the 2015 data tables for lorentz and cpt violation
TRANSCRIPT
Reviews of Modern Physics 83, 11 (2011)update: arXiv:0801.0287v8 (January 2015)
Kostelecký, NR
Second IUCSS Summer School on theLorentz- and CPT-violating Standard-Model ExtensionJune 12-18, 2015Indiana University, Bloomington
Neil RussellNorthern Michigan University
The 2015 Data Tables for Lorentz and CPT Violation
Fermions:electron (5,6)proton (6)neutron
Photon (5,…,9)Charged leptons:
muon (5,…,9)tau (5,6)
Neutrino (5,6,…)Quark (6)ElectroweakGluonGravity (6)
Matter
Photon
Gravity
Minimal QED lagrangianC,P,T propertiesFermion observablesPhoton combinationsFull SME (Riemann-Cartan):
fermion, boson sectorsNeutrinos:
coefficients, definitionsNonminimal fermion:
Lagrange density, coeffsNonminimal photon:
Lagrange density, coeffsNonminimal neutrino coeffs
Neutrino
Contents of the Data Tables
Explanatory text, References, Tables:
4 Summary Tables S2-S5
30 Data Tables D6-D35
14 Properties Tables P36-P49
2015
(nonminimal dimension)
Explanatory Text• provides additional information about each table• gives definitions and conventions• points to theory references• discusses rounding, methods, assumptions, …• …
References• each data-table entry gives ref. in last column• theory-deduced references have asterisk [34]*• …
Property tables• find Lagrange densities• list properties• convert rectangular/spherical• use spin-weighted spherical harmonics• give coefficient properties• see notation• …
Sun centered inertial reference frame
2015
Activity by sector:Growth:1000+ papers on SME Lorentz violation
2008
1st Edition: 12 pages 2 summary tables10 data tables
2nd Ed.: Gravity summary, nonminimal photon, 8 property tables
3rd Ed.: Table of tables, 2 nonminimal photon property tables
4th Ed.
5th Ed. Neutrinos: summary table, nonminimal data tables, 2 property tables
6th Ed. Data tables for higher-d neutrino and photon, fermion property table
7th Ed. Data tables for nonminimal fermions,2 property tables for nonminimal fermions
Rev. Mod. Phys. 83, 11 (2011)
Nonminimal photons, AK/MM, Astrophys. J. Lett. 2008 and Phys. Rev. D 2009
Nonminimal neutrinos, Phys. Rev. D 2012
Nonminimal fermions, Phys. Rev. D 2013
arXiv:0801.0287 versions 1 to 8
Nonminimal gravity, Phys. Rev. D 2015
2009 2010 2011 2012 2013 2014 2015
8th Ed. Updates include:neutron limit from quartzphoton lab limits: kappaslimits on NR muons; limits on boosted muons;gravity -- binary pulsars, gravity -- nonminimal
Pro
per
ty-t
able
exa
mp
le
Exercise: write out the gravity-sector Lagrange density (in Riemann spacetime)
Exercise: write out the gravity-sector Lagrange density (in Riemann spacetime)
Maximal sensitivities in Summary Tables
Current value of 𝑏𝑇𝑒 in the electron summary table 10−26 GeV
Heckel et al PRD 2008, Table IX
+0.9 ± 2.2 × 10−27 𝐺𝑒𝑉
Sensitivity, at 1𝜎 level, to 1
2| 𝑏𝑇
𝑒|
Sensitivity at 2𝜎 level for summary tables
• sensitivity values (not signals)• modulus is understood• 2𝜎 or 90% confidence level• order of magnitude
rounding at 100.5 = 3.16• linear combinations:
assume other coefficients zero• field redefinitions• judgmental issues
how many assumptions?
Fermion Sector
Minimal case
Colladay and Kostelecký, PRD 58, 116002 (1998)
Coverage of minimal matter sector in Minkowski space
(2015)
Minimal case Colladay and Kostelecký, PRD 58, 116002 (1998)
Fermion Sector
Kostelecký and Mewes, PRD 88, 096006 (2013); PRD 85, 096005 (2012)
Nonminimal case, one fermion species
Data in nonminimal fermion sector:
2014: d=5,6 for e, p, quark, 𝜇, 𝜏; astrophysics, ultrarelativistic limit. 12 limits.2015: Includes 𝜇 results, Gomes, Kostelecký, and Vargas, PRD 90, 076009 (2014)
Exercise: Write out the first two operators for g
Exercise: Write out the first two operators for g
Photon Sector
Photon sector (min-, nonmin-)
AF CPT-odd operators
Operators have odd mass dimension d = 3, 5, 7, …
Coefficient counts: 4, 36, 120, …
Number of derivatives: 0, 2, 4, …
All possible gauge-invariant terms of arbitrary mass dimension
Operators have even mass dimension d = 4, 6, 8, …
Coefficient counts: 19+1, 126, 360, …
Number of derivatives: 0, 2, 4, …
F CPT-even operators
Kostelecký, Mewes,
PRD 80, 015020 (2009); ApJ 689, L1 (2008);
PRL 99, 011601 (2007)
Lab exper iment s (cavit y osci l lat or s)
9 independent combinat ions
~· e¡ : 5 combinat ions
~· o+ : 3 combinat ions
~· t r : 1 combinat ion
Bounds on the d=4 coefficients in the photon sector
~· e+ ; ~· o¡
c(4)
( I )2;m; c
(4)
(I )1;m; c
(4)
( I )0;0or:
k(4)
(E )2;m; k
(4)
(B )2;m
10 independent coe± cients
or:
No dispersion for d=4
(~·e
+)X
Y
(~·e
+)X
Z
(~·e
+)Y
Z
(~·e
+)X
X¡
(~·e
+)Y
Y
(~·e
+)Z
Z
(~·o
¡)X
Y
(~·o
¡)X
Z
(~·o
¡)Y
Z
(~·o
¡)X
X¡
(~·o
¡)Y
Y
(~·o
¡)Z
Z
(~·e
¡)X
Y
(~·e
¡)X
Z
(~·e
¡)Y
Z
(~·e
¡)X
X¡
(~·e
¡)Y
Y
(~·e
¡)Z
Z
(~·o
+)X
Y
(~·o
+)X
Z
(~·o
+)Y
Z
~·tr
(2015)Log(s
ensitiv
ity)
Photon-sector evolution:
Example: d=4 coefficient
optical and microwave resonators
sensitivity improved by 106 in < 10yrs
log
scal
e
20
21
(2015)
22
(2012)
mostly minimal coefficients
mostly nonminimal coefficients
indicated with *in tables
Some photon-sector observations
Astrophysical birefringence and CMB polarizationAstrophysical dispersionLaboratory tests
nu
mb
er o
f lim
its
dimension
23
(2012)
Neutrino Sector
Lorentz and CPT Violation in the neutrino sectorKostelecky, Mewes, PRD 69, 016005 (2004)
Usual massive-neutrino case
Neutrino sector, with nonminimal terms:
Kostelecký and Mewes, PRD 85, 096005 (2012)
Results inlude:cartesian coeffsspherical coeffs
(June 2013)
Gravity sector
Pure-gravity sectorKostelecký, Bailey, PRD 74, 045001 (2006)
Kostelecký PRD 69, 105009 (2004)
Matter couplings in gravity sector
Minkowski case Colladay and Kostelecký, PRD 58, 116002 (1998)
Couplings in gravity sector via vierbein
Kostelecký, Tasson,
PRL 102, 010402 (2009);
PRD 83, 016013 (2011)
Kostelecký PRD 69, 105009 (2004)
“Countershading”
Some unmeasured and potentially large
Lorentz violations can be tested only via
weak-gravity couplings.
Gravity sector
(2015)
Gravity-sector summary table
(2015)
Data Tables for Lorentz and CPT violation, arXiv:0801.0287v8 (January 2015)
Questions?
