Transcript Quantum Gravity Phenomenology and Lorentz violatiion

Stefano Liberati
SISSA/ISAS, Trieste 2004
Quantum Gravity
Phenomenology and
Lorentz violation
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
Collaborators: D. Mattingly, T. Jacobson, F. Stecker
The Quantum Gravity problem…


Why we need it?

Philosophy of unification QM-GR (reductionism in physics)

Lack of predictions by current theories (e.g. GR singularities)
To eventually understand QG, we will need to


observe phenomena that depend on QG
extract reliable predictions from candidate theories & compare with
observations
Old “dogma” we cannot access any quantum gravity effect…
Possible QG Phenomena?
Motivated by tentative theories, partial calculations, potential
symmetry violation, hunches, philosophy…
 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 : Mp2=Rn Mp(4+n)n+2


dev. from Newton’s law
collider black holes
 Violation of global internal symmetries

Violation of spacetime symmetries
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…
 Is there an Aether? (Dirac 1951)
 Dispersion & LV (Pavlopoulos,
1967)
 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-…)
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-off
Since 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 scenarios
UHECR 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 pZ p (problem: needs very large initial energy for p)
• Lorentz violating dispersion relations: threshold shift due to modified dispersion relations
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?
EFT, all dimension ops, rotation inv., non-universal
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
QG phenomenology
via modified dispersion relations
Missing a definite prediction from QG one approach can be to consider dispersion
relations of the kind
2
2
2
E  p  m  ( p, M, )
  some particle mass scale
M  1019 GeV  M Planck
We 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


1
2
3
4
n
˜
˜
˜
˜
˜
( p)  1 p  2 p  3 p  4 p  ... n p
˜1  1

2
M
,
˜ 2  1


,
˜ 3  3

M
wit h i  O(1)
1
,
M
˜ 4  4

1
M2
Constraints at lowest orders

In a such a framework the n=1,2 terms will dominate at low energies p«.
 At high energies, p», the p3 term, if present, will dominate.
 If p3 is absent then the p4 term will dominate if p2»M 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 =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
˜1 p1  
˜ 2 p2  
˜ 3 p3  
˜ 4 p4  ... 
˜ n pn
E 2  p2  m 2  
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
˜ 3  3

1
 1
˜2

 
M MM
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!
Observability of O(E/MP)
Lorentz violations
Lab experiments:
 Time-dependence of spin resonance frequencies
Astrophysical observations:
Accumulation over long travel times: dispersion & birefringence
Purely kinematical effects (presume only modified dispersion relation and
standard definition of group velocity).

 Anomalous threshold reactions or threshold shift in standard ones
Need assumptions on energy/momentum conservation and dynamics.
 Reactions affected by “speeds limits” (e.g. synchrotron radiation)
Need assumption of effective quantum field theory
Constraining n=3
Lorentz violations in the QED sector
Times of flight
First 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 scale
of 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
Key point: the effect of the non LI dispersion relations can be important at energies
well below the fundamental scale
2 2
n2 

mc
p

E 2  c 2 p 2
1


2
n2 

p
M 

Corrections start to be relevant when the last term is
of the same order as the second.
m2
If  is order unity, then

p2

p n2
n m 2 M n2

p

crit
M n2
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

For n=3
m   p / M  p  (m M /  )
2
3
2
1/ 3
 10 T eV
1/ 3
 constraint
1
3
pmax
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,FIRBe++eBest limit so far from Mkr 501

For proton-pions GZK reaction: p++CMB 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
Nature 424, 1019 (2003)
The synchrotron radiation

LI synchrotron critical frequency:
1/ 2
  (1 v 2 )1/ 2
m 2
E 
 
E 2  2M 


QG 
LI
c
3 eB  2

2 m
e - electron charge, m - electron mass
B - magnetic field
Naively, corrections
important when :
E 3
m 2 MQG
2
If synchrotron source electrons have E>10 TeV, sensitive to LV!
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:
The key point is that for negative ,  is now a bounded
function of E! There is now a maximum achievable
synchrotron frequency max for ALL electrons!
So one gets a constraints from asking max≥ (max)observed

c 
3 eB 3

2 E
 max 10()1/ 3 T eV

Stronger constraint for smaller B/observed
Best case is Crab nebula...
The Crab nebula:
a key object for QG phenomenology
The Crab Nebula
A supernova remnant SNR at about 2Kpc.
Appeared on 4 July 1054 A.D.
Optical
Radio
X-ray
The EM spectrum of the Crab nebula
From
Aharonian and Atoyan,
astro-ph/9803091
Crab alone provides three of the best constraints.
We use:
synchrotron
Inverse Compton
Crab nebula (and other SNR) well explained by self-synchrotron Compton model.
SSC Model:
1. Electrons are accelerated to very high energies at pulsar
2. High energy electrons emit synchrotron radiation
3. High energy electrons undergo inverse Compton with ambient photons
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 ) should allow an Emax100 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
FIRB
Blazar- Mkn 501~ 147 Mpc
Earth
TeV photons are expected to loose energy by pairproduction due to scattering with the far infrared
background (FIRB) photons
+ FIRB e++e-
Observational evidence
It 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.

Requirements:
A.
B.
We do not want to lower the
standard threshold at 10 TeV
We assume incompatible with
observation to shift the
threshold of 20 TeV to the
region were the 10 TeV are
normally absorbed.
We shall assume that
observations are in fair
agreement with standard

expectations at least up to 20 TeV.
Stecker-de Jagger 2001, Stecker 2002
Dispersion relations from EFT
The 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
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
All violate CPT
photon helicities have
opposite LIV coefficients
Moreover electron and positron have inverted and
opposite positive and negatives helicities LIV
coefficients.
Electron spin resonance in a
Penning trap yields
| L  R |  4
electron helicities have independent LIV
coefficients
Positive Helicity
Negative helicity
Electron
R
Positron
-L
L
- R
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 R,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  such that  >-710-8. Let’s call it s
1.
For any s calculate the electron energy required to get 100 MeV synchrotron.
is VERY INSENSITIVE TO .
2.
Calculate the value of  for which vacuum Cerenkov starts to happen
3.
s,  must lie on the line segment between , since electron
cannot Cerenkov with either helicity photon.
This
Joining the Synch: Cerenkov with IC Cerenkov (why s is the same that satisfies the Cherenkov constraint)
1.
As s becomes more and more positive, the required electron energy
for 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 wavevector k:
 2  k 2   k 3    k  12  k 2
e
2)
3)
4)
it ikx
e
ik(xt )
e
i
2
k 2t
2
k
   12  t  12  E 2 d rot ation of linear polarizat ion
Observation of polarized radiation
M from distant sources can hence be used to constraint 
The difference in rotation angle for two different energies is
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.
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 a
TIFF (Uncompressed) decompressor
are needed to see this picture.
The Reuven Ramaty High Energy Solar Spectroscopy Imager
Major portion of flux from 0.1-0.5 MeV,
require < 3/2 in this range, take conservatively z 0.1 (0.5 Gpc)
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
  2 104
Combined constraints
The 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 R,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?
The combined constraints severely limit first order Planck suppressed LV, making any theory
that predicts this type of LV very unlikely.
Constraints of n=4 LIV

If GZK confirmed (Auger observatory)
m 2 ~  p 4 / M 2  p ~ m M  1/ 4
p ~ 100 T eV (neutrino), 3 1018 eV (proton)
Proton Cerenkov:
 GZK threshold: > O(102)

Neutrino vacuum Cerenkov *IF* 10 20 eV detected *AND* rate high enough: O(1021)
(Amanda, IceCube)
 Neutrino/photon/GW time delay?

Better measures of energy, timing, polarization from distant -ray sources
(GLAST?, SWIFT?, VERITAS?)
O(105)

What’s next?


Definitively rule out n=3 LV, O(E/M), including chirality effects
 Strengthen the positive  and |R- L| bounds: e.g. via helicity decay.
 (a) Rule out or (b) see LV at O(E 2/M2), n=4
A true messenger of QG phenomenology will arrive?
We’ll be there!
A possible new constraint:
helicity decay
If R and L are unequal, say R>L then a positive helicity electron can
decay into a negative helicity electron and a photon, e-Re-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 R,L is solely a matter of the decay rate which
depends on |R- L|
With the current constraints on |R- L| 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 |    | 102

L
R
Standard Model Extension
(Colladay & Kostelecky, 1997)
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:
Why now QG phenomenology?
Observational improvements
By increasing detector size, or going into space, or using
technological improvement, or technique improvement,
observations are probing…
 Higher energies
 Weaker interactions




Lower fluxes
Lower temperatures
Shorter time resolution
Longer distances
 Gravitational waves
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)