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 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

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

!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. gˆµ⌫ = ⌘µ⌫ + hˆµ⌫

!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.

2 2 2 mj mk m L iEat ⌫f (t) >= Vfae ⌫a > jk = 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 !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 2 3 L m 10TeV ! x 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 ‘phase of oscillation’ to give a probability for the neutrino to be detected in a ﬂavor state of: P (⌫ ⌫ )= V 2 V 2 ↵ ! | i| | ↵i| i X !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:

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 ik,j +ik,j G P⌫f ⌫ (E,L)= Vf 0j Vf 0ke Vfj⇤ Vfk⇤ ! f0 k,j = k,j ! Xj,k h i 1 rd GM = dl h i L c2r neutronstar = 0.20 Penrose decoherenceZrc for neutrinosh i is this combined with quantum collapse models (CSL-like).

!9 OUTLINE

Introduction Quantum decoherence Neutrino-graviton scattering Graviton bremsstrahlung Detection Conclusions

!10 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⌫ 2 ⇠ MPl

!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.

m2 i a L ⌫ ⌫ = e 2E⌫ Vaf f ! a

!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):

2 dT AK ,K A⇤ dEE V ⇤ V˜,K V↵,M V˜ ⇤ D(p0 )P (pK )⇤ (p0 )⇤ (pM )FK,K F ⇤ ! 0 M 0,M ⇠ ↵,K 0 ,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

!14 OUTLINE

Introduction Quantum decoherence Graviton bremsstrahlung First order calculation Photon bremsstrahlung Towards second order calculation Detection Conclusions

!15 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. !16 νa νa

G G (b) GRAVITON BREMSSTRAHLUNG

6 2 2 d  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⌫ GBH 6 ,M E⌫ m⌫ ⇠ MPl 57 2 6 4 M 10 GeV gives M /M 1GeV ⇠ Pl ⇠ !17 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.

!18 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 spherical wave; and $, is the final wave function asymptotically 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 probability 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. !19 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. aaa M. P. b Q D 40

2.0 2.0

0 I I I I 0 50 60 90 120 150 180 0 I I I I 0 30 60 90 120 150 180 photon angle (deg. ) FIG. 8. Comparison of present results (solid line for photon angle (deg. ) HFS field, double-dotted-broken line for point-Coulomb FIG. 7. Comparison of present results (solid line for field) with the Born-approximation results (broken line), HFS field, double-dotted-broken line for point-Coulomb the results of BZRP (dotted-broken line), the results of field) with the Born-approximation results (broken line), EH (crosses), the experimental data of MP (triangles) the results of BZRP (dotted-broken line), the results of and of Rester (circles), and the nonrelativistic results EH (crosses), and the experimental data of MP (triangles) (dotted line for N. R.W. O. R. , triple-dotted-broken line and — of Rester (circles) for the case Z=13, T& =0.050 for N. R.W. R. ) for the case Z=13, T& —0.050 MeV, MeV, k = 0.030 MeV. k = 0.020 MeV. TOWARDS SECOND ORDER CALCULATION

Loop corrections are important but won’t change ﬁrst order result (‘large’). Effective quantum gravity is equivalent to semi- classical quantum gravity at 2-loop. Overall differential cross section will be sensitive to Quantum Gravity models.

!20 OUTLINE

Introduction Quantum decoherence Graviton bremsstrahlung Detection Detection Detection with Earth MSW Analytical formula Story Conclusions

!21 DETECTION

For certain neutrino production mechanisms (pion or muon), neutrinos of high energy (>10 TeV) won’t experience propagation decoherence:

2 8 ! dL L m 10TeV 3 10 sec .1 2 ⇥ x ⇠ 100Mpc 8 10 5eV E ⌧muon ⇥ ✓ ◆ However, even for coherent fluxes, due to detector limitations, no measurable difference can be seen between coherent fluxes and decoherent fluxes (without the consideration of Earth MSW). m2L ! jk = 4E⌫ For extremely high energy (10 EeV) and close (10 kpc), the phase may be small and the flux coherent. In this case the coherent flux may be compared to the decoherent flux due to graviton interaction. NEUTRINO PROPAGATION

Df G ⇤ ⌫a Pi Di Pi ⌫a Di ⌫f

G Pf Df Pf Neutrino produced and detected in detector Neutrino produced and detected in flavor state, exists as a definite mass in flavor state, exists in state (due to graviton ‘observation’), superposition of mass states, decoherence due to only single neutrino decoherence caused by separation state propagating. of mass states. !23 DETECTION: EARTH MSW

Neutrinos which are decoherent due to propagation exist as a decoherent superposition of mass eigenstates. Neutrinos which are decoherent due to quantum gravity exist as a single mass eigenstate. For signiﬁcant changes of matter potential, the neutrino state’s ﬂavor is matched for both propagating bases. Expect an (energy and location dependent) >10% effect for decoherent electron neutrinos which have not had an interaction with a graviton, ~0% for neutrinos which have (for low energy). Ratio

1.04 Analytic calculation in 2 ﬂavor 1.02 approximation without Earth’s Core. Orange is neutrinos which have 1.00 experienced propagation decoherence. 0.98 Constant density approximation. 0.96

Neutrino Energy MeV !24 5 10 15 20

H L DETECTION: EARTH MSW (CONST. DENSITY, 2 REGION, 2 FLAVOR APPROXIMATION) Space Flavor Match Earth

2 i 2 i 2 im 2 im cos (✓) e +sin (✓) e cos (✓m) e +sin (✓m) e νe

νe i i i i sin (✓)cos(✓) e e sin (✓ )cos(✓ ) e m e m m m Coherent

2 i 3⇡ 2 i 3⇡ 2 i 2 i cos (✓) e 4 +sin (✓) e 4 cos (✓ ) e m +sin (✓ ) e m m m νe

νe i 3⇡ i 3⇡ im im sin (✓)cos(✓) e 4 e 4 sin (✓m)cos(✓m) e e Propagation⇣ Decoherence⌘ 2 im 2 im 2 cos (✓) cos (✓m) e +sin (✓m) e Pe1 =cos (✓) ν1 i i νe sin (✓) sin (✓ )cos(✓ ) e m e m Or m m νe 2 2 im 2 im Pe2 =sin (✓) ν2 sin (✓) cos (✓m) e +sin (✓m) e im im cos (✓) sin (✓m)cos(✓m) e e Quantum Gravity Decoherence !25 ANALYTICAL RESULT

The ratio of neutrinos which have experienced propagation decoherence:

cos (˜x)2 (3 + cos (4✓)) + (2 + cos (4✓ 8✓)+cos(4✓ 4✓)) sin (˜x)2 2sin(2˜x)sin(2✓ 2✓)sin(2✓) ! m m m ⇣ 3+cos(4✓) ⌘ The ratio of neutrinos which have experienced quantum gravity decoherence: 5+cos(4✓ )+cos(4✓ 4✓)+cos(4✓)+4cos(2˜x)cos(2✓)sin(2✓ 2✓) ! m m m 6+2cos(4✓) This is for 2 region vacuum/constant density and 2 ﬂavor approximation. Here

2 2 2 sin (2✓) 2 2AE⌫ sin (2✓ ) = m 2 2 x˜ = x sin (2✓) + cos (2✓) 2 2AE⌫ m sin (2✓) + cos (2✓) 2 s ✓ ◆ m !26 WITH CORE - 3 FLAVOR

2 10

1.8

1.6

1.4 1.2 Ratio with and without 1 1

0.8 0.6 Earth MSW effect due to 0.4 0.2 initial electron neutrino. 0 10-1 0246810121416 024681012141618202224 Energy (MeV) Energy (MeV) (a) Earth MSW (500 keV) (b) Earth MSW (50 keV)

3 30

2.5 25

2 20

1.5 15

1 10 1.1

0.5 5 1.08

1.06 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 10 20 30 40 50 60 70 80 Energy (MeV) Energy (MeV) 1.04

(d) Earth MSW (500 keV) (c) Earth MSW (500 keV) MSW Earth to due Difference 1.02

0.98

0.96

0.94 0 2 4 6 8 10 12 14 16 18 20 Without Core Neutrino Energy (MeV) STORY

Neutrino ~Solar Mass Production Star BH DM ν Earth

Detector AGN Detector SNe GRB

!28 OUTLINE

Introduction Quantum decoherence Graviton bremsstrahlung Detection Conclusions Interaction conclusions Neutrino observatories Detection conclusions Summary

!29 INTERACTIVE CONCLUSIONS

Gravity QFT interactions, due to hard graviton emission, have reasonably high cross-section in the presence of classical masses. Effective versus fundamental QFT? Neutrino oscillation behavior can be used as an observable to measure this cross- section. Due to the difference between quantum gravity induced decoherence and decoherence due to propagation, existing in a single mass eigenstate versus a decoherent superposition of mass eigenstates, measuring the Earth MSW effect can provide an energy dependent >10% difference in expectations. Quantum Gravity can be measured! For astrophysical neutrinos a point source is required (SNe/GRB/AGN) and large (low energy?) neutrino detectors at multiple points around the world (Chile, Japan, North America, Europe, Antarctica) to differentiate the quantum gravity induced decoherence from other sources of decoherence. !30 NEUTRINO OBSERVATORIES

Active Modern Planned

Sudbury LAGUNA Sanford Underground Lab Gran Sasso KM3NeT Kamioka

ANDES ? ?

IceCube !31 LOW ENERGY NEUTRINO OBSERVATORIES

Observatory Size + Type Location near SNe # Super-K 32 kT (Water) Japan - Now 7000 Borexino 0.3 kT (Scint) Italy - Now 100 SNO+ 0.8 kT (Scint) Canada-Now* 300 LBNE(1) 10 kT (Argon) USA-201X 1000 HALO 0.08 kT (Lead) Canada-Now* 30 LAGUNA** 100 kT (Mixed) Europe - 202X 15000 ANDES*** 3 kT (Scint) Chile - 202X 1000 Hyper-K 530 kT (Water) Japan -202X? 110000 Beyond DC 1 MT (Ice) Antarctica-203X? ?? DETECTION CONCLUSIONS

Neutrino observatories in South America, South Africa, and Australia will improve chance to measure response to the Earth matter effect (with core). Especially interested in < 1 GeV (below IceCube). Need to investigate possible source spectrums (GRB, DM annihilation/decay, SuperNova, etc). Need Quantum Gravity theorists to improve theory so that proper calculation can be done for structure (point versus star/DM halo/etc).

!33 SUMMARY

Neutrino travelling through a massive field experiences radically different effects depending on describing the interaction in QFT framework or in GR framework. In STG, cross section for graviton bremsstrahlung may be large to first order. STG and ETG are equivalent in far field, high mass limit. Corrections needed. Decoherent neutrino fluxes due to propagation decoherence (where each neutrino is decoherent) and quantum gravity decoherence (where each neutrino is coherent) may be discriminated using the Earth MSW. Thank you for listening.