QUANTUM GRAVITY EFFECT ON NEUTRINO OSCILLATION Jonathan Miller - - PowerPoint PPT Presentation

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QUANTUM GRAVITY EFFECT ON NEUTRINO OSCILLATION

Jonathan Miller Universidad Tecnica Federico Santa Maria

ARXIV 1305.4430 (Collaborator Roman Pasechnik)

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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’

• f a black hole or star.

Decoherence is used with respect to the experimental

• bservation of a given neutrino flux. Neutrino fluxes

which no longer demonstrate oscillation demonstrate

• decoherence. Sources of decoherence can then be

compared.

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OUTLINE

Introduction Semi-classical gravity Neutrino physics Propagation decoherence Classical gravity Quantum decoherence Graviton bremsstrahlung Detection Conclusions

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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 (MPl2) ~1038 GeV2 Many sources of astrophysical neutrinos (SNe, GRB, ..) Neutrino states during propagation are different from neutrino states during (weak) interactions

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SEMI-CLASSICAL QUANTUM GRAVITY

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.

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ˆ gµν = ηµν + ˆ hµν

• Class. Quantum Grav. 27 (2010) 145012

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CLASSICAL NEUTRINO OSCILLATION

Pνf →νf0 (E, L) = X

j,k

Vf 0jVf 0ke−i

m2 j 2Eν Lei m2 k 2Eν LV ∗

fjV ∗ fk

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.

|νf (t) >= X

a

Vfae−iEat|νa >

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φjk = m2

j − m2 k

2Eν L = ∆m2L 4Eν

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MATTER EFFECT

neutrinos interact due to flavor (via W/Z) with particles (leptons, quarks) as flavor eigenstates MSW effect: neutrinos passing through matter change

• scillation 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.

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PROPAGATION DECOHERENCE

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 wavepacket size (production process, depending on process can be ~10

• 4),

neutrino energy, length of propagation, and mass difference:

• After decoherence due to propagation, a single neutrino still exists as a

superposition of mass eigenstates (in vacuum) but has a constant ‘phase of

• scillation’ to give a probability for the neutrino to be detected in a flavor

state of:

• M. Beuthe, Phys. Rept. 375, 105 (2003).
• Y. Farzan and A. Y. Smirnov, Nucl. Phys. B 805, 356 (2008).

σx ⌧ dL = 3 ⇥ 10−3cm L 100Mpc ∆m2 2.5 ⇥ 10−3eV2 ✓10TeV E ◆2

P (να → νβ) = X

i

|Vβi|2|Vαi|2

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CLASSICAL NEUTRINO GRAVITY INTERACTION

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:

• Giving the standard transition probability but with a extra phase

due to the gravitational interaction.

• Penrose decoherence for neutrinos is this combined with

quantum collapse models (CSL-like).

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D.V . Ahluwalia, and C. Burgard, Phys. Rev. D 57, 4724 (1998).

e− i

~

R td

tc Hdt+ i ~

R rd

rc P ·dx|νii = e− i ~

R Rd

Rc (ηµν+ 1 2 hµν)dxν|νii

Pνf →νf0 (E, L) = X

j,k

Vf 0jVf 0keiφk,j+iφG

k,jV ∗

fjV ∗ fk

φG

k,j = hΦiφk,j hΦi = 1 L Z rd

rc

dlGM c2r

hΦineutronstar = 0.20

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OUTLINE

Introduction Quantum decoherence Neutrino-graviton scattering Graviton bremsstrahlung Detection Conclusions

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G G νa νf νa

NEUTRINO- GRAVITON SCATTERING

Analogical to Compton Scattering

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“Graviton physics”, BR Holstein, 2006.

σ ∼ E2

ν

M 2

P l

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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

• n being in a superposition of mass states.

Ψνf →νa = e−i

m2 a 2Eν L Vaf

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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):

• For the graviton interaction, V is diagonal.

The condition on the graviton energy:

Z dTAK0,KA⇤

M 0,M ∼

Z dEE2 X

K0,K,M 0,M

V ⇤

α,K ˜

Vβ,K0Vα,M ˜ V ⇤

β,M 0ΦD(p0 K0)ΦP (pK)Φ⇤ D(p0 M 0)Φ⇤ P (pM)FK,K0F ⇤ M,M 0

EG > F (∆m)

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NEUTRINO DETECTION

Probability for initial electron neutrino to be in mass eigenstate depends on PMNS matrix element. Independent of energy, distance travelled, phase. Flavor measurement depends on PG, The probability for neutrino to have interacted with graviton

Pe→1 = cos2 θ12 cos2 θ13 Pe→2 = cos2 θ13 sin2 θ12 Pe→3 = sin2 θ13 Ne,det Ne,init = P vac

ee (1 − PG)+

PG X

i=1,2,3

VeiV ∗

ieVeiV ∗ ie

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OUTLINE

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

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G∗ G νa νf νa

NEUTRINO- MASSIVE SOURCE SCATTERING

Analogical to Photon Bremsstrahlung on Nucleus

• B. M. Barker, S. N. Gupta, J. Kaskas,
• Phys. Rev. 182 (1969) 1391-1396.

GRAVITON BREMSSTRAHLUNG

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GRAVITON BREMSSTRAHLUNG

scattering of small mass (m) off large mass (M) more correct then considering external field spinless approximation, result after summation over polarization

dσ dk0dΩkdΩp0 = κ6M 2 (4π)5 |p0| |p| k0 (I (p, k, p0))2 (k + p0 − p)4 M ∼ 1057 GeV gives M 2/M 6

P l ∼ 1 GeV−4

σGBH ⇠ M 2E2

ν

M 6

P l

, M Eν mν

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GRAVITON BREMSSTRAHLUNG

0.1 1 10 100 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 d/dEG, mb/GeV EG, MeV + BH -> + G + BH E=1 MeV differential cross section in graviton energy EG 0.001 0.01 0.1 1 10 100 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 , mb E, GeV + BH -> + G + BH cross section

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.5 1 1.5 2 2.5 3 d/d, mb , rad + BH -> + G + BH E=1 MeV differential cross section in neutrino angle

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.

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E XAC T SCREENED

CAL CU LAT IONS

~ ~

103

8.0— Z* I3

TI E O.OSOMeV

N

E 0.040MeV

• - —Born

Approx.

xxx E.H.

—

.—B.Z. R.P.

HFS

g Present Point Coulomb —.

• - J Theory

= —

22tt Mt 4 f't(E, — E2 —

k) Here

M&; = (2tt 42/k)' f d rtt2 tr

4:~ g, e ' ' .

(2. 4)

b

ce

D '0

'0 4p

2.0

0 0

I

50

I

60

I

90

120

J o o o Rester

p' )aaa

M.P.

fx t. )

150 180

• are the familiar

2x 2 Pauli matrices;

g& is

the initial

wave function

asymptotically

nor-

malized to a unit-amplitude modified

plane wave

• f four-momentum

(E„pt) plus

an outgoing

spher-

ical wave;

and $, is the final wave function

asymp- totically normalized to a unit-amplitude

modified plane wave of four-momentum (E2, p2) plus

an in-

coming spherical

• wave. '

The transition

prob-

ability per unit time between the states is then

&y; =»

I Myt I

&(Et —

E2 — k)

photon angle

(deg. )

• FIG. 6.

Comparisons

• f present

results

(solid line

for HFS field,

double-dotted-broken line for point-Cou-

lomb field) with the Born-approximation

results

(broken

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,

T& =0.050 MeV,

k =0.040 MeV.

from which we can obtain the cross section by sum-

ming over the energies of the final state and divid- ing by the flux of incoming

particles

(in this case

the velocity of the incident

electron v, relative

to

=-(p, k

I l —

te fd x: 4'(x)4"'(x)+ (x):

Ip, )

(2&/k)1/2 f d 4 xqt ~ f Q tlt e i2'r e-i &ElE2-tt)t- 10.0—

Z

= I3

T, = O.OSOMeV

it

= 0.020MeV

— —

—Born

Approx.

xxx E.H.

—

B.Z. R.P.

HFS

) Present

Point

Coulomb —

"—

3 Theory

8.0—

Ol

6.0—

E

b Q

D 40

Z= I3

Ti

E 0 050 MeV

k * 0030MeV

— ——Bor n

Appr ox.

xxx

—

' —

B.Z. R.P. HFS

) Present

Point Coulomb —

"—

J Theory

• o o Rester

E xpt.

aaa

• M. P.

8.0—

ul

Cl

E

~ 6.0 b 0

f o o o Rester

a a M.P. —

• N. R.W. R.

' '' N. R.W. O.R.

2.0 2.0

0 0

50

I

60

I I

90

120

I

150

180

0 0

I

30

I I I

60 90

120 photon angle

(deg. )

150

180

• FIG. 7.

Comparison

• f present

results

(solid line for HFS field, double-dotted-broken line for point-Coulomb field) with the Born-approximation

results

(broken 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,

T& =0.050

MeV,

k =0.030 MeV. photon angle

(deg. )

• FIG. 8.

Comparison

• f present

results

(solid line for HFS field, double-dotted-broken line for point-Coulomb field) with the Born-approximation

results

(broken line), the results

• f BZRP (dotted-broken

line),

the results

• f

EH (crosses), the experimental data of MP (triangles)

and of Rester (circles), and the nonrelativistic

results

(dotted line for N. R.W.O. R. , triple-dotted-broken

line

for N. R.W. R. ) for the case Z=13,

T& —

—

0.050 MeV,

k =0.020 MeV.

PHOTON BREMSSTRAHLUNG

Comparisons between tree level and more accurate models have been made for photon bremsstrahlung. Tree level is accurate to first order, corrections of less than factor of ~10. Requires theory input for quantum gravity.

• H. K. Tseng and R. H. Pratt, Phys. Rev. A 3 (1971) 100-115.

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TOWARDS SECOND ORDER CALCULATION

Loop corrections are important but won’t change first

• rder 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.

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OUTLINE

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

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DETECTION

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

• 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).

• 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.

dL σx ∼ .1 L 100Mpc ∆m2 8 × 10−5eV2 ✓10TeV E ◆ 3 × 10−8sec τmuon

φjk = ∆m2L 4Eν

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NEUTRINO PROPAGATION

Pf Df Pi νf Di

Pf Df Pi νa G∗ νa G Di

Neutrino produced and detected in flavor state, exists in superposition of mass states, decoherence caused by separation

• f mass states.

Neutrino produced and detected in detector in flavor state, exists as a definite mass state (due to graviton ‘observation’), decoherence due to only single neutrino state propagating.

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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).

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

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5 10 15 20 Neutrino Energy HMeVL 0.96 0.98 1.00 1.02 1.04 Ratio

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DETECTION: EARTH MSW (CONST. DENSITY , 2 REGION, 2 FLAVOR APPROXIMATION)

νe

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Earth Coherent Propagation Decoherence Quantum Gravity Decoherence νe νe Space

Pe1 = cos2 (θ) Pe2 = sin2 (θ)

Flavor Match Or ν1 ν2 νe νe νe

cos2 (θ) eiφ + sin2 (θ) e−iφ cos2 (θm) eiφm + sin2 (θm) e−iφm cos2 (θm) eiφm + sin2 (θm) e−iφm cos2 (θm) eiφm + sin2 (θm) e−iφm cos2 (θm) eiφm + sin2 (θm) e−iφm

cos (θ) cos (θ) sin (θ) − sin (θ)

sin (θm) cos (θm)

• e−iφm − eiφm

sin (θm) cos (θm)

• e−iφm − eiφm

sin (θm) cos (θm)

• e−iφm − eiφm

sin (θm) cos (θm)

• e−iφm − eiφm

sin (θ) cos (θ)

• e−iφ − eiφ

sin (θ) cos (θ) ⇣ e−i 3π

4 − ei 3π 4

⌘

cos2 (θ) ei 3π

4 + sin2 (θ) e−i 3π 4

SLIDE 26

ANALYTICAL RESULT

The ratio of neutrinos which have experienced propagation decoherence:

• The ratio of neutrinos which have experienced quantum

gravity decoherence:

• This is for 2 region vacuum/constant density and 2 flavor
• approximation. Here

⇣ cos (˜ x)2 (3 + cos (4θ)) + (2 + cos (4θm − 8θ) + cos (4θm − 4θ)) sin (˜ x)2 − 2 sin (2˜ x) sin (2θm − 2θ) sin (2θ) ⌘ 3 + cos (4θ)

5 + cos (4θm) + cos (4θm − 4θ) + cos (4θ) + 4 cos (2˜ x) cos (2θ) sin (2θm − 2θ) 6 + 2 cos (4θ)

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˜ x = x s sin (2θ)2 + ✓ cos (2θ) − 2AEν ∆m2 ◆2

sin (2θm)2 = sin (2θ)2 sin (2θ)2 +

• cos (2θ) − 2AEν

∆m2

2

SLIDE 27

WITH CORE - 3 FLAVOR

Energy (MeV)

• 2

4 6 8 10 12 14 16 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Energy (MeV)

• 2

4 6 8 10 12 14 16 18 20 22 24

• 1

10 1 10 Energy (MeV)

• 200

400 600 800 1000 1200 1400 1600 1800 2000 0.5 1 1.5 2 2.5 3 Energy (MeV)

• 10

20 30 40 50 60 70 80 5 10 15 20 25 30

(a) Earth MSW (500 keV) (b) Earth MSW (50 keV) (c) Earth MSW (500 keV) (d) Earth MSW (500 keV)

Neutrino Energy (MeV) 2 4 6 8 10 12 14 16 18 20 Difference due to Earth MSW 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

Without Core Ratio with and without Earth MSW effect due to initial electron neutrino.

SLIDE 28

STORY

~Solar Mass Neutrino Production Earth Detector ν AGN SNe GRB Star BH DM Detector

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OUTLINE

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

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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.

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NEUTRINO OBSERVATORIES

Modern IceCube Kamioka Gran Sasso Sudbury Active Planned ANDES KM3NeT LAGUNA Sanford Underground Lab ? ?

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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? ??

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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).

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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.