introduction motivation (i): philosophical necessity physics is an experimental science → solid...
TRANSCRIPT
Introduction
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 theStandard Model („quantum gravity“) canaccomodate tiny violations of Relativity
common approach (top-down):
scan predictions of a given theory for sub-Planckeffects accessible with near-future technology, e.g.,
- novel particles (SuSy)- large extra dimensions & microscopic black holes- gravitational-wave background …
Issue: attainable E << quantum-gravity (QG) scale
Planck suppression of QG observables
bottom-up motivation: What can be measured with Planck precision? Is there a corresponding quantum-gravity effect?
Symmetries:
- allow exact theoretical prediction- are typically amenable to ultrahigh-precision (null)
tests
Quantum gravity: likely to affect spacetime structure
- More than 4 dimensions?- Non-commuting coordinates?- Discreteness?- “Foamy” structure?- …
Tests of spacetime symmetries
could probe Planck-scale physics
Sec A: Construction of general test framework(SME) for violations of Lorentz and CPT symmetry
Outline
Sec B: Mechanisms for Lorentz- and CPT breakdown
Strings?Topology?
Noncomm.geometry?
Loop quantum gravity?
VaryingScalars?
Other?
Sec C:Phenomenologyand exp. tests astrophysics
Penning traps
other
quantum optics
satellites
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, ...)
effective theory (SME test model)
E
~EPlanck
~ELHC
Problem 1: many theory approachesProblem 2: low-E limit can be unclear?
SME must be constructed by hand guided by gen. principlesAdvantage: 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
Remarks:
- 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)
- . . .
(1) Spontaneous Lorentz breaking in string theory
conventional case:gauge
symmet.
B. Mechanisms for Lorentz breakdown
string theory:Lorentz
symmetry
Kostelecký, Perry, Potting, Samuel ’89; ’90; ’91; ’95; '00
(2) Cosmol. varying scalars (e.g., fine-structure parameter)
intuitiveargument:
spacetime
small scalar
large scalar
gradient of thescalar selectspref. 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)
Seiberg-Witten: 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...
Example (1): free particles
E
dispersion relation now contains Lorentz-violating terms:
usual 4-fold degeneracy for is lifted
Sample effect: threshold modification in particle reactions
C. Phenomenology and Tests
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 + (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: + e- +
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?)
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- . . .
Example (2): corrections to bound-state levels
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)
Hydrogen and Antihydrogen spectroscopyBluhm, Kostelecký, Russell '99Phillips et al. '01
Penning-Trap experimentsBluhm, Kostelecký, Russell '97; '98Gabrielse et al. '99Mittelman et al. '99Dehmelt et al. '99
Studies of muonsBluhm, Kostelecký, Lane '99Hughes et al. '00(g-2) collaboration ‘08
Clock-comparison testsKostelecký, Lane '99Hunter et al. '99Stoner '99Bear et al. '00Cane et al. ‘04
Other phenomenological studies performed within SME
Satellite-based testsKostelecký et al. '02; '03ACESPARCS?RACE?SUMO?OPTIS
Tests involving photons and radiative effectsCarroll, Field, Jackiw '90Colladay, Kostelecký '98Kostelecký, Mewes '01; '02; ‘06; ‘07Lämmerzahl et al. '03Lipa et al. '03Stanwix et al. '05Klinkhamer et al. '07
GravityBailey, Kostelecký '06Battat et al. ‘07Müller et al. ‘08
Studies of baryogenesisBertolami et al. '97
Studies of neutrinosBarger, Pakvasa, Weiler, Whisnant '00Kostelecký et al. '03; '04Katori et al. '06Barger, Marfatia, Whisnant ‘07
Kinematical studies of cosmic rays (see many talks at this meeting)Coleman, Glashow '99Bertolami, Carvalho '00R.L. '03Altschul ‘06; ‘07
Studies of neutral-meson systemsKostelecký et al. '95; '96; '98; '00KTeV Collaboration, Hsiung et al. '99FOCUS Collaboration, Link et al. '03OPAL Collaboration, Ackerstaff et al. '97DELPHI Collaboration, Feindt et al. '97BELLE CollaborationBaBar Collaboration ‘08
Summary 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 matter”Data Tables for Lorentz and CPT Violation”
arXiv: 0801.0287v4
Bounds on photon SME coeff.”Data Tables for Lorentz and CPT Violation”
arXiv: 0801.0287v4