quantum gravity phenomenologyepoisson/ccgrra/myers.pdf · amelino-camelia, ellis, mavromatos,...
Post on 27-Jun-2018
217 Views
Preview:
TRANSCRIPT
Quantum Gravity Phenomenology
RCM and Maxim Pospelov,hep-ph/0301124
10th Conference on General Relativity and Relativistic Astrophysics
Planck scale physics has captured the imaginationof theorists in the quest for a consistent frameworkunifying general relativity and quantum field theory
? superstrings, loop quantum gravity, causalsets, noncommutative geometry, . . . .
GeV 10195
Planck ≈=Gc
Eη
Must this search be a purely theoretical exercise,devoid of any contact with experiment?
Amelino-Camelia, Ellis, Mavromatos,Nanopoulos & Sarkar, Nature 1998
“Quantum Gravity Phenomenology”
violations of local Lorentz invariance may bemanifest in modified dispersion relations:
++= 222 mpE ααη +2
Pl
pM
1
and are phenomenological parametersη α
. . . . +
NO!
“Sacred Symmetries”:CPT, spin-statistics, Lorentz symmetry, …..
Why think of violations of local Lorentz invariance (LLI)?
• certain scenarios of quantum gravity suggest LLIbroken or modified at Planck scale
e.g., loop quantum gravity – spacetime replacedwith discrete structure at ?
noncommutative geometry emerges at ?
braneworld scenarios?
• Lorentz group has infinite volume
Planckλ
Planckλ
Amelino-Camelia et al, Nature 1998
“Quantum Gravity Phenomenology”
violations of local Lorentz invariance may bemanifest in modified dispersion relations:
++= 222 mpE ααη +2
Pl
pM
1
and are phenomenological parametersη α
. . . . +
Look for energy/time-of-arrivalcorrelations for high energy
photons from gamma-ray bursters
3
Pl
22 pM
pE :1ξ
α +==
CGRO, 1998:
GLAST, 2006:
310≤ξ( )1O≤ξ
cL
tPlM
Eξ≈∆
pM
1pE
vPl
gξ
+=∂∂
=
Other ideas:? Examining UltraHigh Energy Cosmic Rays
(GZK cutoff: 5 × 1010 GeV)
? Detecting spacetime foam with gravity wave interferometers
? Induced phase incoherence of light overcosmological distance scales
? Imprints in the cosmic microwave background
? Birefringence effects
? Threshold tests
(Jacobson et al; Konopka & Major)
Constraints on p3 parameters: electron η; photon ξ
γ+→ −− eeCerenkov:
Photon decay:+− +→ eeγ
Crab synchrotron radiation: 910−−≥η
vacuum Cerenkov effect:modify only electron dispersion relation
if >0, high-E electrons can emit (null) photons
3
Pl
222 pM
mpE η
++=
p
E222 mpE +=
0>η
η
(Jacobson et al; Konopka & Major)
Constraints on p3 parameters: electron η; photon ξ
γ+→ −− eeCerenkov:
Photon decay:+− +→ eeγ
Crab synchrotron radiation: 910−−≥η
Effective field theory and Lorentz violations:
Standard Model and General Relativity provide anexcellent description of physics for E << MPl = 1019 GeV
Dimension 3,4 operators are extensively studiedand tremendously constrained!!
(Kostelecky; Coleman; Glashow; Carroll; ...)
( ) cdababcd
abab FFk
41
FF41
F−−e.g.,
31F 10k −≤
(Kostelecky & Mewes)
Effective field theory and Lorentz violations:
Standard Model and General Relativity provide anexcellent description of physics for E << MPl = 1019 GeV
Dimension 3,4 operators are extensively studiedand tremendously constrained!!
(Kostelecky; Coleman; Glashow; Carroll; ...)
Dimension 5 operators may generate p3 terms in dispersion relations.
Strategy: Ignore dim–3,4 operators (however, we use these results later)
Define preferred frame withfixed timelike vector na (n·n=+1)
Dim–5 Operators:
1. Quadratic in the same field2. One extra derivative beyond kinetic term3. Gauge invariant4. Lorentz invariant except for na
5. Not reducible to lower dimension operatorby equations of motion
6. Not reducible to a total derivative
Also, assume the operators are suppressed by 1/MPl
(Only appearance of “gravity” in the following )
Complex Scalar:
Dispersion relation:
with na=(1,0,0,0) and pE ≅
• no such term for real scalar (e.g., Higgs)• odd under CPT and C• don’t consider: ( ) ( )φφφφ ∂⋅−≅∂⋅∂ nn 22 m
( ) φφκ
φφ 3
Pl
222n
M∂⋅+−∂ im
3
Pl
222 pM
pEκ
++≅ m
( ) 0pM
pE yx3
Pl
22 =±
±− εε
ξi
( ) ( )bdbad
a
Pl
2 F~
nnFnM
F41
∂⋅+−ξVector:
Dispersion relation:
with ka=(E,0,0,p) , na=(1,0,0,0) and pE ≅
• chiral dispersion relation → birefringence• CPT odd; C even• nonabelian extension straightforward
( ) 0M
p2pE 521
Pl
3222 =
+−−− ψγηηm
Spinor:
( ) ( ) ( ) ψγγηηψψγψ 2521
Pl
nnM
1∂⋅⋅++−∂⋅ mi
Dispersion relation:
with na=(1,0,0,0) and pE ≅
• two independent parameters• chiral basis: (as required by SM)• both CPT odd; C(η1) odd, C(η2) even
21LR, ηηη ±=
Dispersion relations incompatible with field theory!!
Constraints revisited: electron η; photon ξ
γ+→ −− eeCerenkov:
Photon decay:+− +→ eeγ
Crab synchrotron radiation: 910−−≥η
Constraints revisited: electron η1 (η2=0) ; photon ξ
γ+→ −− eeCerenkov:Photon decay:
+− +→ eeγ
Crab synchrotron radiation: 91 10−−≥η
.2-.2-.2
.2
ξ
η1
Polarization constraint: 410−≤ξ (Gleiser & Kozameh)
Loops and all that:
x2η
ψγγψη 5Pl
2UV
2 nM
⋅Λ
≈
even if cutoff is SUSY scale (TeV), all parameters are bounded smaller than 10 –10 !!
as a result of quantum fluctuations,dim–5 operators naturally feed down to dim–3,4:
Loops with a twist:
x
ψγγψψηγγψ
cba5UV
bca52UV
pplogΛ+Λ≈
ψγγψ cba5 ∂∂
Replace vector–triple by traceless combination:
( )abccabbcacbaabccba nnn61
nnnCnnn ηηη ++−=→
• log divergences → RG flow• high energy dispersion relations unchanged
Laboratory tests:
Precision terrestial experiments can competewith limits from astrophysical tests!
na defines preferred frame but does notcoincide with earth-bound laboratory frame
v),1(na ≅
e.g., if preferred frame is that of CMB: 3i 10vn −≅≅
Motion establishes preferred spatial direction, which can be searched for in spin interactions
Lepton couplings:
“Chiral” electron coupling is boundedby torsion balance tests
GeV10b 28i
−≤e
4n
M GeV10i2
Pl28
2 ≅≤−
e
e
mη
( ) ψγγψηψγγψη i
5iPl
2
22
5Pl
2 nM
nnM
eee m
≈∂⋅⋅
(Heckel; Adelberger; …..)
Quark and photon couplings:
• can be bounded by “clock comparison” experiments,which search for spatial anisotropies from frequencyvariation of Zeeman hyperfine transition
• estimate induced neutron coupling from dim–5Lagrangian for quarks and photon with QCD sum rule
(Berglund et al, 1995)
( ) Ψ∂⋅⋅Ψ≈ 25
Pl
25 nn
MNLN γγ
η
( ) ( ) ξπ
αηηηηη
413.005.01.0 QuQd2 +−−−≅
( ) ψγγψηψγγψη i
5iPl
2N
22
5Pl
2 nM
nnM
m≈∂⋅⋅
GeV10b 31i
−≤
9i2
N
Pl31
2 10n
M GeV10 −−
≅≤m
η
As before:
( ) ( ) 83QuQd 10105.0 −− ≤+−−− ξηηηη
Loop Quantum Gravity Results:
Heuristic calculations suggest for:
Dirac fermion:
Vector: )1(O≈ξ
,01 =η 1MM
Pl
coh2 <<
≈ Oη
Challenge now is to provide rigorous predictions.
(Gambini & Pullin; Alfaro et al; Sahlmann & Thiemann)
Breaking versus deforming Lorentz symmetry
• our experimental bounds rely on existence of apreferred frame → LLI broken
• some suggestions are that symmetry is deformedby appearance of a dimensionful parameter MPl
→ “doubly special relativity”na = (1,0,0,0) for all observers
• some bounds still applye.g., polarization constraint |ξ| ≤ 10–4
(Amelino-Camelia; Magueijo & Smolin; ...)
Beyond effective field theory
• using EFT is a “theoretical prejudice”
• can study eom, not derivable from an action
( ) ( ) ( ) ( )aba
2
Pl
aba
2
Plab
a FnnM
~F~nn
MF ∂⋅+∂⋅=∂
ξξ
( ) ( ) 0~
Mp
pE yxPl
322 =±
±+− εεξξ i
Dispersion relation:
Fixed vector versus General Relativity
• for generic curved space, there are no constant vectors!
• may apply for FRW cosmology but not for our “lumpy” universe
• perhaps na corresponds to expectationvalue of Planck mass field
(Mattingly & Jacobson)
Conclusions:• Effective field theory constrains form of higherorder dispersion relations [ at O(p3) ]
• Dim–3,4 operators are not induced throughloops from higher twist dim–5 operators
• Effective field theory provides a frameworkwhere terrestial experiments provide stringentbounds on pheno parameters [ at O(p3) ]
4
1010
21
8Qdu,
5
≤−
≤−≤
−
−
ee ηη
ηηξ
What next?
• use RG flows to bound operators at Planck scale(consider effects of dim–5 interactions? No!
e.g., )
• produce predictions for loop quantum gravity
• dim–6 operators?better ideas for experimental bounds
bab
a nFψγψ
S.D. Biller et al (gr-qc/9810044)rapid flare on May 15, 1996 from Markarian 421
z=.031 L=1.1 × 1016 l-sec
(280 sec. bins)
250<ξ
top related