Motivation (i): philosophical necessity
physics is an experimental science
→ solid experimental confirmation of
foundations of physics is crucial
Motivation (ii): discovery potential
various approaches to physics beyond the
Standard Model („quantum gravity“) can
accomodate tiny violations of Relativity
Issue: attainable E << quantum-gravity (QG) scale
 Planck suppression of QG observables
common approach (top-down):
scan predictions of a given theory for sub-Planck
effects accessible with near-future technology, e.g.,
- novel particles (SuSy)
- large extra dimensions & microscopic black holes
- gravitational-wave background …
bottom-up motivation: What can be measured with Planck
precision? Is there a corresponding quantum-gravity effect?
- allow exact theoretical prediction
- are typically amenable to ultrahigh-precision (null) tests
Tests of spacetime symmetries
could probe Planck-scale physics
Quantum gravity: likely to affect spacetime structure
- More than 4 dimensions?
- Non-commuting coordinates?
- Discreteness?
- “Foamy” structure?
Loop quantum gravity?
Sec B:
Mechanisms for Lorentzand CPT breakdown
Sec A: Construction of general test framework
(SME) for violations of Lorentz and CPT symmetry
Sec C:
and exp. tests
quantum optics
Penning traps
A. The Standard-Model Extension (SME)
A test framework that allows for deviation
from exact Lorentz symmetry is desirable:
- to identify suitable tests
- to interpret and analyze experimental observations
- to compare tests in different physical systems
- to study the theoretical consistency
Example: CPT symmetry
- if CPT holds  particle mass m1 = antiparticle mass m2
- if CPT is broken  ??? (in SME, m1 = m2 is still OK)
- usual CPT test for Kaons uses model only valid for Kaon
interferometry  precludes comparison with other tests
How can one get a test framework for Lorentz violation?
underlying physics (strings, loop gravity,
noncommutative geometry, SUGRA, ...)
Problem 1: many theory approaches
Problem 2: low-E limit can be unclear
effective theory (SME test model)
SME must be constructed by hand guided by gen. principles
Advantage: generality; independence of underlying physics
Construction of the SME
- k, s, ... coefficients for Lorentz violation
- minimal SME  fermion 44, photon 23, ...
- generated by underlying physics (Sec B)
- amenable to ultrahigh-precision tests (Sec C)
Colladay, Kostelecký ‘97;’98; Kostelecký ‘04; Coleman, Glashow ‘99
- can consider operators of higher mass dimension
(Myers, Pospelov ‘03; Anselmi, Halat ’07; …)
- in gravity context, the above explicit Lorentz breaking
is typically inconsistent  spont. Lorentz violation needed
(Kostelecký ‘03; Jacobson, Mattingly ‘04)
sample theoretical investigations of the SME
- radiative corrections (Jackiw, Kostelecký '99; Y.-L. Wu’s talk?)
- causality and stability (Kostelecký, R.L. '01)
- gravity: LV must be dynamical (e.g., spontaneous) (Kostelecký '04)
- supersymmetry (Berger, Kostelecký '02)
- "Anti-CPT Theorem" (Greenberg '02)
- one-loop renormalizability (Kostelecký, Lane, Pickering '02)
- dispersion relations and kinematical analyses (R.L. '03)
- generalization of conventional math. formulas (R.L. '04; '06)
- symmetry studies (Cohen, Glashow '06; Hariton, R.L. '07)
B. Mechanisms for Lorentz breakdown
(1) Spontaneous Lorentz breaking in string theory
gauge symmet.
string theory:
Kostelecký, Perry, Potting, Samuel ’89; ’90; ’91; ’95; '00
(2) Cosmol. varying scalars (e.g., fine-structure parameter)
small scalar
large scalar
gradient of the
scalar selects
pref. direction
mathematical argument:
= (x) ... varying coupling
... dynamical fields
Integration by parts:
slow variation of :
Kostelecký, R.L., Perry '03; Arkani-Hamed et al. '03; X. Zhang’s talk?
Other mechanisms for Lorentz violation
Noncommutative geometry (QM of spacetime points)
 usual Minkowski coordinates x 
 SME terms emerge:
e.g., Carroll et al. ‘01
Topology (1 spatial dim. is compact: large radius R)
Vacuum fluctuations along this dim.
have periodic boundary conditions
 preferred direction in vacuum
 calculation:
Klinkhamer ‘00
C. Phenomenology and Tests
Example (1): free particles
dispersion relation now contains Lorentz-violating terms:
 usual 4-fold degeneracy for
is lifted
Sample effect: threshold modification in particle reactions
kinematical changes in particle collisions:
p dependence of E is modified:
Energy-momentum conservation:
thresholds may be shifted
decays/reactions normally allowed may now be forbidden
decays/reactions normally forbidden may now be allowed
kinematical modifications in existing effects
Vacuum Cherenkov radiation: e  e + g (D. Anselmi’s talk?)
- not seen for 104.5 GeV electrons at LEP
 can extract bound: certain LV < 10-11
(Hohensee, R.L., Phillips, Walsworth, PRL ’09)
Sidereal variations of the Compton edge: g+ e-  g + e- not seen at ESRF’s GRAAL facility
 can extract bound: certain LV < 10-13
(Bocquet et al., PRL ’10; Bo-Qiang Ma’s talk?)
GBR measurements (Zi-Gao Dai’s and Xue-Feng Wu’s talks?)
UHECR anisotropies (Xiao-Bo Qu’s talk?)
GZK cut-off modifications (Xiao-Jun Bi’s talk?)
Photon birefringence (Ming-Zhe Li’s and Lijing Shao’s talks?)
Example (2): corrections to bound-state levels
Conventional electrodynamics:
in QED Lagrangian, coupling of E, B fields to electrons is:
nontrivial potential A affects, e.g., atomic spectra:
- Stark effect
- Zeeman effect
How can Lorentz/CPT breakdown affect matter?
SME Lagrangian contains
Expect: Lorentz/CPT violation shifts energy levels
Antihydrogen spectroscopy:
- ALPHA, ASACUSA, ATRAP will trap & study anti H
 projected bound: certain LV < 10-26 GeV
(Bluhm, Kostelecký, Russell, PRL ‘99)
Clock-comparison type tests:
- clock = atomic/nuclear transition
 many bounds: certain LV < 10-20…-30 GeV
(many papers; e.g., nEDM, PRL ‘09, EPL ‘10)
Muonic Hydrogen/Helium spectrum:
- What are the level shifts?
 What (muon) bounds can be extracted?
(R.L., work in progress)
Other phenomenological studies performed within SME
Hydrogen and Antihydrogen spectroscopy
Bluhm, Kostelecký, Russell '99
Phillips et al. '01
Penning-Trap experiments
Bluhm, Kostelecký, Russell '97; '98
Gabrielse et al. '99
Mittelman et al. '99
Dehmelt et al. '99
Studies of muons
Bluhm, Kostelecký, Lane '99
Hughes et al. '00
(g-2) collaboration ‘08
Clock-comparison tests
Kostelecký, Lane '99
Hunter et al. '99
Stoner '99
Bear et al. '00
Cane et al. ‘04
Satellite-based tests
Kostelecký et al. '02; '03
Tests involving photons and radiative effects
Carroll, Field, Jackiw '90
Colladay, Kostelecký '98
Kostelecký, Mewes '01; '02; ‘06; ‘07
Lämmerzahl et al. '03
Lipa et al. '03
Stanwix et al. '05
Klinkhamer et al. '07
Bailey, Kostelecký '06
Battat et al. ‘07
Müller et al. ‘08
Studies of baryogenesis
Bertolami et al. '97
Studies of neutrinos
Barger, Pakvasa, Weiler, Whisnant '00
Kostelecký et al. '03; '04
Katori et al. '06
Barger, Marfatia, Whisnant ‘07
Kinematical studies of cosmic rays (see many talks at this meeting)
Coleman, Glashow '99
Bertolami, Carvalho '00
R.L. '03
Altschul ‘06; ‘07
Studies of neutral-meson systems
Kostelecký et al. '95; '96; '98; '00
KTeV Collaboration, Hsiung et al. '99
FOCUS Collaboration, Link et al. '03
OPAL Collaboration, Ackerstaff et al. '97
DELPHI Collaboration, Feindt et al. '97
BELLE Collaboration
BaBar Collaboration ‘08
presently no credible exp. evidence for Relativity violations, but:
(1) various theoretical approaches to
quantum gravity can cause such violations
(2) at low E, such violations are
described by SME test framework
(eff. field theory + background fields)
(3) high-precision tests (gravity waves,
astrophysical studies, satellite missions,
atomic clocks, interferometry, ...) possible
Bounds on SME coeff. for
”Data Tables for Lorentz and CPT Violation”
arXiv: 0801.0287v4
Bounds on photon SME
”Data Tables for Lorentz and CPT Violation”
arXiv: 0801.0287v4

Effective-field- theory description of Lorentz violation

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