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QUANTUM GRAVITY EFFECT on NEUTRINO OSCILLATION Jonathan Miller Universidad Tecnica Federico Santa Maria

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QUANTUM GRAVITY EFFECT on NEUTRINO OSCILLATION Jonathan Miller Universidad Tecnica Federico Santa Maria QUANTUM GRAVITY EFFECT ON NEUTRINO OSCILLATION Jonathan Miller Universidad Tecnica Federico Santa Maria ARXIV 1305.4430 (Collaborator Roman Pasechnik) !1 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 2 38 2 graviton interactions suppressed by (MPl ) ~10 GeV Many sources of astrophysical neutrinos (SNe, GRB, ..) Neutrino states during propagation are different from neutrino states during (weak) interactions !2 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. gˆµ⌫ = ⌘µ⌫ + hˆµ⌫ !3 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. 2 2 2 mj mk ∆m L iEat ⌫f (t) >= Vfae− ⌫a > φjk = − L = | | 2E⌫ 4E⌫ a X 2 m m2 i j L i k L 2E⌫ 2E⌫ P⌫f ⌫ (E,L)= Vf 0jVf 0ke− e Vfj⇤ Vfk⇤ ! f0 j,k X !4 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. !5 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 2 3 L ∆m 10TeV ! σx dL =3 10− cm ⌧ ⇥ 100Mpc 2.5 10 3eV2 E ⇥ − ✓ ◆ After decoherence due to propagation, a single neutrino still exists as a superposition of mass eigenstates (in vacuum) but has a constant in ‘phase of oscillation’ to give a probability for the neutrino to be detected in a flavor state of: P (⌫ ⌫ )= V 2 V 2 ↵ ! β | βi| | ↵i| i !6X 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: t i d i rd i Rd 1 ⌫ ! t Hdt+ P dx (⌘µ⌫ + hµ⌫ )dx e− ~ c ~ rc · ⌫i = e− ~ Rc 2 ⌫i R R | i R | i Giving the standard transition probability but with a extra phase due to the gravitational interaction. G iφk,j +iφk,j G P⌫f ⌫ (E,L)= Vf 0j Vf 0ke Vfj⇤ Vfk⇤ ! f0 φk,j = Φ φk,j ! Xj,k h i 1 rd GM Φ = dl h i −L c2r Φ neutronstar = 0.20 Penrose decoherenceZrc for neutrinosh i is this combined− with quantum collapse models (CSL-like). !7 νf νa νa G ∗ G (a) black hole NEUTRINO- νf GRAVITON νa νa SCATTERING Analogical to Compton G Scattering G (b) “Graviton physics”, BR Holstein, 2006. 2 E⌫ σ 2 ⇠ MPl !8 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. m2 i a L ⌫ ⌫ = e− 2E⌫ Vaf f ! a !9 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): 2 dT AK ,K A⇤ dEE V ⇤ V˜β,K V↵,M V˜ ⇤ ΦD(p0 )ΦP (pK )Φ⇤ (p0 )Φ⇤ (pM )FK,K F ⇤ ! 0 M 0,M ⇠ ↵,K 0 β,M0 K0 D M 0 P 0 M,M0 Z Z K0,K,MX 0,M For the graviton interaction, V is diagonal. The condition on the graviton energy: EG >F(∆m) NEUTRINO DETECTION 2 2 Probability for initial Pe 1 = cos ✓12 cos ✓13 ! electron neutrino to be in 2 2 Pe 2 = cos ✓13 sin ✓12 mass eigenstate depends on ! PMNS matrix element. 2 Pe 3 =sin ✓13 ! Independent of energy, distance travelled, phase. Ne,det vac = Pee (1 PG)+ Flavor measurement Ne,init − depends on PG, The probability for neutrino to PG VeiVie⇤VeiVie⇤ i=1,2,3 have interacted with graviton X !11 GRAVITON BREMSSTRAHLUNG NEUTRINO- νf MASSIVE SOURCE νa νa SCATTERING Analogical to Photon Bremsstrahlung on Nucleus G ∗ G (a) black hole B. M. Barker, S. N. Gupta, J. Kaskas, νf Phys. Rev. 182 (1969) 1391-1396. !12 νa νa G G (b) GRAVITON BREMSSTRAHLUNG 6 2 2 dσ M p0 k0 (I (p, k, p0)) = 5 | | 4 dk0d⌦kd⌦p (4⇡) p (k + p p) 0 | | 0 − scattering of small mass (m) off large mass (M) more correct then considering external field spinless approximation, result after summation over polarization 2 2 M E⌫ σGBH 6 ,M E⌫ m⌫ ⇠ MPl 57 2 6 4 M 10 GeV gives M /M 1GeV− ⇠ Pl ⇠ !13 GRAVITON BREMSSTRAHLUNG 100 100 + BH -> + G + BH cross section + BH -> + G + BH E =1 MeV 0.01 + BH -> + G + BH E =1 MeV differential cross section in graviton energy E G differential cross section in neutrino angle 10 0.001 10 1 0.0001 , mb , mb , mb/GeV G /d 0.1 d /dE 1 1e-05 d 0.01 1e-06 0.1 0.001 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 1e-07 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 EG, 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 Eν may be measurable. May be sensitive to next order corrections. !14 PHOTON BREMSSTRAHLUNG E XAC T SCREENED CAL CU LAT IONS ~ ~ 103 = — — — 22tt Mt 4 f't(E, E2 k) (2. 4) Z* I3 8.0— E Here Comparisons between TI O.OSOMeV N E 0.040MeV — = 42/k)' 4:~ ' - - Born Approx. M&; (2tt f d rtt2 tr g, e ' . xxx E.H. tree level and more —.—B.Z. R.P. HFS g Present Point Coulomb —.-- J Theory o o o Rester accurate models have fx t. J p' M. P. ))aaa o are the familiar 2x 2 Pauli matrices; g& is ce b '0 the initial wave function asymptotically nor- been made for photon D '0 4p malized to a unit-amplitude modified plane wave bremsstrahlung. of four-momentum (E„pt) plus an outgoing spher- ical wave; and $, is the final wave function asymp- totically normalized to a unit-amplitude modified 2.0 plane wave of four-momentum plus an in- ' (E2, p2) Tree level is accurate to coming spherical wave. The transition prob- ability per unit time between the states is then first order, corrections of 0 I I I — — 0 50 60 90 120 150 180 &y; =» I Myt I &(Et E2 k) less than factor of ~10. photon angle (deg. ) from which we can obtain the cross section by sum- FIG. 6. Comparisons of present results (solid line ming over the energies of the final state and divid- for HFS field, double-dotted-broken line for point-Cou- ing by the flux of incoming particles (in this case lomb field) with the Born-approximation results (broken the velocity of the incident electron v, relative to Requires theory input line), the results of BZRP (dotted-broken line), the results of EH (crosses), and the experimental data of MP (triangles) and of Rester (circles) for the case Z=13, for quantum gravity. T& = 0.050 MeV, k = 0.040 MeV. Z = I3 H. K. Tseng and R. H. Pratt, Phys. Rev. A 3 (1971) 100-115. !15 T, = O.OSOMeV =-( — it = 0.020MeV k I l te d 4'(x) 4"'(x) x: I p, f + (x): p, ) ———Born Approx. xxx E.H. 10.0— — Z. R.P. 4 Q i2'r e-i &El B. (2&/k)1/2 d xqt ~ f tlt e E2-tt)t- f HFS ) Present Point Coulomb —"—3 Theory f o o o Rester a a M. P. 8.0— —N. R.W. R. Z= ' '' N. R.W. O. R. I3 ul 8.0— Ti E 0 050 MeV * Cl k 0030MeV E ———Bor n Appr ox. xxx ~ 6.0 —' — P. b 0 Ol B.Z. R. 6.0— HFS ) Present Point Coulomb —"— E J Theory o o o Rester E xpt.
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