Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.arcetri.astro.it/cpr/PdfPresentations/Mewes.pdf Äàòà èçìåíåíèÿ: Sun Oct 11 19:40:31 2015 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 02:58:56 2016 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: cygnus

Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Lorentz Violation & Cosmological Polarization
Matthew Mewes California Polytechnic State University
Cosmic Polarization Rotation Workshop, 2015


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Outline
introduction motivation test theories & Standard-Model Extension (SME) SME photons birefringence CMB tests GRB tests


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Introduction

Intro duction


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Introduction: PRELIMINARIES
Lorentz invariance: ­ symmetry under rotations & b oosts (need b oth) ­ explicit in b oth General Relativity and ­ Standard Model of particle physics Lorentz violation = smoking-gun signal of new physics ­ can test Lorentz invariance with extreme precision


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Introduction: PRELIMINARIES
Lorentz invariance: ­ symmetry under rotations & b oosts (need b oth) ­ explicit in b oth General Relativity and ­ Standard Model of particle physics Lorentz violation = smoking-gun signal of new physics ­ can test Lorentz invariance with extreme precision CPT theorem: ­ Lorentz invariance CPT invariance ­ CPT violation Lorentz violation ­ note: Lorentz violation CPT violation /


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Introduction: THE ANSWER
­ In the Standard-Model Extension, ­ p olarization of low-energy photons (CMB) is affected by ­ 4 CPT-breaking coefficients for Lorentz violation. (kAF )µ = {(kAF )0 , (kAF )1 , (kAF )2 , (kAF )3 } {k(V
(3) )00 (3) (3) (3) (3) (3)

, k(V

(3) )1-1

, k(V

(3) )10

, k(V

(3) )11

}


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Introduction: THE ANSWER
­ In the Standard-Model Extension, ­ p olarization of low-energy photons (CMB) is affected by ­ 4 CPT-breaking coefficients for Lorentz violation. (kAF )µ = {(kAF )0 , (kAF )1 , (kAF )2 , (kAF )3 } {k(V ­ rotation of p olarization: =
dz Hz (1+z ) jm (3) )00 (3) (3) (3) (3) (3)

, k(V

(3) )1-1

, k(V

(3) )10

, k(V

(3) )11

}

Y

jm

(n)k(V ^

(3) )j m


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Introduction: THE ANSWER
­ In the Standard-Model Extension, ­ p olarization of low-energy photons (CMB) is affected by ­ 4 CPT-breaking coefficients for Lorentz violation. (kAF )µ = {(kAF )0 , (kAF )1 , (kAF )2 , (kAF )3 } {k(V ­ rotation of p olarization: = ­ for CMB: (n) ^
dz Hz (1+z ) jm (3) )00 (3) (3) (3) (3) (3)

, k(V

(3) )1-1

, k(V

(3) )10

, k(V

(3) )11

}

Y

jm

(n)k(V ^

(3) )j m

3.5 â 1043 GeV

Y
jm

jm

(n)k(V ^

(3) )j m


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Introduction: THE ANSWER
Why consider direction dep endence?

Preferred-frame (isotropic) models are nice, but ­ they capture only a small fraction of all p ossible effects, ­ most Lorentz-violating models have no preferred frame, ­ b oost violations necessarily imply rotation violations, ­ if there is a preferred frame, we're probably not in it.


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation

Motivation


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation: WHY BREAK RELATIVITY?
Lorentz violation may provide hints of the Theory of Everything (TOE) Lorentz violation = tiny remnants of fundamental physics Which TOE?

loop quant. grav.

strings

no nc o geommm. etry

blue -c theoheese ry

mul tive rses


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation: WHY BREAK RELATIVITY?

Newton's Laws

E. & M., Atoms, Molecules,...

Cosmology, Astrophysics,...

Newtonian Gravity

Standard Mo del
Qua nt um Mechanics Lorentz Symmetry

General Relativity
Curved Spacetime

Theory of Everything


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation: WHY BREAK RELATIVITY?

Newton's Laws

E. & M., Atoms, Molecules,...

Cosmology, Astrophysics,...

Newtonian Gravity

Standard Mo del
Qua nt um Mechanics Lorentz Symmetry

General Relativity
Curved Spacetime

Theory of Everything


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation: WHY BREAK RELATIVITY?
SME = general description of LV at low energies

Newton's Laws

E. & M., Atoms, Molecules,...

Cosmology, Astrophysics,...

Newtonian Gravity

Standard Mo del
Qua nt um Mechanics Lorentz Symmetry

General Relativity
Curved Spacetime

Theory of Everything


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation: POSSIBLE ORIGINS
Spontaneous Symmetry Breaking

U (x) = a(x2 - b2 )2


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation: POSSIBLE ORIGINS
Higgs Mechanism
hot universe cold universe

U () = a(2 - b2 )2


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation: POSSIBLE ORIGINS
Spontaneous Lorentz Breaking
hot universe cold universe

U (E ) = a(E 2 - b2 )2

bumbleb ee models: U (Bµ ) = a(B µ Bµ ± b2 )2

Bluhm & Kosteleck´ '05 y


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Motivation: POSSIBLE ORIGINS
other p ossibilities: ­ spacetime variations in physical "constants" ­ or new slowly varying scalar field (e.g. quintessence) µ (scalar) direction in spacetime ­ noncommutative geometry [xµ , x ] = ­ spacetime foam ­ multiverses ­ ...
µ


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Standard-Model Extension

Standard-Mo del Extension


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

How to build a test theory.
1) ad hoc approach - build phenomenology for each measurement e.g., LV disp ersion relations: E 2 = p2 + 3 p3 + 4 p4 + . . . advantages: ­ straightforward di s a d ­ ­ ­ vantages: hard to compare different exp eriments might miss interesting physics might b e "crazier" than exp ected e.g., 3 p3 term contradicts CPT theorem can't come from standard quantum theory


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

How to build a test theory.
2) models (LV = intended or unintended) advantages: ­ straightforward ­ can compare different exp eriments disadvantages: ­ not general, might miss interesting physics


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

How to build a test theory.
3) St ­ ­ ­ andard-Model Extension (SME) add all p ossible modifications to standard physics that are realistic but violate Lorentz invariance often make "craziness" cuts by keeping ­ energy-momentum conservation ­ gauge invariance ­ renormalizability ­ ...

advantages: ­ very general ­ all exp eriments describ ed by single framework ­ describ e all realistic LV in self-consistent way disadvantages: ­ often cumb ersome


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Standard-Model Extension:
SME = general description of LV at low energies

Newton's Laws

E. & M., Atoms, Molecules,...

Cosmology, Astrophysics,...

Newtonian Gravity

Standard Mo del
Qua nt um Mechanics Lorentz Symmetry

General Relativity
Curved Spacetime

Theory of Everything


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Standard-Model Extension:

SME series expansion ab out known physics known physics S M + GR ua n m + ... = qgravtiuy t

+

+

+


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Standard-Model Extension: EXPERIMENTS
kaon oscillations:
KLOE collaboration, PLB 730, 89 (2014) KLOE collaboration, Found. Phys. 40, 852 (2010) KLOE collaboration, J. Phys. Conf. Ser. 171, 012008 (2009) KLOE collaboration, arXiv:0805.1969 KTeV collaboration, arXiv:hep-ex/0112046 KTeV collaboration, Nucl. Phys. Proc. Suppl. 86, 312 (2000) FOCUS collaboration, PLB 556, 7 (2003) FOCUS collaboration, arXiv:hep-ex/0112040 D0 collaboration, arXiv:1506.04123 BaBar collaboration, PRL 100, 131802 (2008) BaBar collaboration, arXiv:hep-ex/0607103 BaBar collaboration, PRD 70, 012007 (2004) BaBar collaboration, PRL 92, 142002 (2004) BaBar collaboration, arXiv:hep-ex/0303043 BELLE collaboration, PRL 86, 3228 (2001) OPAL collaboration, Z. Phys. C 76, 401 (1997) DELPHI collaboration, DELPHI 97-98 CONF 80 (1997) D0 collaboration, PRL 108, 261603 (2012) BNL g-2 collaboration, PRL 100, 091602 (2008) V.W. Hughes et al., PRL 87, 111804 (2001) BNL g-2 collaboration, arXiv:hep-ex/0110044

neutral-D oscillations: neutral-B oscillations:

top quark: muons:


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Standard-Model Extension: EXPERIMENTS
clock-comparison exp eriments:
T. Pruttivarasin et al., Nature 517, 592 (2015) B. Botermann et al., PRL 113, 120405 (2014) F. Allmendinger et al., arXiv:1307.5604 M.A. Hohensee et al., PRL 111, 050401 (2013) A. Matveev et al., PRL 110, 230801 (2013) S.K. Peck et al., PRA 86, 012109 (2012) M. Smiciklas et al., PRL 107, 171604 (2011) C. Gemmel et al., PRD 82, 111901 (R) (2010) K. Tullney et al., arXiv:1008.0579 J.M. Brown et al., PRL 105, 151604 (2010) I. Altarev et al., PRL 103, 081602 (2009) T.W. Kornack, et al., CPT and Lorentz Symmetry IV P. Wolf et al., PRL 96, 060801 (2006) P. Wolf et al., arXiv:hep-ph/0509329 P. Wolf et al., arXiv:physics/0506168 F. Cane et al., PRL 93, 230801 (2004) D.F. Phillips et al., PRD 63, 111101 (2001) M.A. Humphrey et al., PRA 68, 063807 (2003) D. Bear et al., PRL 85, 5038 (2000) R. Walsworth et al., AIP Conf. Proc. 539, 119 (2000) L.R. Hunter et al., CPT and Lorentz Symmetry S. Ulmer et H. Dehmelt R. Mittleman G. Gabrielse al et et et ., Nature al., PRL al., PRL al., PRL 524, 196 83, 4694 83, 2166 82, 3198 ( ( ( ( 2015) 1999) 1999) 1999)

QED tests in Penning traps:

spin-p olarized torsion p endulum:

B. Heckel et al., PRD 78, 092006 (2008) B. Heckel et al., PRL 97, 021603 (2006) L.-S. Hou et al., PRL 90, 201101 (2003)


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Standard-Model Extension: EXPERIMENTS
gravity:
A. Hees et al., arXiv:1508.03478 C.-G. Shao et al., PRD 91, 102007 (2015) J. Long and V.A. Kostelecky, PRD 91, 092003 (2015) L. Shao, PRD 90, 122009 (2014) L. Shao, PRL 112, 111103 (2014) M.A. Hohensee et al., PRL 111, 151102 (2013) M.A. Hohensee et al., PRL 106, 151102 (2011) D. Bennett, arXiv:1008.3670 K.-Y. Chung et al., PRD 80, 016002 (2009) D. Bennett et al., arXiv:1008.3670 K.-Y. Chung et al., PRD 80, 016002 (2009) H. Mueller et al., PRL 100, 031101 (2008) J.B.R. Battat et al., PRL 99, 241103 (2007) Super-Kamiokande Collaboration, PRD 91, 052003 (2015) Super-K Collaboration, arXiv:1308.2210 J.S. Diaz et al., PLB 727, 412 (2013) T. Katori and J. Spitz, arXiv:1307.5805 B. Rebel and S. Mufson, Astropart. Phys. 48, 78 (2013) Double Chooz Collaboration, PRD 86, 112009 (2012) MiniBooNE Collaboration, MPLA 27, 1230024 (2012) MINOS Collaboration, PRD 85, 031101 (2012) MiniBooNE Collaboration, arXiv:1109.3480 IceCube Collaboration, PRD 82, 112003 (2010) MiniBooNE Collaboration, arXiv:1008.0906 MINOS Collaboration, PRL 105, 151601 (2010) MINOS Collaboration, PRL 101, 151601 (2008) LSND Collaboration, PRD 72, 076004 (2005)

neutrinos:


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Standard-Model Extension: EXPERIMENTS
photons:
S.R. Parker et al., arXiv:1508.02490 F. Kislat and H. Krawczynski, PRD 92, 045016 (2015) M. Nagel et al., arXiv:1412.6954 A. Lo et al., arXiv:1412.2142 Y. Michimura et al., PRD 88, 111101(R) (2013) V. Vasileiou et al., PRD D 87, 122001 (2013) Y. Michimura et al., PRL 110, 200401 (2013) F. Baynes et al., PRD 84, 081101 (2011) S. Parker et al., PRL 106, 180401 (2011) Fermi GBT and LAT Collaborations, arXiv:1008.2913 M.A. Hohensee et al., PRD 82, 076001 (2010) J.-P. Bocquet et al., PRL 104, 241601 (2010) S. Herrmann et al., PRD 80, 105011 (2009) M. Tobar et al., PRD 80, 125024 (2009) Ch. Eisele et al., PRL 103, 090401 (2009) S. Reinhardt et al., Nature Physics 3, 861 (2007) H. Mueller et al., PRL 99, 050401 (2007) M. Hohensee et al., PRD 75, 049902 (2007) P.L. Stanwix et al., PRD 74, 081101 (R) (2006) J.P. Cotter and B.T.H. Varcoe, arXiv:physics/0603111 P. Antonini et al., PRA 72, 066102 (2005) M. Tobar et al., PRA 72, 066101 (2005) S. Herrmann et al., PRL 95, 150401 (2005) M. Tobar et al., Lect. Notes Phys. 702, 415 (2006) P.L. Stanwix et al., PRL 95, 040404 (2005) P. Antonini et al., PRA 71, 050101 (2005) M. Tobar et al., PRD 71, 025004 (2005) P. Wolf et al., PRD 70, 051902 (2004) P. Wolf et al., Gen. Rel. Grav. 36, 2352 (2004) H. Mueller et al., PRD 68, 116006 (2003) H. Mueller et al., PRL 91, 020401 (2003) J. Lipa et al., PRL 90, 060403 (2003)


Introduction

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Standard-Model Extension

SME photons

Birefringence

Summary

IUHET 591, January 2015

Data Tables for Lorentz and CPT Violation
Physics Department, Indiana University, Bloomington, IN 47405 Physics Department, Northern Michigan University, Marquette, MI 49855
a

V. Alan Kosteleckya and Neil Russell ´

b

b

IUHET 591; January 2015 up date to Reviews of Modern Physics 83, 11 (2011) [arXiv:0801.0287]

arXiv:0801.0287v8 [hep-ph] 19 Jan 2015

This work tabulates measured and derived values of coefficients for Lorentz and CPT violation in the Standard-Model Extension. Summary tables are extracted listing maximal attained sensitivities in the matter, photon, neutrino, and gravity sectors. Tables presenting definitions and prop erties are also compiled.

CONTENTS

I. Intro duction .............. II. Summary tables ......... III. Data tables ............. IV. Properties tables ........ A. Minimal QED extension B. Minimal SME ....... C. Nonminimal sectors . References .................. Table 1: List of tables . . . . . . . Summary tables S2­S5 . . . . . . . Data tables D6­D35 . . . . . . . . . Properties tables P36­P49 . . .

. . . .

.. .. .. .. .. ... .. ... .. ... .. ... .. ... .. ... .. ... ..

. . . .

. . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

1400 1constraints The 1 30 data taexclusivs ultthseummarciendtsheroer concertnzprimartionbut not bleres s coeffi ize f Loren viola ily in the ely 1 minimal SME. We compile 30 data tables for these SME 1 75 pages coefficients, including both existing experimental mea6

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . .

1 2 3 5 6 7 8 0 4 5 9 4

The Lorentz-violating operators in the SME are systematically classified according to their mass dimension, and operators of arbitrarily large dimension can appear. At any fixed dimension, the operators are finite in number and can in principle be enumerated. A limiting case of particular interest is the minimal SME, which can be viewed as the restriction of the SME to include only Lorentz-violating operators of mass dimension four or less. The corresponding co efficients for Lorentz violation are dimensionless or have positive mass dimension.

I. INTRODUCTION

Recent years have seen a renewed interest in experimental tests of Lorentz and CPT symmetry. Observable signals of Lorentz and CPT violation can be described in a model-independent way using effective field theory [1]. The general realistic effective field theory for Lorentz violation is called the Standard-Model Extension (SME) [2, 3]. It includes the Standard Model coupled to General Relativity along with all possible operators for Lorentz

surements and theory-derived limits. Each of these data tables provides information about the results of searches for Lorentz violation for a specific sector of the SME. For each measurement or constraint, we list the relevant coefficient or combination of co efficients, the result as presented in the literature, the context in which the search was performed, and the source citation. The tables include results available from the literature up to December 31, 2014. The scope of the searches for Lorentz violation listed in the data tables can be characterized roughly in terms of depth, breadth, and refinement. Deep searches yield


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

26
Table D10. Photon sector, d = 3 Combination |k(V | |kAF | 6|k(V
(3) (3) 2 )11 | (3) )10 (3) k(V )11

Result < 16 â 10 < 12 â 10
-21 -21 -43 -43 -42 -43

System GeV GeV GeV GeV GeV GeV Schumann resonances " CMB polarization " " "

Ref. [91]* [91]* [19]* [13]*, [14]* [13]* [13]*

| |
(3) 2 )10 | 1/2

+ 3|k(V
(3)

/ 4

(10

+4 -8

) â 10

|kAF | (3) k(V )10 Re k(V
(3)

(15 ± 6) â 10 ±(3 ± 1) â 10 ±(21
+7 -9

(3) )11

) â 10

|

j

|kAF | (3) |2kAF | (3) m Yj m k(V )j m | |k(V
(3) )00 (3) )00

(0.57 ± 0.70)H0 10-41 GeV < 6 â 10-43 GeV < 14 â 10 (1.1 ± 1.3 ± 1.5) â 10
-21 -43

Astrophysical birefringence [92]* " [93]* " [94]*, [14]* Schumann resonances CMB polarization [91]* [95] 6]* 7] 8] 9] 9]* 00]* 01], 3]* 02]* 03]* 04]* 2]* 4]*,

|

GeV GeV GeV GeV GeV GeV GeV GeV GeV GeV GeV GeV GeV GeV

k(V

" " " " " " " " " " " " "

(0.04 ± 0.35) â 10-43 (-0.64 ± 0.50 ± 0.50) â 10-43 (4.3 ± 4.1) â 10-43 (-1.4 ± 0.9 ± 0.5) â 10-43 (2.3 ± 5.4) â 10-43 < 2.5 â 10-43 (1.2 ± 2.2) â 10-43 (12 ± 7) â 10-43 (2.6 ± 1.9) â 10-43 (2.5 ± 3.0) â 10-43 (6.0 ± 4.0) â 10-43 (1.1 ± 1.4)H0 < 2 â 10-42

" [9 " [9 " [9 " [9 " [1 " [1 " [1 " [1 " [1 " [1 " [1 Astrophysical birefringence [9 " [9

, [19]* [19]* , [19]* , [19]* , [13]* [14]*


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

SME photons

SME photons


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

SME photons: THEORY
(minimal extension - only dimension 3 & 4 op erators) 1 L = - Fµ F 4
µ

(convention)


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

SME photons: THEORY
(minimal extension - only dimension 3 & 4 op erators) 1 L = - Fµ F 4
µ

+ 1 (kAF ) 2

(3)

µ

A F

µ

(convention)

(CPT-odd)


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

SME photons: THEORY
(minimal extension - only dimension 3 & 4 op erators) 1 L = - Fµ F 4
µ

+ 1 (kAF ) 2

(3)

µ

A F

µ

1 (4) - (kF ) 4

µ

F



F

µ

(convention)

(CPT-odd)

(CPT-even)


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

SME photons: THEORY
(minimal extension - only dimension 3 & 4 op erators) 1 L = - Fµ F 4
µ

+ 1 (kAF ) 2

(3)

µ

A F

µ

1 (4) - (kF ) 4

µ

F



F

µ

(convention)

(CPT-odd)

(CPT-even)

modified Maxwell equations: â H - 0 D = 0, · D = 0 D = E + 2kAF â A + DE · E + DB · B H = B - 2(kAF )0 A + 2kAF A0 + H B · B + H E · E


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

SME photons: THEORY

1 L = - Fµ F 4

µ

+ 1 (kAF ) 2

(3)

µ

A F

µ

1 (4) - (kF ) 4

µ

F



F

µ

(convention)

(CPT-odd)

(CPT-even)

coefficient (kAF )µ (4) (e+ )j k ~ (4) (e- )j k ~ (4) (o+ )j k ~ (4) (o- )j k ~ (4) tr ~
(3)

numb er 4 5 5 3 5 1

CPT o dd even even even even even

birefringent X X

X


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

SME photons: PHOTON TESTS
tests birefringence (interferometric, astrophysical) disp ersion (kinematics, astrophysical) cavities (interferometric, lab oratory) others (kinematics, lab oratory)

sensitivity


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence

Birefringence


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: THEORY
disp ersion relation: E 1 - 0 ± ( 1 )2 + ( 2 )2 + ( 3 )2 p birefringence 0 = 1 ± i 2 = 3 =
1 E 0 Yj m

(n) c(I ^

(4) )j m

, ik(B ,
(4) )j m

j = 0, 1, 2 , j=2 j = 0, 1 n ^ ^ ^ p ^

±2 Y j m

(n) k(E ^ (n) k(V ^

(4) )j m (3) )j m

0 Yj m

Stokes parameters of modes = ±( 1 , 2 , 3 ) source direction = n ^


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: THEORY
disp ersion relation: E 1 - 0 ± ( 1 )2 + ( 2 )2 + ( 3 )2 p birefringence ­ light propagates as sup erp osition of two birefringent modes ­ phase velocities differ: ­ p olarizations differ: v 1 - 0 ± ( 1 )2 + ( 2 )2 + ( 3 )2

Stokes parameters = ±( 1 , 2 , 3 )

p olarization evolves


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: STOKES PARAMETERS
s s s
1 2 3

E E - E E Q = U = E E + E E V iE E - iE E
RH circular p olarization ellipse

linear

Stokes vector

LH circular


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: STOKES PARAMETERS
birefringence rotation ab out = ( 1 , 2 , 3 ) CPT-odd case CPT-even case

rotation axis rotation angle E
d-3

â distance â coeffs


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: STOKES PARAMETERS
example: CPT-even case


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: CPT-ODD CONSTRAINTS
­ kAF gives energy-indep endent birefringence want large distance, any energy use CMB
(3)

­ Stokes rotation axis p oints to p ole gives simple rotation of linear p olarization
(3) )j m

Stokes rotation angle = 2 =
dz Hz (1+z )

dz Hz (1+z )

jm

Y

jm

(n)k(V ^

jm

Y

jm

(n)k(V ^

(3) )j m


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: CPT-ODD CONSTRAINTS
Coefficients |k
(3) AF

Result (15 ± 6) â 10-43 GeV 4 (10+8 ) â 10-43 GeV - (6.0 ± 4.0) â 10-43 GeV (2.5 ± 3.0) â 10-43 GeV (12 ± 7) â 10-43 GeV (1.2 ± 2.2) â 10-43 GeV (2.6 ± 1.9) â 10-43 GeV < 2.5 â 10-43 GeV (2.3 ± 5.4) â 10-43 GeV (-1.4 ± 0.9 ± 0.5) â 10-43 GeV (-0.64 ± 0.50 ± 0.50) â 10-43 GeV (0.04 ± 0.35) â 10-43 GeV (1.1 ± 1.3 ± 1.5) â 10-43 GeV

Reference
K & M, PRL '07 K & M, ApJL '08 Feng et al., PRL '06 Cabella et al., PRD '07 K & M, PRL '08 Komatsu et al., ApJS '09 Xia et al., AA '08 Kahniashvili et al., PRD '08 K & M, ApJL '08 Wu et al., PRL '09 Brown et al., ApJ '09 Xia et al., PLB '10 Komatsu et al., ApJS '11

|

k(V

(3) )00

d = 3: need 4 sources d = 3: have full-sky (CMB)


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: CPT-EVEN CONSTRAINTS
­ kF gives energy-dep endent birefringence want large distance & high energy us e G R B s
(4)

­ Stokes rotation angle = 2E
z (1+z )d Hz 0
-4

dz â

j m +2 Y j m

(n) k(E ^

(4) )j m

± ik(B

(4) )j m

­ necessarily direction dep endent - no isotropic birefringence ­ some p olarizations remain unaffected - those aligned with rotation axis


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: CPT-EVEN CONSTRAINTS
GRB 930131 GRB 960924 GRB 041219A GRB 100826A GRB 110301A GRB 110721A z 0.1 0.1 0.02 0.71 0.21 0.45 energy 31 ­ 98 keV 31 ­ 98 keV 100­ 1000 keV 70 ­ 300 keV 70 ­ 300 keV 70 ­ 300 keV ( , ) (98 , 182 ) (87 , 37 ) (27 , 6 ) (112 , 279 ) (61 , 229 ) (129 , 333 )

d > 3: have 6 high-energy constraints


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Birefringence: CPT-EVEN CONSTRAINTS
GRB 930131 GRB 960924 GRB 041219A GRB 100826A GRB 110301A GRB 110721A z 0.1 0.1 0.02 0.71 0.21 0.45 energy 31 ­ 98 keV 31 ­ 98 keV 100­ 1000 keV 70 ­ 300 keV 70 ­ 300 keV 70 ­ 300 keV ( , ) (98 , 182 ) (87 , 37 ) (27 , 6 ) (112 , 279 ) (61 , 229 ) (129 , 333 )

d = 4: need 10


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Summary

Summary


Introduction

Motivation

Standard-Model Extension

SME photons

Birefringence

Summary

Summary:
­ Lorentz invariance must b e tested ­ SME = general framework of Lorentz-violation studies ­ p olarimetry = among b est tests of Lorentz invariance ­ CMB p olarimetry b est test of birefringence from dimension-3 LV ­ GRB p olarimetry b est test of birefringence from d > 3 LV