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Neutrino quantum states and spin light in matter

Neutrino quantum states and spin light in matter. Neutrino quantum states and spin light in matter. Neutrino motion and radiation in matter. Alexander Studenikin. Moscow State University. 08/03/2005 Turin. References. A.Studenikin, A.Ternov, Phys.Lett . B 608 (2005) 107.

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Neutrino quantum states and spin light in matter

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  1. Neutrino quantum states and spin light in matter Neutrino quantum states and spin light in matter Neutrino motion and radiation in matter Alexander Studenikin Moscow State University 08/03/2005 Turin

  2. References A.Studenikin, A.Ternov, Phys.Lett.B608 (2005) 107 A.Studenikin, Nucl.Phys.B (Proc.Suppl.), 2005, in press A.Grigoriev, A.Studenikin, A.Ternov, Grav.& Cosm.(2005) in press M.Dvornikov, A.Grigoriev, A.Studenikin, Int.J Mod.Phys.D14 (2005), in press A.Studenikin, Phys.Atom.Nucl.67(2004) 1014 M.Dvornikov, A.Studenikin, Phys.Rev.D69 (2004) 073001 JETP99 (2004)254 JHEP09 (2002) 016 A.Lobanov, A.Studenikin, Phys.Lett.B 601(2004) 171 Phys.Lett.B564(2003) 27 Phys.Lett.B 515 (2001) 94 A.Grigoriev, A.Lobanov, A.Studenikin, Phys.Lett.B535 (2002) 187 A.Egorov, A.Lobanov, A.Studenikin, Phys.Lett.B491(2000) 137

  3. Matter effects in neutrino flavour oscillations L.Wolfenstein, Neutrino oscillations in matter, Phys.Rev.D 17 (1978) 2369; S.Mikheyev, A.Smirnov, Resonance amplification of neutrino oscillations in matter and the spectroscopy of the solar neutrino , Sov.J.Nucl.Phys.42 (1985) 913. , the particle number density , MSW effect

  4. Chirality (I)

  5. Chirality (II)

  6. Matter effects in neutrino spin (spin-flavour) oscillations neutrino magnetic moment magnetic field C.-S.Lim, W.Marciano, Resonant spin-flavour precession of solar and supernova neutrinos, Phys.Rev.D37 (1988) 1368; E.Akhmedov, Resonant amplification of neutrino spin rotation in matter and the solar-neutrino problem, Phys.Lett.B213 (1988) 64. resonance in neutrino spin-flavour oscillations

  7. Modified Dirac equation for neutrino in background matter Outline “Quantum approach” to neutrino motion in matter Modified Dirac-Pauli equation for neutrino in background matter Exact solutions of modified Dirac and Dirac-Pauliequations in matter Neutrino wave function and energy spectrum in matter Neutrino oscillations in matter and magnetic field Quantum theory of neutrino spin light in matter Transition rate, radiation power, photon’s energy Spatial angular distribution and polarization

  8. Standard model electroweak interaction of a flavour neutrino in matter(f = e) Interaction Lagrangian (it is supposed that matter contains onlyelectrons) Charged current interactions contribution to neutrino potential in matter Neutral current interactions contribution to neutrino potential in matter

  9. Matter current and polarization When the electron field bilinear is averaged over the background i = 1, 2, 3 it can be replaced by the matter (electrons) current invariant number density speed of matter and polarization

  10. ModifiedDirac equation for neutrino in matter matter current matter polarization Addition to the vacuum neutrino Lagrangian where A.Studenikin, A.Ternov, hep-ph/0410297; Phys.Lett.B608(2005) 107 It is supposethat there is a macroscopic amountof electrons in the scale of a neutrino de Broglie wavelength. Therefore,the interaction of a neutrino with the matter (electrons) is coherent. This is the most general equation of motion of a neutrino in which the effective potential accounts for both the charged and neutral-current interactions with thebackground matter and also for the possible effects of the matter motion and polarization. L.Chang, R.Zia,’88; J.Panteleone,’91; K.Kiers, N.Weiss, M.Tytgat,’97-’98; P.Manheim,’88; D.Nötzold, G.Raffelt,’88; J.Nieves,’89; W.Naxton, W-M.Zhang’91; M.Kachelriess,’98; A.Kusenko, M.Postma,’02.

  11. negative-helicity Neutrinowave function and energy spectrum in matter (I) In the rest frame of unpolarized matter The Hamiltonian form of the equation: where number density of background matter (electrons) The form of the Hamiltonian implies that the operators of themomentum, andlongitudinal polarization, are the integrals of motion: positive-helicity In the relativistic limit the negative-helicity neutrino state is dominated by the left-handed chiral state: .

  12. Stationary states neutrino wave function in matter and neutrino energy spectrum in matter for two helicity states where the matter density parameter J.Panteleone, 1991 (if NC interaction were left out) density of matter in a neutron star for Neutrinoenergy in the background matterdepends on the state of the neutrino longitudinal polarization (helicity), i.e. in the relativistic casethe left-handed and right-handed neutrinos with equal momenta have different energies.

  13. Neutrino wave function in matter (II) A.Studenikin, A.Ternov, hep-ph/0410297; Phys.Lett.B608(2005) 107 The quantity splits the solutions into the two branches that in the limit of vanishingmatter density, reproduce the positive and negative-frequencysolutions,respectively.

  14. Modified Dirac equation for matter composed of electrons, protons and neutrons (I) The generalizations of the modified Dirac equation for more complicated matter compositions and theother flavour neutrinosare just straightforward. For matter composed of electrons , protons and neutrons : where polarization current isospin third component of a fermionf electric charge

  15. An important note (I) The modified Dirac equation for a neutrino in the background matter (and the obtained exact solution and energy spectrum) establish a basis for an effective method in investigations of differentphenomena that can appear when neutrinos are moving in media. similar to the Furry representation of quantum electrodynamics

  16. Neutrino and antineutrino energy spectra in matter For the fixed magnitude of the neutrino momentumP there are the two values for the “positive sign” energies negative-helicity neutrino energy positive-helicity neutrino energy particle (neutrino) energies in matter Thetwo other values of the energy for the “negative sign” correspond to the antiparticle solutions. By changing the sign of the energy, we obtain the values negative-helicity antineutrino energy positive-helicity antineutrino energy antiparticle (antineutrino) energies in matter

  17. Neutrino processes in matter Neutrinoreflection from interface between vacuum and matter Neutrino trapping in matter Neutrino-antineutrino pair annihilationat interface between vacuum and matter Spontaneousneutrino-antineutrino pair creation in matter L.Chang, R.Zia,’88 A.Loeb,’90 J.Panteleone,’91 K.Kiers, N.Weiss, M.Tytgat,’97-’98 M.Kachelriess,’98 A.Kusenko, M.Postma,’02 H.Koers,’04 A.Studenikin, A.Ternov,’04

  18. Neutrinoreflection from interface between vacuum and matter forbidden energy zone neutrino is reflected from the interface. If the neutrino energy in vacuum isless than the neutrino minimal energy in medium vacuum matter matter density parameter forbidden energy zone then the appropriate energy level inside the medium isnot accessible for neutrino

  19. Neutrino trapping in matter forbidden energy zone Antineutrino in mediumwith energy can not escapefrom the medium because this particular range of energies exactly falls on the forbiddenenergy zone invacuum : matter density parameter vacuum matter forbidden energy zone Antineutrino has not enough energy to survivein vacuum it is trapped inside the medium.

  20. Neutrino-antineutrino pair annihilationat interface between vacuum and matter matter density parameter Consider a neutrino with energy propagating in vacuum towards the interface with matter. If not all of “negative sign” energy levels are occupied and, in particular, the level with energy exactly equal to is available an antineutrino exists in matter : vacuum matter forbidden energy zone forbidden energy zone neutrino-antineutrino annihilation at the interface of vacuum and matter.

  21. Spontaneousneutrino-antineutrino pair creation in matter ”Negative sign” energy levels in matter have their counterparts in ”positive sign” energy levels in vacuum: vacuum matter matter density parameter forbidden energy zone forbidden energy zone A.Loeb,’90; K.Kiers, M.Tytgat, N.Weiss,’97-’98; M.Kachelrieß,’98; A.Kusenko, M.Postma,’02; H.Koers,’04 Neutrino-antineutrinopair creationcan be interpretedas a process of appearance of particle state of in the ”positive sign” energy rangeaccompanied by appearance of the hole state in the ”negative sign” energy sea. Spontaneous electron-positron pair creation according to Klein’s paradox of electrodynamics.

  22. An important note (II) The neutrino energyspectrum in the relativistic case and in the low density limit the energies of theneutrinohelicity states correct energies of theneutrinochiral states active left-handed neutrino sterile right-handed neutrino

  23. Neutrino flavour oscillations in matter Consider the two flavour neutrinos, and , propagating in electrically neutral matter of electrons , protons and neutrons : . The matter density parameters are and , respectively. The energies of the relativistic active neutrinos are and the energy difference MSW effect

  24. Modified Dirac-Pauli equation for neutrino in matter Recently we have developed the quasi-classical approachto a massive neutrino spin evolution in the presence of external electromagnetic fields and background matter.The well known Bargmann-Michel-Telegdi equation of QED has been generalized for the caseof a neutrino moving in matter and externalelectromagnetic fieldsby the following substitution of the electromagnetic field tensor: matter current where (for a neutrino with zero dipole electric moment) neutrino speed (matter content) matter polarization in particular plays the role of a magnetic field

  25. Dirac-Pauli equation of electrodynamics The Dirac-Schwinger equation for a massive neutrino in an external electromagnetic field neutrino mass operator in electromagnetic field in the linear approximation over the electromagnetic field the Dirac-Pauli equation : neutrino magnetic moment the Hamiltonian form of which reads for the case of a magnetic field reads

  26. Modified Dirac-Pauli equation for neutrino in matter From with the substitution neutrino speed For the electron neutrino moving in unpolarized matter (electrons) at rest In the Hamiltonian form: number density of matter

  27. Stationary states neutrino wave function in matter neutrino energy spectrum in matter and for two helicity states where thematter density parameter Neutrino wave function

  28. The two energy spectra Dirac Dirac-Pauli In the limit of low density: are not equal However, the differences of energies of the two neutrino helicity states equals

  29. Modified Dirac-Pauli equation in matter and magnetic field simultaneouslyaccounts for interactionswith external electromagnetic fields andalso weakinteraction with background matter . If a constant magneticfield is present in the background and a neutrino is moving parallel (oranti-parallel) to the field vector , then the neutrino energyspectrum can be obtained by and . The energy gap between the two neutrino helicity states in magnetized matter

  30. Neutrino oscillation in magnetized matter The Dirac-Pauli energy spectrum of a neutrino in magnetized matter can be used for derivation of the neutrino oscillation probability . In the case of relativistic neutrino energies and constant magnetic field oscillation probability (adiabatic approx.) A.Lobanov, A.Studenikin, Phys.Lett.B 515 (2001) 94

  31. Spin Light of Neutrino in matter Quantum theory of A.Studenikin, A.Ternov, Phys.Lett.B608 (2005) 107; A.Grigoriev, A.Studenikin, A.Ternov, Grav. & Cosm.(2005), in press; A.Grigoriev, A.Studenikin, A.Ternov, hep-ph/0502210, hep-ph/0502231; A.Studenikin, A.Ternov, hep-ph/0410296, hep-ph/0410297.

  32. Spin light of neutrino in matter and electromagnetic fields

  33. Quasi-classical theory ofspin light of neutrino in matter A.Lobanov, A.Studenikin, Phys.Lett.B 564(2003) 27, Phys.Lett.B 601(2004) 171

  34. Quasi-classical approach to radiation process

  35. Generalized BMT equation in matter Neutrinospin precession is described by the generalized Bargmann-Michel-Telegdi equation: A.Lobanov, A.Studenikin, Phys.Lett.B 564(2003) 27 A.Egorov, A.Lobanov, A.Studenikin PLB 491 (2000) 137, PLB 515 (2001) 94 speed of neutrino and are transversal and longitudinal e.m. fields in laboratory frame.

  36. Quantum theory of spin light of neutrino (I) Quantum treatment of spin light of neutrino in matter shownsthat this process originates from thetwo subdivided phenomena: the shift of the neutrino energy levels in the presence of thebackground matter, which is different for the two opposite neutrino helicity states, the radiation of the photon in the process of the neutrino transition from the ”exited”helicity state to the low-lying helicity state in matter A.Studenikin, A.Ternov,Phys.Lett.B608(2005) 107 neutrino-spin self-polarization effect in the matter A.Lobanov, A.Studenikin,Phys.Lett.B564(2003) 27

  37. Quantum theory of spin light of neutrino Within the quantum approach, the correspondingFeynman diagram is theone-photon emission diagram with the initialand final neutrino states described by the "broad lines“that account for the neutrino interaction with matter. Neutrino magnetic momentinteraction withquantized photon theamplitude of the transition momentum polarization of photon

  38. Spin light of neutrino photon’s energy transition amplitude after integration : For not very high densities of matter , , in the linear approximation over Energy-momentum conservation For electron neutrino moving in matter composed of electrons photon’s energy neutrino self-polarization In the radiation process: neutrino speed in vacuum

  39. Spinlight transition rate (I) The matter density parameter is accounted for exactly: momentum for low densities is the angle between the initial neutrino and photon momenta: : energy of initial neutrino energy of final neutrino Non-trivial dependence on the matter density parameter : .

  40. Spin light transition rate (II) Performing the integration over the photon’s angle one obtains for the spin light of neutrino rate in matter : where the matter density parameter and the initial neutrino energy .

  41. “relativistic” case “non-relativistic” case Spin light transition rate (III) transition rate for different neutrino momentum and matter density parameter neutrino momentum mass neutrino magnetic moment

  42. Spin light radiation power “relativistic” case “non-relativistic” case radiation power angular distribution :

  43. radiation power transition rate “relativistic” case “non-relativistic” case Spin light photon’s average energy energy range of span up to gamma-rays

  44. Spatial distribution of radiation power From the angular distribution of maximum in radiation power distribution for and neutrino momentum for and matter density mass increase of matter density projector-like distribution cap-like distribution

  45. The case of relativistic neutrino : and rather dense plasma Only photonswith energy that exceedsplasmon frequency fine-structure constant can propagate in electron plasma. maximal value of photon’s energy photon’s energy in direction of radiation power maximum photon energy plasmon frequency radiation power Propagation of spin light photon in plasma Angular distributions of photon energy and radiation power for

  46. Polarization properties of photons (I) Radiation power of linearly polarized photons: where and . In the limit of low matter density : is linearly polarized. In dense matter spin light of neutrino is not polarized : .

  47. Polarization properties of photons (II) correspond to the photonright and leftcircular polarizations. however Radiation power of circulary polarized photons: where In the limit of low matter density : . In dense matter : In a dense matter is right-circular polarized.

  48. Conclusions Quantum approach to neutrino propagation in a dense matter Modified Dirac equation for a neutrino wave function in a background Modified Dirac-Pauli equation for neutrino in background matter Exact solution of modified Dirac and Dirac-Pauli equation in matter Neutrino wave function and energy spectrum in matter Neutrino oscillations in matter and magnetic field Quantum theory of neutrino spin light in matter Transition rate, radiation power, photon’s energy and polarization Spatial angular distribution and polarization

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