QUANTUM GRAVITY EFFECT ON NEUTRINO OSCILLATION Jonathan Miller Universidad Tecnica Federico Santa Maria ARXIV 1305.4430 (Collaborator Roman Pasechnik) � 1
NOTES ON LANGUAGE Strong gravity in the paper referred to the gravitational field that a particle would experience due to a classical mass. Examples would be in the ‘vicinity’ of a black hole or star. Decoherence is used with respect to the experimental observation of a given neutrino flux. Neutrino fluxes which no longer demonstrate oscillation demonstrate decoherence. Sources of decoherence can then be compared. � 2
OUTLINE Introduction Semi-classical gravity Neutrino physics Propagation decoherence Classical gravity Quantum decoherence Graviton bremsstrahlung Detection Conclusions � 3
INTRODUCTION Neutrinos are ideal probes of distant ‘laboratories’ as they interact only via the weak and gravitational forces. 3 of 4 forces can be described in QFT framework, 1 (Gravity) is missing (and exp. evidence is missing): semi-classical theory is the best understood graviton interactions suppressed by (M Pl2 ) ~10 38 GeV 2 Many sources of astrophysical neutrinos (SNe, GRB, ..) Neutrino states during propagation are different from neutrino states during (weak) interactions � 4
SEMI-CLASSICAL QUANTUM GRAVITY Class. Quantum Grav. 27 (2010) 145012 Considered in the limit where one mass is much greater than all other scales of the system. Considered in the long range limit. Up to loop level, semi-classical quantum gravity and effective quantum gravity are equivalent. Produced useful results (Hawking/etc). Tree level approximation. g µ ν = η µ ν + ˆ h µ ν ˆ � 5
CLASSICAL NEUTRINO OSCILLATION Neutrino Oscillation observed due to Interaction (weak) - Propagation (Inertia) - Interaction (weak) Neutrino oscillation depends both on production and detection hamiltonians. Neutrinos propagates as superposition of mass states. φ jk = m 2 j − m 2 L = ∆ m 2 L k X V fa e − iE a t | ν a > | ν f ( t ) > = 2 E ν 4 E ν a m 2 m 2 j k X V f 0 j V f 0 k e − i 2 E ν L e i 2 E ν L V ∗ fj V ∗ P ν f → ν f 0 ( E, L ) = fk j,k � 6
MATTER EFFECT neutrinos interact due to flavor (via W/Z) with particles (leptons, quarks) as flavor eigenstates MSW effect: neutrinos passing through matter change oscillation characteristics due to change in electroweak potential effects electron neutrino component of mass states only, due to electrons in normal matter neutrino may be in mass eigenstate after MSW effect: resonance Expectation of asymmetry for earth MSW effect in Solar neutrinos is ~3% for current experiments. � 7
PROPAGATION DECOHERENCE M. Beuthe, Phys. Rept. 375, 105 (2003). Y. Farzan and A. Y. Smirnov, Nucl. Phys. B 805, 356 (2008). During propagation neutrinos may experience dispersion or separation of the eigenstates which are the state of propagation (this changes based on the electromagnetic potential). As the neutrino propagates, the coherence (in vacuum) depends on -4 ), wavepacket size (production process, depending on process can be ~10 neutrino energy, length of propagation, and mass difference: ◆ 2 ∆ m 2 ✓ 10TeV L � σ x ⌧ d L = 3 ⇥ 10 − 3 cm 2 . 5 ⇥ 10 − 3 eV 2 100Mpc E After decoherence due to propagation, a single neutrino still exists as a superposition of mass eigenstates (in vacuum) but has a constant ‘phase of oscillation’ to give a probability for the neutrino to be detected in a flavor state of: X | V β i | 2 | V α i | 2 P ( ν α → ν β ) = i � 8
CLASSICAL NEUTRINO GRAVITY INTERACTION D.V . Ahluwalia, and C. Burgard, Phys. Rev. D 57, 4724 (1998). Different mass states travel in different geodesics, creating a gravitational phase which builds up over distances. In the region of a classical mass, using GR, the propagation can be given in terms of the flat and Schwarzschild metric: � R td R rd R Rd Rc ( η µ ν + 1 2 h µ ν ) dx ν | ν i i e − i tc Hdt + i rc P · dx | ν i i = e − i ~ ~ ~ Giving the standard transition probability but with a extra phase due to the gravitational interaction. V f 0 j V f 0 k e i φ k,j + i φ G X k,j V ∗ fj V ∗ φ G P ν f → ν f 0 ( E, L ) = k,j = �h Φ i φ k,j fk � j,k Z r d dlGM h Φ i = � 1 h Φ i neutronstar = � 0 . 20 L c 2 r Penrose decoherence for neutrinos is this combined with r c quantum collapse models (CSL-like). � 9
OUTLINE Introduction Quantum decoherence Neutrino-graviton scattering Graviton bremsstrahlung Detection Conclusions � 10
NEUTRINO- ν f GRAVITON ν a ν a SCATTERING Analogical to Compton G G Scattering “Graviton physics”, BR Holstein, 2006. σ ∼ E 2 ν M 2 P l � 11
GRAVITON INTERACTION Neutrinos interact due to mass (via gravitons) with particles (for example: solar masses) as mass eigenstates. Propagating neutrino is ‘observed’ by hard graviton, has definitive mass, propagates in a mass eigenstate. Neutrino in definitive mass state due to Interaction (weak) - Propagation (inertia) - Graviton Interaction (gravitation) - Propagation (inertia) - Interaction (weak) Neutrino ceases to demonstrate oscillation phenomena or effects depending on being in a superposition of mass states. m 2 2 E ν L V af a Ψ ν f → ν a = e − i � 12
GRAVITON INTERACTION: DETAILS The probability can be given in terms of the transition amplitude squared. In any real measurement, energy is integrated over (Detection, Production, momentum): Z Z α ,K ˜ V β ,K 0 V α ,M ˜ X dEE 2 dTA K 0 ,K A ⇤ V ⇤ V ⇤ β ,M 0 Φ D ( p 0 K 0 ) Φ P ( p K ) Φ ⇤ D ( p 0 M 0 ) Φ ⇤ P ( p M ) F K,K 0 F ⇤ M 0 ,M ∼ � M,M 0 K 0 ,K,M 0 ,M For the graviton interaction, V is diagonal. The condition on the graviton energy: E G > F ( ∆ m )
NEUTRINO DETECTION P e → 1 = cos 2 θ 12 cos 2 θ 13 Probability for initial electron neutrino to be in P e → 2 = cos 2 θ 13 sin 2 θ 12 mass eigenstate depends on PMNS matrix element. P e → 3 = sin 2 θ 13 Independent of energy, distance travelled, phase. N e , det = P vac ee (1 − P G )+ Flavor measurement N e , init depends on P G , The X V ei V ∗ ie V ei V ∗ P G probability for neutrino to ie have interacted with graviton i =1 , 2 , 3 � 14
OUTLINE Introduction Quantum decoherence Graviton bremsstrahlung First order calculation Photon bremsstrahlung Towards second order calculation Detection Conclusions � 15
GRAVITON BREMSSTRAHLUNG NEUTRINO- ν f MASSIVE SOURCE ν a ν a SCATTERING Analogical to Photon Bremsstrahlung on Nucleus G ∗ G B. M. Barker, S. N. Gupta, J. Kaskas, Phys. Rev. 182 (1969) 1391-1396. � 16
GRAVITON BREMSSTRAHLUNG k 0 ( I ( p , k , p 0 )) 2 dk 0 d Ω k d Ω p 0 = κ 6 M 2 | p 0 | d σ (4 π ) 5 ( k + p 0 − p ) 4 | p | scattering of small mass (m) off large mass (M) more correct then considering external field spinless approximation, result after summation over polarization σ GBH ⇠ M 2 E 2 ν , M � E ν � m ν M 6 P l M ∼ 10 57 GeV gives M 2 /M 6 P l ∼ 1 GeV − 4 � 17
GRAVITON BREMSSTRAHLUNG 100 100 0.01 � + BH -> � + G + BH E � =1 MeV � + BH -> � + G + BH cross section � + BH -> � + G + BH E � =1 MeV differential cross section in graviton energy E G differential cross section in neutrino angle � 10 0.001 10 d � /dE G , mb/GeV 1 0.0001 d � /d � , mb � , mb 0.1 1 1e-05 0.01 1e-06 0.1 0.001 1e-07 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.5 1 1.5 2 2.5 3 E � , GeV E G , MeV � , rad The bulk of the cross section comes form soft graviton emission in forward limit. The cross section is larger than electron-neutrino cross section by 16-18 order of magnitudes. Real, hard gravitons may be produced. Cross section with respect to E ν may be measurable. May be sensitive to next order corrections. � 18
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