Quantum Gravity Phenomenology and Lorentz violation

Stefano LiberatiSISSA/ISAS, Trieste 2004

Collaborators: D. Mattingly, T. Jacobson, F. Stecker

T. Jacobson, SL, D. Mattingly: PRD 66, 081302 (2002); PRD 67, 124011-12 (2003)T. Jacobson, SL, D. Mattingly: Nature 424, 1019 (2003)

T. Jacobson, SL, D. Mattingly, F. Stecker: astro-ph/0309681

The Quantum Gravity problem…

To eventually understand QG, we will need to observe phenomena that depend on QG extract reliable predictions from candidate

theories & compare with observations

Why we need it? Philosophy of unification QM-GR (reductionism in

physics) Lack of predictions by current theories (e.g. GR

singularities)

Old “dogma” we cannot access any quantum gravity effect…

Possible QG Phenomena?

Primordial gravitons from the vacuum Loss of quantum coherence or state collapse QG imprint on initial cosmological

perturbations Scalar moduli or other new field(s) Extra dimensions and low-scale QG : Mp

2=Rn Mp(4+n)

n+2

dev. from Newton’s law collider black holes

Violation of global internal symmetries Violation of spacetime symmetries

Motivated by tentative theories, partial calculations, potential symmetry violation, hunches, philosophy…

Lorentz violation as the first evidence of QG?

LI linked to scale-free spacetime: unbounded boosts expose ultra-short distances…

Suggestions for Lorentz violation come from: need to cut off UV divergences of QFT & BH entropy tentative calculations in various QG scenarios, e.g.

semiclassical spin-network calculations in Loop QG (caveat: not solutions of the Hamiltonian constraints) string theory tensor VEVs spacetime foam non-commutative geometry some brane-world backgrounds

possibly missing GZK cutoff on UHE cosmic rays

Milestones in LV investigations…

Emergent LI in gauge theory? (Nielsen & Picek, 1983) LV modification of general relativity (Gasperini, 1987, Jacobson and coll.) Spontaneous LV in string theory (Kostelecky & Samuel, 1988) LV Dispersion & Hawking radiation (Unruh-Jacobson, 1994-1995) Possibilities of LV phenomenology (Gonzalez-Mestres, 1995-…)

Is there an Aether? (Dirac

1951) Dispersion & LV (Pavlopoulos, 1967)

The turning LV tide

“Standard model extension” & lab. experimental limits(Colladay & Kostelecky, 1997, & many experimenters)

High energy threshold phenomena: photon decay, vacuum Cerenkov, GZK cutoff (Coleman & Glashow, 1997-8)

GRB photon dispersion limits (Amelino-Camelia et al, 1997)

Trans-GZK events? (AGASA collab. 1998)

GZK cut-offSince the sixties it is well-known that the universe is opaque to protons (and other nuclei) on cosmological distances via the interactions

In this way, the initial proton energy is degraded with an attenuation length of about 50 Mpc. Since plausible astrophysical sources for UHE particles (like AGNs) are located at distances larger than 50-100 Mpc, one expects the so-called Greisen-Zatsepin-Kuzmin (GZK) cutoff in the cosmic ray flux at the energy given by

• The data collected show about twenty cosmic ray events with

energies just above the GZK energy. • Yet, the whole observational status in the UHE regime is controversial.

• HiRes collaboration claim that they see the expected event reduction

• A recent reevaluation of AGASA data seems to confirm the violation of the

GZK cutoff.

A GZK cutoff puzzle?The observational status is not settled, but it is clear that if the GZK

violation is confirmed, the origin of the super-GZK particles constitutes one of the most pressing puzzles in modern high-energy

astrophysics. We need better statistic: Future crucial role of the Auger

observatory. Approximately 100 times higher event rate, better systematics

Some proposed explanations to super-GZK events

Bottom-Up scenariosUHECR accelerated in objects (AGN, GRBs, SNR…) within the GZK

range Top-Down scenarios

decay of ultra-heavy particles: cosmic strings, topological defects, Wimpzillas! (109-1019 GeV)

Particles without GZK cut-off Z-bursts: true UHECR are neutrinos that finally hit relic DM neutrinos and produce hadrons via a Z-resonance pZ p (problem: needs very

large initial energy for p)• Lorentz violating dispersion relations: threshold shift due to modified

dispersion relations

Theoretical Framework for LV?Theoretical Framework for LV?

EFT? Renormalizable, or higher dimension operators?

Stochastic spacetime foam?

Rotational invariant?

Lorentz Violation or Doubly Special Relativity? (i.e. preferred frame or possibly a relativity with two invariant scales?, c and lp)

Universal, or species dependent?

Not because it *must* be true, but because:

• EFT well-defined & simple implies energy-momentum conservation (below the cutoff scale) covers standard model, GR, condensed matter systems, string theory ...

• All dimension ops: who knows?

• Rot. invariance simpler cutoff idea only implies boosts are broken, rotations maybe not boost violation constraints likely also boost + rotation violation constraints

• Non-universal EFT implies it for different polarizations & spins different particle interactions suggest different spacetime interactions "equivalence principle" anyway not valid in presence of LV

EFT, all dimension ops, rotation inv., non-universal

QG phenomenologyvia modified dispersion relationsMissing a definite prediction from QG one approach can be to consider dispersion relations of the kind

€

E 2 = p2 + m2 + Δ(p,M,μ)

€

Δ( p) = ˜ η 1 p1 + ˜ η 2 p2 + ˜ η 3 p3 + ˜ η 4 p4 + ...+ ˜ η n pn

€

˜ η 1 = η1μ 2

M, ˜ η 2 = η1

μM

, ˜ η 3 = η 31M

, ˜ η 4 = η 41

M 2

with η i ≈ O(1)

€

M =1019 GeV ≈ MPlanck

€

μ =some particle mass scaleWe presume that any Lorentz violation is associated with quantum gravity and suppressed by at least one inverse power of the Planck scale M and we violate only boost symmetry

Constraints at lowest orders In a such a framework the n=1,2 terms will dominate at

low energies p«μ. At high energies, p»μ, the p3 term, if present, will

dominate. If p3 is absent then the p4 term will dominate if p2»μM and

so on…A large amount of both theoretical and experimental work has been carried out in the case n≤2 which includes the “standard model extension proposal” and models like those proposed in VSL and by Coleman-Glashow

Compared to “Planck-suppressed” expectation (with μ=relevant mass scale for observation/experiment)

Laboratory ~ 1-2 orders weaker High energy astrophysics ~ 1-2 orders weaker GZK (if confirmed) ~ comparable Vacuum birefringence ~ few orders stronger

So is it n=3 the next relevant order?

An open problem: un- naturalness of small LV.

Renormalization group arguments might suggest that lower powers of momentum in

will be suppressed by lower powers of M so that n≥3 terms will be further suppressed w.r.t. n≤2 ones. I.e. one could have that

€

E 2 = p2 + m2 + ˜ η 1 p1 + ˜ η 2 p2 + ˜ η 3 p3 + ˜ η 4 p4 + ...+ ˜ η n pn

This need not be the case if a symmetry or other mechanism protects the lower dimensions

operators from violations of Lorentz symmetry

Of course we do not know at the moment if this is indeed the case!

€

˜ η 3 = η 31M

= μM

1M

<< ˜ η 2

Observability of O(E/MP)Lorentz violations

Accumulation over long travel times: dispersion & birefringencePurely kinematical effects (presume only modified dispersion relation and standard definition of group velocity).

Anomalous threshold reactions or threshold shift in standard onesNeed assumptions on energy/momentum conservation and dynamics.

Reactions affected by “speeds limits” (e.g. synchrotron radiation)Need assumption of effective quantum field theory

Lab experiments: Time-dependence of spin resonance frequencies

Astrophysical observations:

Constraining n=3 Lorentz violations in the QED sector

Times of flightFirst idea:Just constrain the photon LIV coefficient by using the fact that different colors will travel at different speeds. On long distances one expects different time of flight corresponding to different speed of propagations. Then

Best constraint up to date is Schaefer (1999) using GRB930131, a gamma ray burst at a distance of 260 Mpc that emitted gamma rays from 50 keV to 80 MeV on a time scaleof milliseconds. The constraint is ||<122. Very recently (Oct. 2003) Corburn et al. using GRB021206 obtained ||<77

However, probably GRB are not “good” objects (different enrgies emission at different times), then best constraint is Biller (1998, Markarian 421) <252.

Threshold reactions

3max

1 constraint

p∝η

Key point: the effect of the non LI dispersion relations can be important at energies well below the fundamental scale

€

m2

p2 ≈ pn−2

M n−2 ⇒ pcrit ≈ m2M n−2n

Corrections start to be relevant when the last term is of the same order as the second.If η is order unity, then

n pcrit for e pcrit for e- pcrit for p+

2 p ≈ m~1 eV p≈me=0.5 MeV p≈me=0.938 GeV

3 ~1 GeV ~10 TeV ~1 PeV

4 ~100 TeV ~100 PeV ~3 EeV

€

E 2 = c 2 p2 1+ m2c 2

p2 + η pn−2

M n−2

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

3/13/1232 TeV10)/(/ −≈≈↔≈ ηηη MμpMpμ

For n=3

Threshold reactions: new phenomena

New threshold reactions Vacuum Cherenkov: e-e-+

Moreover now possible Cherenkov with emission of an hard photon Gamma decay: e++e-

These reactions are almost instantaneous (interaction with zero point modes)If allowed the particle won’t propagate.

Anomalous thresholds (modification of standard threshold reactions) Shift of lower thresholds (Coleman-Glashow, …) Emergence of upper thresholds (Klusniak, JLM) Asymmetric pair production (JLM)So far constraints from

Photon pair creation using AGN: +CMB,FIRBe++e-

Best limit so far from Mkr 501 For proton-pions GZK reaction: p++CMB p++p-

Novelties in threshold reactions: why

Asymmetric configurations: Pair production can happen with asymmetric distribution of the final momenta

Upper thresholds: The range of available energies of

the incoming particles for which the reactions happens is changed.

Lower threshold can be shifted and upper thresholds can be

introduced

The synchrotron radiationLI synchrotron critical frequency:

Naively, corrections important when :

e - electron charge, m - electron mass

B - magnetic field

If synchrotron source electrons have E>10 TeV, sensitive to LV!€

ωcLI = 3

2eBγ 2

m

€

=(1− v2)−1/ 2 ≈ m2

E 2 − 2η EMQG

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

−1/ 2

€

E ≈m2MQG

2η3

The key point is that for negative η, is now a bounded function of E! There is now a maximum achievable synchrotron frequency ωmax for ALL electrons!So one gets a constraints from asking ωmax≥ (ωmax)observed

To get a real constraint one needs a detailed re-derivation of the synchrotron effect with LIV. One needs

to presume that EQFT holds. This leads to a modified formula for the peak frequency:

€

ωmax =10(−η )−1/ 3 TeV€

ωc = 32

eBE

γ 3

Stronger constraint for smaller B/ωobservedBest case is Crab nebula...

Nature 424, 1019 (2003)

The Crab nebula: a key object for QG phenomenology

The Crab NebulaA supernova remnant SNR at about 2Kpc. Appeared on 4 July 1054 A.D.

X-ray

Radio

Optical

The EM spectrum of the Crab nebula

Crab alone provides three of the best constraints.We use:

FromAharonian and Atoyan,

astro-ph/9803091

Crab nebula (and other SNR) well explained by self-synchrotron Compton model.SSC Model:

1. Electrons are accelerated to very high energies at pulsar2. High energy electrons emit synchrotron radiation3. High energy electrons undergo inverse Compton with ambient photons

synchrotron Inverse Compton

We shall assume SSC correct and use Crab observation to constrain LV.

Observations from Crab Gamma rays up to 50 TeV reach us from Crab: no photon annihilation up to 50 TeV.

By energy conservation during the IC process we can infer that electrons of at least 50 TeV propagate in the nebula: no vacuum Cherenkov up to 50 TeV

The synchrotron emission extends up to 100 MeV (corresponding to ~1500 teV electrons if LI is preserved):LIV for electrons (with negative η) should allow an Emax100 MeV.B at most 0.6 mG

Constraints from Crab

No photon annihilation up to 50 TeV

No vacuum Cherenkov up to 50 TeV

Synchrotron photons up to 100 MeV

Photon absorption of gamma rays from Markarian 501

Blazar- Mkn 501~ 147 Mpc Earth

Gamma raysFIRB

TeV photons are expected to loose energy by pair-production due to scattering with the far infrared background (FIRB) photons

+ FIRB e++e-

Observational evidenceIt was recently shown by Konopelko et al. (2003) that the observation is fully consistent with a synchrotron-Self-Compton origin of emission and the best available model for the FIRB spectrum at least up to 20 TeV.

Stecker-de Jagger 2001, Stecker 2002

We shall assume that observations are in fair

agreement with standard expectations at least up to 20

TeV.

η

Requirements:A. We do not want to lower the

standard threshold at 10 TeVB. We assume incompatible with

observation to shift the threshold of 20 TeV to the region were the 10 TeV are

normally absorbed.

Dispersion relations from EFTThe constraints just shown were obtained by making use of simple dispersion relations considered on a purely phenomenological basis. Are this the more general obtainable within a EFT framework? No

photon helicities have opposite LIV coefficients

All violate CPT

electron helicities have independent LIV coefficientsMoreover electron and positron have

inverted and opposite positive and negatives helicities LIV coefficients. Positive

HelicityNegative helicity

Electron ηR ηL

Positron -ηL - ηR

Let’s consider all the Lorentz-violating dimension 5 terms (n=3 LIV in dispersion relation) that are quadratic in fields, gauge & rotation invariant, not reducible to lower order terms (Myers-Pospelov, 2003). For E»m

Electron spin resonance in a Penning trap yields

4|| ≤− RL ηη

Consequences of helicity dependence on previous constraints Photon time of flight: the opposite coefficients for photon

helicities imply larger dispersion 2||p/M rather than (p2-p1)/M. Now best limits (using Biller. 1998) ||<63

(or, using Boggs et al. 2003, ||<34).

Photon decay and photon absorption (i.e. pair creation processes): one needs new analysis but order of magnitude of the

constraint remains the same.

Synchrotron: we can constraint at most only one of the electron parameters ηR,L since we cannot exclude that all the synchrotron is

produced by electrons of one helicity.

Vacuum Cherenkov: neither photon helicities can be emitted so || is bounded but we cannot exclude that one electron helicity is “cherenking” and the other produces the spectrum IC. So we can

say that at least one electron helicity is bounded.

New constraints using EFT: New Cherenkov-Synchrotron constraint

The logic: Consider larger and larger values of the one η such that η >-710-8. Let’s call it ηs

1. For any ηs calculate the electron energy required to get 100 MeV synchrotron. This is VERY INSENSITIVE TO .

2. Calculate the value of for which vacuum Cerenkov starts to happen3. ηs, must lie on the line segment between since electron

cannot Cerenkov with either helicity photon.

Joining the Synch: Cerenkov with IC Cerenkov (why ηs is the same that satisfies the Cherenkov constraint)

1. As ηs becomes more and more positive, the required electron energyfor 0.1 Gev synch. radiation becomes lower and lower.

2. Beyond the IC Cerenkov line it is below 50 TeV. Producing the observed amount of radiated energy with lower energy electrons requires many more electrons(in LI case electron energy is 1500 TeV).

3. Different electron populations would be producing IC radiation and synch.radiation. Problems with population ‘tuning’, i.e. 30 times IC producing electrons would be too numerous to match observed spectrum. Future work?

New constraints using EFT: New Birefringence constraint

Opposite for the photon helicities imply different phase velocities: birefringence of vacuum

1) There is a rotation of linear polarization direction through an angle. For a plane wave of wave-vector k:

2) Observation of polarized radiation from distant sources can hence be used to constraint

3) The difference in rotation angle for two different energies is4) The constraint araises from the fact that if the difference is too large

over the range of the observed polarized flux, then the instantaneous polarization at the detector would fluctuate enough to suppress the net polarization well below the observed value.

€

ω 2 = k 2 ± ξ k 3 →ω = k ± 12 ξ k 2

e−iωt +ikx = e ik(x−t )em i2ξ k 2t

⇒ θ = 12 ξ k 2

Mt ≈ 1

2 ξ E 2d rotation of linear polarization

Birefringence constraint from GRB021206

Recently polarized gamma rays in the energy range 0.15--2 MeV were observed (Coburn-Boggs, 2003) in the prompt emission from the -ray burst GRB021206 using the RHESSI detector. A linear polarization of 80%20% was measured by analyzing the net asymmetry of their Compton scattering from a fixed target into different directions.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

This then yields the constraint where d0.5 is the distance

to the burst in units of 0.5 Gpc.

N.B. This constraint could be improved with detailed analysis.N.B.II Recently Boggs and Coburn was criticized by Ritledge and Fox. Boggs-Coburn defended their analysis. If this observation not correct best limit so far from Birefringence is obtained by Gleiser and Kozameh using observed 10% polarization from distant, z=1.82, radio galaxy 3C 256

The Reuven Ramaty High Energy Solar Spectroscopy Imager

Major portion of flux from 0.1-0.5 MeV, require Δ< 3p/2 in this range, take conservatively z 0.1 (0.5 Gpc)

€

≤2 ×10−4

Combined constraintsThe vast improvement in the birefringence constraint overwhelms the new synchrotron-Cherenkov constraint, while the latter improves the previous birefringence constraint (Gleiser-Kozameh, 2001) by a factor 102.

The allowed region is defined above and below by the birefringence bound O(10-14), on the left by the synchrotron bound O(10-7), and on the right by the IC Cherenkov bound O(10-2).

For negative parameters minus the logarithm of the absolute value is

plotted, and a region of width 10-18 is excised around each axis. The synchrotron and Cherenkov

constraints are known to apply only for at least one ηR,L. The IC and

synchrotron Cherenkov lines are truncated where they cross. Prior

photon decay and absorption constraints are shown in dashed lines since they do not account for the EFT relations between the LV parameters.

The future?

Constraints of n=4 LIV

proton)( eV103 ,(neutrino) TeV100~

~/~18

4/1242

×

⇔ −

p

μMpMpμ ηη If GZK confirmed (Auger observatory)

Proton Cerenkov: η GZK threshold: η

Neutrino vacuum Cerenkov *IF* 1020 eV detected *AND* rate high enough: η

Amanda, IceCube) Neutrino/photon/GW time delay? Better measures of energy, timing, polarization from distant -ray sources (GLAST?, SWIFT?, VERITAS?)

What’s next? Definitively rule out n=3 LV, O(E/M), including chirality effects

Strengthen the positive η and |ηR- ηL| bounds: e.g. via helicity decay.

(a) Rule out or (b) see LV at O(E2/M2), n=4 A true messenger of QG phenomenology will arrive?

The combined constraints severely limit first order Planck suppressed LV, making any theory that predicts this type of LV very unlikely.

We’ll be there!We’ll be there!

A possible new constraint: helicity decay

If ηR and ηL are unequal, say ηR>ηL then a positive helicity electron can decay into a negative helicity electron and a photon, e-

Re-L+

even when the LV parameters do not permit the vacuum Cherenkov effect.

Such ``helicity decay" has no threshold energy, so whether this process can be used to set constraints on ηR,L is solely a matter of the decay rate which

depends on |ηR- ηL|

With the current constraints on |ηR- ηL| the transition energy is approximately 10 TeV and the lifetime for electrons below this energy is greater than 104 seconds. This is long enough to preclude any terrestrial

experiments from seeing the effect.

The lifetime above the transition energy is instead of about 10-11 seconds for energies just above 10 TeV. The lifetime might therefore be short enough to

provide new constraints. From Crab might get

€

|η L −η R | ≤10−2

Standard Model Extension

Add to the Standard Model Lagrangian all possible Lorentz-violating terms that preserve field content, gauge symmetry, and renormalizability.

E.g., leading order terms in the QED sector:

If rotationally invariant:

(Colladay & Kostelecky, 1997)

Why now QG phenomenology?Observational improvements

Higher energies Weaker interactions Lower fluxes Lower temperatures Shorter time resolution Longer distances Gravitational waves

By increasing detector size, or going into space, or using technological improvement, or technique improvement, observations are probing…

Phenomenology of Lorentz Violation Time-dependence of spin or hyperfine resonance, or energy levels as lab moves w.r.t. preferred frame or directions …

Long baseline dispersion (GRB’s, AGN’s, pulsars) and vacuum birefringence (e.g. spectropolarimetry of galaxies)

New thresholds (photon decay, vacuum Cerenkov)

Shifted thresholds (photon annihilation from blazars, GZK, …)

Maximum velocity (synchrotron peak from SNR)

Gravitational effects (static fields, waves)