The 2015 Data Tables for Lorentz and CPT Violation

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?