The 2015 Data Tables for Lorentz and CPT Violation

Transcription

1 The 2015 Data Tables for Lorentz and CPT Violation Reviews of Modern Physics 83, 11 (2011) update: arxiv: v8 (January 2015) Kostelecký, NR Second IUCSS Summer School on the Lorentz- and CPT-violating Standard-Model Extension June 12-18, 2015 Indiana University, Bloomington Neil Russell Northern Michigan University

2 Contents of the Data Tables Explanatory text, References, Tables: 4 Summary Tables S2-S5 Matter Photon Neutrino Gravity 30 Data Tables D6-D35 (nonminimal dimension) Fermions: electron (5,6) proton (6) neutron Photon (5,,9) Charged leptons: muon (5,,9) tau (5,6) Neutrino (5,6, ) Quark (6) Electroweak Gluon Gravity (6) 14 Properties Tables P36-P49 Minimal QED lagrangian C,P,T properties Fermion observables Photon combinations Full SME (Riemann-Cartan): fermion, boson sectors Neutrinos: coefficients, definitions Nonminimal fermion: Lagrange density, coeffs Nonminimal photon: Lagrange density, coeffs Nonminimal neutrino coeffs 2015

3 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]* Sun centered inertial reference frame Property tables find Lagrange densities list properties convert rectangular/spherical use spin-weighted spherical harmonics give coefficient properties see notation 2015

4 Activity by sector: papers on SME Lorentz violation Growth:

5 arxiv: versions 1 to 8 1 st Edition: 12 pages 2 summary tables 10 data tables 2 nd 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 8th Ed. Updates include: neutron limit from quartz photon lab limits: kappas limits on NR muons; limits on boosted muons; gravity -- binary pulsars, gravity -- nonminimal Rev. Mod. Phys. 83, 11 (2011) Nonminimal gravity, Phys. Rev. D 2015 Nonminimal fermions, Phys. Rev. D 2013 Nonminimal neutrinos, Phys. Rev. D 2012 Nonminimal photons, AK/MM, Astrophys. J. Lett and Phys. Rev. D 2009

6 Property-table example

7 Exercise: write out the gravity-sector Lagrange density (in Riemann spacetime)

8 Exercise: write out the gravity-sector Lagrange density (in Riemann spacetime)

9 Maximal sensitivities in Summary Tables Current value of b e T in the electron summary table GeV Heckel et al PRD 2008, Table IX +0.9 ± GeV sensitivity values (not signals) modulus is understood 2σ or 90% confidence level order of magnitude rounding at = 3.16 linear combinations: assume other coefficients zero field redefinitions judgmental issues how many assumptions? Sensitivity, at 1σ level, to 1 2 b T e Sensitivity at 2σ level for summary tables

10 Fermion Sector Minimal case Colladay and Kostelecký, PRD 58, (1998)

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12 Coverage of minimal matter sector in Minkowski space (2015)

13 Fermion Sector Minimal case Colladay and Kostelecký, PRD 58, (1998) Nonminimal case, one fermion species Kostelecký and Mewes, PRD 88, (2013); PRD 85, (2012) 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, (2014)

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15 Exercise: Write out the first two operators for g

16 Exercise: Write out the first two operators for g

17 Photon Sector

18 Photon sector (min-, nonmin-) Kostelecký, Mewes, PRD 80, (2009); ApJ 689, L1 (2008); PRL 99, (2007) All possible gauge-invariant terms of arbitrary mass dimension AF CPT-odd operators Operators have odd mass dimension d = 3, 5, 7, Coefficient counts: 4, 36, 120, Number of derivatives: 0, 2, 4, F CPT-even operators Operators have even mass dimension d = 4, 6, 8, Coefficient counts: 19+1, 126, 360, Number of derivatives: 0, 2, 4,

19 Bounds on the d=4 coefficients in the photon sector (~ 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 ~ t r Log(sensitivity) (2015) 10 independent coe± cients ~ e+ ; ~ o or: k (4) (E )2;m ; k(4) (B )2;m L ab exper iment s (cavit y oscillat or s) 9 independent combinat ions ~ e : 5 combinations ~ o+ : 3 combinations ~ tr : 1 combination or: No dispersion for d=4 c (4) (I )2;m ; c(4) (I )1;m ; c(4) (I )0;0

20 log scale Photon-sector evolution: Example: d=4 coefficient optical and microwave resonators sensitivity improved by 10 6 in < 10yrs 20

21 (2015) 21

22 Some photon-sector observations mostly nonminimal coefficients mostly minimal coefficients indicated with * in tables (2012) 22

23 number of limits dimension Astrophysical birefringence and CMB polarization Astrophysical dispersion Laboratory tests (2012) 23

24 Neutrino Sector

25 Lorentz and CPT Violation in the neutrino sector Kostelecky, Mewes, PRD 69, (2004) Usual massiveneutrino case Neutrino sector, with nonminimal terms: Kostelecký and Mewes, PRD 85, (2012)

26 (June 2013) Results inlude: cartesian coeffs spherical coeffs

27 Gravity sector

28 Pure-gravity sector Kostelecký, Bailey, PRD 74, (2006) Kostelecký PRD 69, (2004)

29 Matter couplings in gravity sector Minkowski case Colladay and Kostelecký, PRD 58, (1998) Couplings in gravity sector via vierbein Kostelecký PRD 69, (2004) Countershading Some unmeasured and potentially large Lorentz violations can be tested only via weak-gravity couplings. Kostelecký, Tasson, PRL 102, (2009); PRD 83, (2011)

30 Gravity sector (2015)

31 Gravity-sector summary table (2015)

32 Questions? Data Tables for Lorentz and CPT violation, arxiv: v8 (January 2015)

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