor Lazarev, Vadim Shakhov, Konstantin Stankevich, Alexander Studenikin
aa r X i v : . [ h e p - ph ] F e b Astrophysical neutrino oscillations accounting forneutrino charge radii
Konstantin Kouzakov, ๐ Fedor Lazarev, ๐ Vadim Shakhov, ๐ Konstantin Stankevich ๐, โ and Alexander Studenikin ๐,๐ ๐ Faculty of Physics, Lomonosov Moscow State University,Moscow 119991, Russia ๐ Joint Institute for Nuclear Research,Dubna 141980, Moscow Region, Russia
E-mail: [email protected], [email protected]
We derive for the ๏ฌrst time an e๏ฌective neutrino evolution Hamiltonian accounting for neutrinointeractions with external magnetic ๏ฌeld due to neutrino charge radii and anapole moment. Theresults are interesting for possible applications in astrophysics. โ Speaker ยฉ 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 di๏ฌerent astrophysical environments (see, for example, [2โ4]). Weconsider for the ๏ฌrst time neutrino ๏ฌavour, spin and spin-๏ฌavour oscillations engendered by neutrinointeractions with an external magnetic ๏ฌeld due to neutrino charge radii and anapole moment. Note,that in this case only the toroidal and poloidal magnetic ๏ฌelds matters. We perform similarcalculations that were performed for derivations of the neutrino e๏ฌective evolution Hamiltonians inthe presence of magnetic ๏ฌelds and moving matter [5, 6].The neutrino electromagnetic interactions is described by the e๏ฌective interaction Hamiltonian[1] ๐ป ๐๐๐ก ( ๐ฅ ) = ๐ ( ๐ ) ๐ ( ๐ฅ ) ๐ด ๐ ( ๐ฅ ) = ร ๐, ๐ ยฏ ๐ ๐ ( ๐ฅ ) ฮ ๐๐ ๐ ๐ ๐ ( ๐ฅ ) ๐ด ๐ ( ๐ฅ ) , (1)where ฮ ๐๐ ๐ is the neutrino electromagnetic vertex function. Here below, we are interested only inthe charge radii h ๐ i ๐ ๐ด in ฮ ๐๐ ๐ , thus we use ฮ ๐๐ ๐ ( ๐ ) = ( ๐ ๐พ ๐ โ ๐ ๐ ๐พ ๐ ๐ ๐ ) " h ๐ i ๐ ๐ + ๐ ๐ด๐ ๐ ๐พ . (2)Within calculations similar to those of [5, 6], we get the following e๏ฌective interaction Hamiltonianfor the considered case: ๐ป ๐ ๐ โฒ ๐ผ๐ผ โฒ = ๐ข โ ๐ ๐ผ (cid:26) [ curl ๐ฉ ] | | (cid:18) h ๐ i ๐ผ๐ผ โฒ + ๐ ๐ด๐ผ๐ผ โฒ ๐ (cid:19) + [ curl ๐ฉ ] โฅ (cid:18) ๐พ โ ๐ผ๐ผ โฒ ๐ ๐ด๐ผ๐ผ โฒ ๐ โ ๐ ห ๐พ โ ๐ผ๐ผ โฒ h ๐ i ๐ผ๐ผ โฒ ๐ (cid:19) (cid:27) ๐ข ๐ โฒ ๐ผ โฒ , (3)where [ curl ๐ฉ ] | | is the component of the curl of the magnetic ๏ฌeld parallel to the neutrino propagationand [ curl ๐ฉ ] โฅ is the perpendicular component, ๐ข ๐ ๐ผ is the neutrino spinor. The gamma factors aregiven by ๐พ โ ๐ผ = ๐ ๐ผ ๐ธ ๐ผ , ๐พ โ ๐ผ๐ฝ = (cid:16) ๐พ โ ๐ผ + ๐พ โ ๐ฝ (cid:17) , ห ๐พ โ ๐ผ๐ฝ = (cid:16) ๐พ โ ๐ผ โ ๐พ โ ๐ฝ (cid:17) . One can see that [ curl ๐ฉ ] | | is responsible for the ๏ฌavour oscillations and [ curl ๐ฉ ] โฅ is responsiblefor the spin and spin-๏ฌavour oscillations. Note, the spin and spin-๏ฌavour oscillations are suppressedby gamma factors. In the ๏ฌavour basis ๐ ๐ = ( ๐ ๐ฟ๐ , ๐ ๐ฟ๐ฅ , ๐ ๐ ๐ , ๐ ๐ ๐ฅ ) the evolution Hamiltonian can bedecomposed into two parts ๐ป ๐ = [ curl ๐ฉ ] | | ๐ป ๐ + [ curl ๐ฉ ] โฅ ๐ป ๐ , (4)where ๐ป ๐ = ยฉ ยซ h ๐ i ๐๐ + ๐ ๐ด๐๐ h ๐ i ๐๐ฅ + ๐ ๐ด๐๐ฅ h ๐ i ๐๐ฅ + ๐ ๐ด๐๐ฅ h ๐ i ๐ฅ๐ฅ + ๐ ๐ด๐ฅ๐ฅ h ๐ i ๐๐ โ ๐ ๐ด๐๐ h ๐ i ๐๐ฅ โ ๐ ๐ด๐๐ฅ h ๐ i ๐๐ฅ โ ๐ ๐ด๐๐ฅ h ๐ i ๐ฅ๐ฅ โ ๐ ๐ด๐ฅ๐ฅ ยชยฎยฎยฎยฎยฎยฌ , (5)2 strophysical neutrino oscillations accounting for neutrino charge radii Konstantin Stankevich ๐ป ๐ = ยฉ ยซ (cid:16) h ๐ i ๐พ (cid:17) ๐๐ + (cid:16) ๐ ๐ด ๐พ (cid:17) ๐๐ (cid:16) h ๐ i ๐พ (cid:17) ๐๐ฅ + (cid:16) ๐ ๐ด ๐พ (cid:17) ๐๐ฅ (cid:16) h ๐ i ๐พ (cid:17) ๐๐ + (cid:16) ๐ ๐ด ๐พ (cid:17) ๐๐ (cid:16) h ๐ i ๐พ (cid:17) ๐ฅ๐ฅ + (cid:16) ๐ ๐ด ๐พ (cid:17) ๐ฅ๐ฅ (cid:16) ๐ ๐ด ๐พ (cid:17) ๐๐ โ (cid:16) h ๐ i ๐พ (cid:17) ๐๐ (cid:16) ๐ ๐ด ๐พ (cid:17) ๐๐ฅ โ (cid:16) h ๐ i ๐พ (cid:17) ๐๐ฅ (cid:16) ๐ ๐ด ๐พ (cid:17) ๐๐ฅ โ (cid:16) h ๐ i ๐พ (cid:17) ๐๐ฅ (cid:16) ๐ ๐ด ๐พ (cid:17) ๐ฅ๐ฅ โ (cid:16) h ๐ i ๐พ (cid:17) ๐ฅ๐ฅ ยชยฎยฎยฎยฎยฎยฎยฎยฎยฌ . (6)The form factors in the ๏ฌavour basis are de๏ฌned as h ๐ i ๐๐ = h ๐ i cos ๐ + h ๐ i sin ๐ + h ๐ i sin 2 ๐, ๐ ๐ด๐๐ = ๐ ๐ด cos ๐ + ๐ ๐ด sin ๐ + ๐ ๐ด sin 2 ๐, h ๐ i ๐ฅ๐ฅ = h ๐ i sin ๐ + h ๐ i cos ๐ โ h ๐ i sin 2 ๐, ๐ ๐ด๐ฅ๐ฅ = ๐ ๐ด sin ๐ + ๐ ๐ด cos ๐ โ ๐ ๐ด sin 2 ๐, h ๐ i ๐๐ฅ = h ๐ i cos 2 ๐ + (cid:16) h ๐ i โ h ๐ i (cid:17) sin 2 ๐, ๐ ๐ด๐๐ฅ = ๐ ๐ด cos 2 ๐ + (cid:16) ๐ ๐ด โ ๐ ๐ด (cid:17) sin 2 ๐, (7)and (cid:18) ๐ ๐ด ๐พ (cid:19) ๐๐ = ๐ ๐ด ๐พ cos ๐ + ๐ ๐ด ๐พ sin ๐ + ๐ ๐ด ๐พ sin 2 ๐, (cid:18) h ๐ i ๐พ (cid:19) ๐๐ = ห ๐พ โ h ๐ i ๐, (cid:18) ๐ ๐ด ๐พ (cid:19) ๐ฅ๐ฅ = ๐ ๐ด ๐พ sin ๐ + ๐ ๐ด ๐พ cos ๐ โ ๐ ๐ด ๐พ sin 2 ๐, (cid:18) h ๐ i ๐พ (cid:19) ๐ฅ๐ฅ = โ ห ๐พ โ h ๐ i ๐, (cid:18) ๐ ๐ด ๐พ (cid:19) ๐๐ฅ = ๐ ๐ด ๐พ cos 2 ๐ + ๐ ๐ด ๐พ โ ๐ ๐ด ๐พ ! sin 2 ๐, (cid:18) h ๐ i ๐พ (cid:19) ๐๐ฅ = ห ๐พ โ h ๐ i ๐. (8)The obtained evolution Hamiltonian can be used for the analysis of the ๏ฌavour, spin and spin-๏ฌavouroscillations and corresponding resonances due to the neutrino electromagnetic interactions with theexternal magnetic ๏ฌeld 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