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CPT Violation and
(Quantum) Gravity
Nick E. Mavromatos
King’s College London &
CERN/PH-TH
London Centre
for Terauniverse
Studies (LCTS)
AdV 267352
金沢市
LEAP 2016,
12th International
Conference
March 6-11 2016,
Kanazawa (Japan)
OUTLINE
I. Motivation: Quantum OR Classical Gravity (Geometrical
Backgrounds in Early Universe) may violate
fundamental space-time symmetries: either
continuous (Lorentz (LV)) or discrete (T & CPT (CPTV))
and/or induced decoherence of quantum matter
Parametrization: Standard Model Extension (SME) and beyond…
Selected Tests in particle physics: From Cosmic
photons and ultra-high energy neutrinos
to low-energy antiprotons & antimatter
factories, spectroscopy, dipole moments,
entangled neutral meson factories
(``smoking-gun for quantum gravity decoherence models)
II. Standard Model Extension (SME): microscopic origin scenarios of
some of the CPTV & LV coefficients: torsionful geometries
III. CPTV-induced Matter-antimatter asymmetry in Early Universe:
Leptogenesis -Baryogenesis from II
IV. Outlook
OUTLINE
I. Motivation: Quantum OR Classical Gravity (Geometrical
Backgrounds in Early Universe) may violate
fundamental space-time symmetries: either
continuous (Lorentz (LV)) or discrete (T & CPT (CPTV))
and/or induced decoherence of quantum matter
Parametrization: Standard Model Extension (SME) and beyond…
Selected Tests in particle physics: From Cosmic
photons and ultra-high energy neutrinos Beyond Local
Effective field
to low-energy antiprotons & antimatter
theories
factories, spectroscopy, dipole moments,
entangled neutral meson factories
(``smoking-gun for quantum gravity decoherence models)
II. Standard Model Extension (SME): microscopic origin scenarios of
some of the CPTV & LV coefficients: torsionful geometries
III. CPTV-induced Matter-antimatter asymmetry in Early Universe:
Leptogenesis -Baryogenesis from II
IV. Outlook
OUTLINE
I. Motivation: Quantum OR Classical Gravity (Geometrical
Backgrounds in Early Universe) may violate
fundamental space-time symmetries: either
continuous (Lorentz (LV)) or discrete (T & CPT (CPTV))
and/or induced decoherence of quantum matter
Parametrization: Standard Model Extension (SME) and beyond…
Selected Tests in particle physics: From Cosmic
photons and ultra-high energy neutrinos
experimental to low-energy antiprotons & antimatter
sensitivities
factories, spectroscopy, dipole moments,
entangled neutral meson factories
(``smoking-gun for quantum gravity decoherence models)
II. Standard Model Extension (SME): microscopic origin scenarios of
some of the CPTV & LV coefficients: torsionful geometries
III. CPTV-induced Matter-antimatter asymmetry in Early Universe:
Leptogenesis -Baryogenesis from II
IV. Outlook
OUTLINE
I. Motivation: Quantum OR Classical Gravity (Geometrical
Backgrounds in Early Universe) may violate
fundamental space-time symmetries: either
continuous (Lorentz (LV)) or discrete (T & CPT (CPTV))
and/or induced decoherence of quantum matter
Parametrization: Standard Model Extension (SME) and beyond…
Selected Tests in particle physics: From Cosmic
photons and ultra-high energy neutrinos
to low-energy antiprotons & antimatter
factories, spectroscopy, dipole moments,
entangled neutral meson factories
(``smoking-gun for quantum gravity decoherence models)
II. Standard Model Extension (SME): microscopic origin scenarios of
some of the CPTV & LV coefficients: torsionful geometries
III. CPTV-induced Matter-antimatter asymmetry in Early Universe:
Leptogenesis -Baryogenesis from II
Estimation of
IV. Outlook
order of magnitude
of CPTV effects
PART I
THEORY
BACKGROUND
Conditions for the Validity of CPT Theorem
CPT Invariance Theorem :
(i) Flat space-times
(ii) Lorentz invariance
(iii) Locality
(iv) Unitarity
Schwinger, Pauli,
Luders, Jost, Bell
revisited by:
Greenberg,
Chaichian, Dolgov,
Novikov…
(ii)-(iv) Independent reasons for violation
Conditions for the Validity of CPT Theorem
CPT Invariance Theorem :
(i) Flat space-times
(ii) Lorentz invariance
(iii) Locality
(iv) Unitarity
Kostelecky, Bluhm, Colladay,
Potting, Russell, Lehnert, Mewes,
Diaz , Tasson….
Standard Model Extension (SME)
(ii)-(iv) Independent reasons for violation
Lorentz & CPT
Violation
Lorentz & CPT
Violation
STANDARD MODEL EXTENSION
,Tasson
Conditions for the Validity of CPT Theorem
CPT Invariance Theorem :
(i) Flat space-times
(ii) Lorentz invariance
(iii) Locality
(iv) Unitarity
Barenboim, Borissov, Lykken
PHENOMENOLOGICAL
models with non-local
mass parameters
(ii)-(iv) Independent reasons for violation
Conditions for the Validity of CPT Theorem
CPT Invariance Theorem :
(i) Flat space-times
(ii) Lorentz invariance
(iii) Locality
(iv) Unitarity
(ii)-(iv) Independent reasons for violation
e.g. QUANTUM SPACE-TIME
FOAM AT PLANCK SCALES
J.A. Wheeler
10-35 m
Conditions for the Validity of CPT Theorem
CPT Invariance Theorem :
(i) Flat space-times
(ii) Lorentz invariance
(iii) Locality
(iv) Unitarity
Hawking,
Ellis, Hagelin, Nanopoulos
Srednicki,
Banks, Peskin, Strominger,
Lopez, NEM, Barenboim…
(ii)-(iv) Independent reasons for violation
QUANTUM GRAVITY INDUCED DECOHERENCE
EVOLUTION OF PURE QM STATES TO MIXED
AT LOW ENERGIES
LOW ENERGY CPT OPERATOR NOT WELL DEFINED
cf. ω-effect in EPR entanglement
10-35 m
Conditions for the Validity of CPT Theorem
CPT Invariance Theorem :
(i) Flat space-times
(ii) Lorentz invariance
(iii) Locality
(iv) Unitarity
Hawking,
Ellis, Hagelin, Nanopoulos
Srednicki,
Banks, Peskin, Strominger,
Lopez, NEM, Barenboim…
(ii)-(iv) Independent reasons for violation
QUANTUM GRAVITY INDUCED DECOHERENCE
EVOLUTION OF PURE QM STATES TO MIXED
AT LOW ENERGIES
LOW ENERGY CPT OPERATOR NOT WELL DEFINED
cf. ω-effect in EPR entanglement
10-35 m
NB: Decoherence & CPTV
Decoherence implies that
asymptotic density matrix
of
low-energy matter :
May induce quantum decoherence
of propagating matter and
intrinsic CPT Violation
in the sense that the CPT
operator Θ is not well-defined 
beyond Local Effective Field theory
If Θ well-defined
can show that
exists !
INCOMPATIBLE WITH DECOHERENCE !
Hence Θ ill-defined at low-energies in
QG foam models
Wald (79)
NB: Decoherence & CPTV
Decoherence implies that
asymptotic density matrix
of
low-energy matter :
May induce quantum decoherence
of propagating matter and
intrinsic CPT Violation
in the sense that the CPT
operator Θ is not well-defined 
beyond Local Effective Field theory
May contaminate initially antisymmetric neutral
INCOMPATIBLE WITH DECOHERENCE !
meson M state by symmetric parts (ω-effect)
Hence Θ ill-defined at low-energies in Wald (79)
Bernabeu, NEM,
QG foam models  may affect EPR
Papavassiliou,…
NB: Decoherence & CPTV
Decoherence implies that
asymptotic density matrix
of
low-energy matter :
May induce quantum decoherence
of propagating matter and
intrinsic CPT Violation
in the sense that the CPT
operator Θ is not well-defined 
beyond Local Effective Field theory
May contaminate initially antisymmetric neutral
INCOMPATIBLE WITH DECOHERENCE !
meson M state by symmetric parts (ω-effect)
Hence Θ ill-defined at low-energies in Wald (79)
Bernabeu, NEM,
QG foam models  may affect EPR
Papavassiliou,…
Bernabeu, NEM,
Papavassiliou,…
I(Δt=0) ≠ 0
if ω-effect present
Bernabeu, NEM,
Papavassiliou,…
Bernabeu, NEM,
Papavassiliou,…
enhancement factor due to CP violation
compared with, eg, B-mesons
Bernabeu, NEM,
Papavassiliou,…
I
I
I
Δt
I
Δt
Δt
Δt
Bernabeu, NEM,
Papavassiliou,…
I
I
I
Current Limits (KLOE Coll.)
I
Perspectives for KLOE-2 : Re(ω), Im(ω)  2 x 10-5
A di Domenico
Δt
I
Current Limits (KLOE Coll.)
Δt
I
Perspectives for KLOE-2 : Re(ω), Im(ω)  2 x 10-5
A di Domenico
Bernabeu, NEM,
Sarkar
close to excluding some string-theory models
PART Ib
CURRENT
EXPERIMENTAL
SENSITIVITIES
(Selected Tests)
STANDARD MODEL EXTENSION
Kostelecky et al.
STANDARD MODEL EXTENSION
Kostelecky et al.
LV & CPTV
CPT symmetry requires atomic transitions between H and anti-H to be identical
Hayano et al.
Lorentz Violation & (Anti)-Hydrogen
• Trapped Molecules:
Forbidden transitions
e.g. 1s  2s
NB: Sensitivity in b3
that rivals astrophysical
or atomic-physics
bounds can only be
attained if spectral
resolution of 1 mHz
is achieved.
Not feasible at present in
anti-H factories
NB
Lorentz Violation & (Anti)-Hydrogen
• Trapped Molecules:
Forbidden transitions
e.g. 1s  2s
NB: Sensitivity in b3
that rivals astrophysical
or atomic-physics
bounds can only be
attained if spectral
resolution of 1 mHz
is achieved.
Not feasible at present in
anti-H factories
NB
Probing CPT Violation via Atomic
Dipole moments
Bolokhov, Pospelov, Romalis 0609.153
Non-relativistic Hamiltonian
In the presence of Lorentz-violating background vector
Total atomic dipole moment
nil result of neutron EDM 
constraint on combination
SME & Atomic Dipole moments
Bolokhov, Pospelov, Romalis 0609.153
aμ , bμ LV background
+
properties
CPT V @ low energies (1 GeV) in SU(2) x U(1)
Bolokhov, Pospelov, Romalis 0609.153
manipulating field identities
light quarks (u, d, s)
+ photons, gluons
Disentangle CP- from CPT-odd operators
CP-odd terms require helicity flip  dim 6 operators . suppressed by
 spin precession with magnetic field
CPT-odd terms do not require helicity flip  dim 5 operators in SU(2) X U(1)
 no spin precession
Current bounds 
EDM neutrons
diamagnetic atoms (Hg, Xe,…)
paramagnetic atoms (Tl, Cs,…)
EDM-induced CPT bounds
Bolokhov, Pospelov, Romalis 0609.153
(2002)
Neutron
CPT-odd EDMs
limited @
Diamagnetic atoms
 if dn ≠ 0  CPTV
paramagnetic atoms
EDMs predicted to be extremely suppressed
higher-loop CPV corrections yields
imprecise estimates
Effects of bμ on dipole moments in
Hydrogen-like atoms
Angular distribution for
spontaneous radiation
for the transition
Corrections to electromagnetic
dipole moments of bound electrons
calculated in 1/c expansion
(Foldy-Wouthysen (FW) method) to
second order in b0  contributions
to anapole moment of the atomic
orbital  asymmetry of angular
distribution of radiation of, e.g.
hydrogen atom
Kharlanov, Zhukovsky 0705.3306
electric & magnetic dipole corrections
Part II
Microscopic Origin of SME
coefficients?
Several ``Geometry-induced’’ examples:
Non-Commutative Geometries
Axisymmetric Background
Geometries of the Early Universe
Torsionful Geometries (including strings…)
Early Universe T-dependent effects:
large @ high T, low values today
for coefficients of SME
Part II
Microscopic Origin of SME
coefficients?
Several ``Geometry-induced’’ examples:
Non-Commutative Geometries
Axisymmetric Background
Geometries of the Early Universe
Torsionful Geometries (including strings…)
Early Universe T-dependent effects:
large @ high T, low values today
for coefficients of SME
STANDARD MODEL EXTENSION
Kostelecky et al.
LV & CPTV
CPTV Effects of different Space-TimeCurvature/Spin couplings between
fermions/antifermions
B. Mukhopadhyay, U. Debnath, N. Dadhich, M. Sinha
Lambiase, Mohanty, NEM, Ellis, Sarkar, de Cesare
In particular,
Space-times with
Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivative
including spin connection
Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivative
including spin connection
Standard Model Extension
type Lorentz-violating
coupling
(Kostelecky et al.)
Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivative
including spin connection
For homogeneous and isotropic
Friedman-Robertson-Walker
geometries the resulting Bμ vanish
Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivative
including spin connection
Can be constant in a given
local frame in Early Universe
axisymmetric (Bianchi) cosmologies
or near rotating Black holes, or
in stringy antisymmetric tensor backgrounds
Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivative
including spin connection
If torsion then Γμν ≠ Γνμ
antisymmetric part is the
contorsion tensor, contributes
in stringy antisymmetric tensor backgrounds
A non-trivial example of Torsion: String Theories with
Antisymmetric Tensor Backgrounds
NEM & Sarben Sarkar, arXiv:1211.0968
John Ellis, NEM & Sarkar, arXiv:1304.5433
De Cesare, NEM & Sarkar arXiv:1412.7077
Massless Gravitational multiplet of (closed) strings: spin 0 scalar (dilaton)
spin 2 traceless symemtric rank 2
tensor (graviton)
spin 1 asntisymmetric rank 2 tensor
A non-trivial example of Torsion: String Theories with
Antisymmetric Tensor Backgrounds
NEM & Sarben Sarkar, arXiv:1211.0968
John Ellis, NEM & Sarkar, arXiv:1304.5433
De Cesare, NEM & Sarkar arXiv:1412.7077
Massless Gravitational multiplet of (closed) strings: spin 0 scalar (dilaton)
spin 2 traceless symemtric rank 2
tensor (graviton)
spin 1 asntisymmetric rank 2 tensor
KALB-RAMOND FIELD
Effective field theories (low energy scale E << Ms) `` gauge’’ invariant
Depend only on field strength :
Bianchi identity :
ROLE OF H-FIELD AS TORSION
EFFECTIVE GRAVITATIONAL ACTION IN STRING LOW-ENERGY LIMIT
4-DIM
PART
)
Contorsion
ROLE OF H-FIELD AS TORSION – AXION FIELD
EFFECTIVE GRAVITATIONAL ACTION IN STRING LOW-ENERGY LIMIT
4-DIM
PART
)
IN 4-DIM DEFINE DUAL OF H AS :
b(x) = Pseudoscalar
(Kalb-Ramond (KR)
axion)
FERMIONS COUPLE TO H –TORSION VIA GRAVITATIONAL COVARIANT DERIVATIVE
TORSIONFUL CONNECTION, FIRST-ORDER FORMALISM
contorsion
Non-trivial contributions to Bμ
FERMIONS COUPLE TO H –TORSION VIA GRAVITATIONAL COVARIANT DERIVATIVE
TORSIONFUL CONNECTION, FIRST-ORDER FORMALISM
contorsion
Non-trivial contributions to Bμ
When db/dt = constant  Torsion is constant
Covariant Torsion tensor
Constant
constant B0
Standard Model Extension type with CPT and Lorentz Violating background b0
When db/dt = constant  Torsion is constant
Covariant Torsion tensor
In string theory a constant
B0 background is guaranteed
by exact solutions
with linear in
FRW time b = (const ) t
Antoniadis, Bachas,
Ellis, Nanopoulos
Constant
constant B0
Standard Model Extension type with CPT and Lorentz Violating background b0
PART III
COSMOLOGICAL
CONSEQUENCES
Matter-antimatter
asymmetry in Universe
-Lepto(Baryo)genesis
Early Universe Matter
Dominance
• Ultimate question: why is the Universe made
only of matter?
• Leptogenesis: physical out of thermal
equilibrium processes in the (expanding)
Early Universe that produce an asymmetry
between leptons & antileptons
• Baryogenesis: The corresponding processes
that produce an asymmetry between baryons
and antibaryons
Early Universe Matter
Dominance
• Ultimate question: why is the Universe made
only of matter?
• Leptogenesis: physical out of thermal
equilibrium processes in the (expanding)
Early Universe that produce an asymmetry
between leptons & antileptons
• Baryogenesis: The corresponding processes
that produce an asymmetry between baryons
and antibaryons
escher
STANDARD MODEL INCOMPATIBLE
WITH BARYOGENESIS
• Matter-Antimatter asymmetry in the
Universe
Violation of Baryon # (B), C & CP
• Tiny CP violation
(O(10-3))
in Labs: e.g.
0
K K
0
• But Universe consists only of matter
T > 1 GeV
Sakharov : Non-equilibrium physics of early Universe, B, C, CP violation
but not quantitatively in SM, still a mystery
Role of Neutrinos?
• Several Ideas to go beyond the SM (e.g. GUT
models, Supersymmetry, extra dimensional models
etc.)
• Massive ν are simplest extension of SM
Shaposhnikov et al. νMSM
• Right-handed massive ν may provide extensions of
SM with:
extra CP Violation and thus Origin of Universe’s
matter-antimatter asymmetry due to neutrino
masses, Dark Matter
Leptogenesis  Baryogenesis in Standard Model
(e.g. Sphaleron-processes B-L conserving
in electroweak sector of Standard Model)
Rubakov, Kuzmin, Shaposhnikov,...
Gavela, Hernandez, Orloff,Pene...
STANDARD MODEL EXTENSION
Gravitational Baryogenesis
Davoudiasl, Kitano, Kribs,
Murayama, Steinhardt
Quantum Gravity (or something else (e.g. SUGRA)) may lead
at low-energies (below Plnack scale or a scale M*) to a term
in the effective Lagrangian (in curved back space-time backgrounds):
Standard Model
extension type
Term Violates CP but is CPT conserving in vacuo
It Violates CPT in the background space-time of an
expanding FRW Universe
Energy differences between particle vs antiparticles
Baryon Asymmetry
Calculate for
various w in
some scenarios
Dynamical CPTV
@ T < TD ,
TD = Decoupling T
GENERATE Baryon and/or Lepton ASYMMETRY
through CPT Violation
Assume CPT Violation was
strong in the Early Universe
Mechanisms
For Torsion-BackgroundInduced Matter-Antimatter
Asymmetry
physics.indiana.edu
STANDARD MODEL EXTENSION
DISPERSION RELATIONS OF FERMIONS ARE DIFFERENT
FROM THOSE OF ANTI-FERMIONS IN SUCH GEOMETRIES
CPTV Dispersion relations (B0 = b0 )
but (bare) masses are equal between particle/anti-particle sectors
Abundances of fermions in Early Universe, then, different from those of
antifermions, if B0 is non-trivial, ALREADY IN THERMAL EQUILIBRIUM
Equilibrium Distributions different between particle-antiparticles
Can these create the observed matter-antimatter asymmetry?
e.g. Neutrinos : m << B0 << |P|, T 
Abundances of neutrinos in Early Universe different from those of antineutrinos
if B0 ≠ 0
Lepton Asymmetry for relativistic neutrinos
GENERATE Baryon and/or Lepton ASYMMETRY
through CPT Violation
Assume CPT Violation was
strong in the Early Universe
Mechanism
For Torsion-BackgroundInduced tree-level
Leptogenesis  Baryogenesis
Through B-L conserving
Sphaleron processes
In the standard model
physics.indiana.edu
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
Constant H-torsion
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Constant H-torsion
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
Contrast with one-loop
conventional
Leptogenesis
in absence of H-torsion
Fukugita, Yanagida,
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
Constant H-torsion
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
Constant H-torsion
B0 ≠ 0 background
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
Constant H-torsion
B0 ≠ 0 background
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
seesaw
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
Constant H-torsion
B0 ≠ 0 background
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
seesaw
Hence... unlike νΜSM, for leptogenesis
heavy M > 100 TeV, right-handed
Neutrinos N are needed
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
Constant H-torsion
B0 ≠ 0 background
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
?
Constant H-torsion
B0 ≠ 0 background
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Constant H-torsion
B0 ≠ 0 background
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
Equilibrated electroweak
B+L violating sphaleron interactions
B-L conserved
Environmental
Conditions Dependent
Observed Baryon Asymmetry
In the Universe (BAU)
Fukugita, Yanagida,
Kuzmin, Rubakov,
Shaposhinkov
Fukugita, Yanagida,
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
Equilibrated electroweak
B+L violating sphaleron interactions
B-L conserved
Environmental
Conditions Dependent
Observed Baryon Asymmetry
In the Universe (BAU)
Estimate BAU by fixing CPTV background parameters
In some models this means fine tuning ….
Constant H-torsion
B0 ≠ 0 background
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Constant H-torsion
B0 ≠ 0 backgroumd
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
Equilibrated electroweak
B+L violating sphaleron interactions
B-L conserved
Environmental
Conditions Dependent
Observed Baryon Asymmetry
In the Universe (BAU)
Estimate BAU by fixing CPTV background parameters
In some models this means fine tuning ….
e.g. May Require
Fine tuning of
Vacuum energy
B0
: (string) theory underwent a phase transition
@ T ≈ Td = 105 GeV, to :
(i) either B0 = 0
(ii) or B0 small today but non zero
If a small Ba is
present today
Standard Model Extension type coupling bμ
Kostelecky, Mewes, Russell, Lehnert …
If due to H-torsion, it should couple universally (gravity)
to all particle species of the standard model (electrons etc)
Very Stringent constraints from astrophysics on spatial ONLY components (e.g. Masers)
If a small Ba is
present today
Standard Model Extension type coupling bμ
Kostelecky, Mewes, Russell, Lehnert …
If due to H-torsion, it should couple universally (gravity)
to all particle species of the standard model (electrons etc)
Very Stringent constraints from astrophysics on spatial ONLY components (e.g. Masers)
Can these small current values of Torsion be connected smoothly,
with some form of temperature T dependence, to the B0 of O(1 MeV)
in our case, required for Leptogenesis at T=105 GeV ?
De Cesare, NEM, Sarkar, Eur.Phys.J. C75 (2015) 10, 514
NB:
Perturbatively we may also have such a constant B0
background in the presence of Lorentz-violating condensates
of fermion axial current temporal component
<0 | J05 |0> ≠ 0
at the high-density, high-temperature Early Universe epochs
Eqs of motion for pseudoscalar:
Condensate may be subsequently destroyed at a temperature Tc <0 | J05 |0>  0
by relevant operators so eventually in an expanding FRW Universe for
T < Tc
De Cesare, NEM, Sarkar, Eur.Phys.J. C75 (2015) 10, 514
NB:
Perturbatively we may also have such a constant B0
background in the presence of Lorentz-violating condensates
of fermion axial current temporal component
<0 | J05 |0> ≠ 0
at the high-density, high-temperature Early Universe epochs
Eqs of motion for pseudoscalar:
Condensate may be subsequently destroyed at a temperature Tc <0 | J05 |0>  0
by relevant operators so eventually in an expanding FRW Universe for
weak torsion today,
compatible
with stringent
experimental limits
T < Tc
De Cesare, NEM, Sarkar, Eur.Phys.J. C75 (2015) 10, 514
B0
: (string) theory underwent a phase transition
@ T ≈ Td = 105 GeV, from B0 = const = 1 MeV to :
B0 small today but non zero, scales with scale factor
as a-3 ≈
const x T3
Quite safe from stringent
Experimental Bounds
De Cesare, NEM, Sarkar, Eur.Phys.J. C75 (2015) 10, 514
B0
: (string) theory underwent a phase transition
@ T ≈ Td = 105 GeV, from B0 = const = 1 MeV to :
B0 small today but non zero, scales with scale factor
as a-3 ≈
const x T3
Or...rather reverse the
logic-scale back with T
B0 ~ T3 to constrain
Leptogenesis
or exclude models.....
m
CPTV Thermal Leptogenesis
Early Universe
T > 105 GeV
CPT Violation
Constant H-torsion
B0 ≠ 0 background
Lepton number & CP Violations @ tree-level
due to Lorentz/CPTV Background
Produce Lepton asymmetry
IF:
B0 (today) ~ 10-31 GeV
If seesaw applies:
Unacceptably small! for
m = O(1 GeV )
(appropriate, e.g., for ``heavy’’
sterile neutrinos in νMSM )
IS THIS CPTV ROUTE WORTH FOLLOWING? ….
CPT Violation
Construct Microscopic (Quantum) Gravity models with
strong CPT Violation in Early Universe, but
maybe weak today… Fit with all available data…
Estimate in this way matter-antimatter asymmetry in Universe.
• Interesting Physics in
the Early Universe
may imply
microscopic origin of
SME & allow for
smooth connection
(T-dependent) with
current era
• Plethora of Tests of SME
• At best it may determine
today’s values of
coefficients and connect
with early universe by
T-scaling
• Quantum Gravity though
may imply effects beyond
SME such as ω-effect on
EPR or decoherence
•
Independent tests of T & CPT
possible in entangled states of
particles  use in antiprotonic
atoms ?
ありがとうございました
GENERATE Baryon and/or Lepton ASYMMETRY
through CPT Violation
Assume CPT Violation was
strong in the Early Universe
ONE POSSIBILITY:
particle-antiparticle mass differences
physics.indiana.edu
Equilibrium Distributions different between particle-antiparticles
Can these create the observed matter-antimatter asymmetry?
Dolgov, Zeldovich
Dolgov (2009)
Assume dominant contributions to Baryon asymmetry from quarks-antiquarks
High-T quark mass >> Lepton mass
Equilibrium Distributions different between particle-antiparticles
Can these create the observed matter-antimatter asymmetry?
Assuming dominant contributions to Baryon asymmetry from quarks-antiquarks
Dolgov, Zeldovich
Dolgov (2009)
photon equilibrium density at temperature T
Dolgov (2009)
Current bound
for proton-anti
proton mass diff.
ASACUSA Coll. (2011)
Too small
βΤ=0
Reasonable to take:
NB: To reproduce
the observed
need
Dolgov (2009)
Current bound
for proton-anti
proton mass diff.
ASACUSA Coll. (2011)
Too small
βΤ=0
Reasonable to take:
NB: To reproduce
need
the observed
CPT Violating quark-antiquark Mass difference
alone CANNOT REPRODUCE observed BAU
Microscopic Origin of SME
coefficients?
Several ``Geometry-induced’’ examples:
Non-Commutative Geometries
Axisymmetric Background
Geometries of the Early Universe
Torsionful Geometries (including strings…)
Early Universe T-dependent effects:
large @ high T, low values today
for coefficients of SME
STANDARD MODEL EXTENSION
Non-commutative effective field theories
CPT invariant SME type field theory (Q.E.D. ) - only
even number of indices appear in effective nonrenormalisable terms. (Carroll et al. hep-th/0105082)
Non-commutative effective field theories
CPT invariant SME type field theory (Q.E.D. ) - only
even number of indices appear in effective nonrenormalisable terms. (Carroll et al. hep-th/0105082)
STANDARD MODEL EXTENSION
Microscopic Origin of SME
coefficients?
Several ``Geometry-induced’’ examples:
Non-Commutative Geometries
Axisymmetric Background
Geometries of the Early Universe
Torsionful Geometries (including strings…)
Early Universe T-dependent effects:
large @ high T, low values today
for coefficients of SME
Can neutrinos provide
an explanation of observed
matter-antimatter asymmetry
via CPT VIOLATION (CPTV)?
NB …CPT Violating neutrino-antineutrino
Mass difference alone MAY REPRODUCE observed BAU
Light ν species
Barenboim,
Borissov, Lykken,
Smirnov (01)
PHENOMENOLOGICAL
MODELS
@ 100 GeV
✔
MINOS Exp. RESULTS ON Potential Neutrino-Antineutrino
OSCILLATION PARAMETER DIFFERENCES
http://www-numi.fnal.gov
−
vμ disapearance-Energy spectrum
[arXiv:1108.1509]
−v vs v Oscillation parameters
μ
μ
[arXiv:1104.0344]
[arXiv1103.0340]
−2=(2.62+0.31-0.28 (stat.) ±0.09 (syst.) )x10-3 eV2,
−
νμ disappearance: Δm
sin2(2Θ)=0.95 +0.10-0.11 (stat.) ±0.01 (syst.).
νμ disappearance: Δm2=(2.32+0.12-0.08)x10-3 eV2 , sin2(2Θ) =1.00 (sin2(2Θ) > 0.90 @ 90% CL
Consistent with equality of mass differences between particle/antiparticles
MINOS Exp. RESULTS ON Potential Neutrino-Antineutrino
OSCILLATION PARAMETER DIFFERENCES
http://www-numi.fnal.gov
−
vμ disapearance-Energy spectrum
[arXiv:1108.1509]
−v vs v Oscillation parameters
μ
μ
[arXiv:1104.0344]
[arXiv1103.0340]
−2=(2.62+0.31-0.28 (stat.) ±0.09 (syst.) )x10-3 eV2,
−
νμ disappearance: Δm
sin2(2Θ)=0.95 +0.10-0.11 (stat.) ±0.01 (syst.).
νμ disappearance: Δm2=(2.32+0.12-0.08)x10-3 eV2 , sin2(2Θ) =1.00 (sin2(2Θ) > 0.90 @ 90% CL
Consistent with equality of mass differences between particle/antiparticles
LORENTZ-VIOLATING QUANTUM ELECTRODYNAMICS
(LV QED)
EFT Approach for dimension 5 operators (relevant for dipole moments)
Bolokhov, Pospelov 0703291.
Contributions to Matter & Gauge sectors  Complete classification
Operators must be:
Bolokhov, Pospelov 0703291.
Gauge Sector of QED
Only term
Because:
Matter Sector of QED
Bolokhov, Pospelov 0703291.
Standard Model
Gauge Sector
Quark Sector
Lepton Sector
Higgs Sector
Higgsquark
HiggsLepton
Higgsgauge
Phenomenology of LV & CPTV dim 5 operators
Bolokhov, Pospelov 0703291.
TIME REVERSAL TESTS
INDEPENDENTLY OF CP VIOLATION
IN EPR ENTANGLED STATES
Testing Time Reversal (T) Symmetry independently of CP & CPT
in entangled particle states : some ideas for antiprotonic Atoms
Early results from
CPLEAR, NA48
Bernabeu, Banuls (99)
+ di Domenico, Villanueva-Perez (13)
Direct evidence for T violation: experiment must show it independently of
violations of CP & potentially CPT
opportunity in entangled states of mesons, such as
neutral Kaons, B-mesons; EPR entanglement crucial
Observed in B-mesons (Ba-Bar Coll) Phys.Rev.Lett. 109 (2012) 21180
Experimental
Strategy:
Use initial (|i>) EPR correlated state for flavour tagging
construct observables by looking at
appropriate T violating transitions
interchanging in & out states, not simply being T-odd
infer flavour
by observation of
flavour specific decay
of the
other meson
T-violation Observables in entangled Kaons
Banuls, Bernabeu (1999)
Bernabeu, di Domenico,
Villanueva-Perez 2012
Relevance to antiprotonic atoms? preliminary ideas…
entangled (EPR correlated) Kaons can produced
by s-wave annihilation in antiprotonic atom
coherent decays of
neutral kaons
have been considered
in the past as
a way of measurement
of CP ε’/ε
Βernabeu, Botella, Roldan (89)
In view of recent T Reversal Violation measurements
exploiting the EPR nature of entangled Kaons
we may use antiprotonic atoms to
measure directly T violation, independently of CPT,
via coherent decays of Kaons from the annihilation?
Relevance to antiprotonic atoms? preliminary ideas…
entangled (EPR correlated) Kaons can produced
by s-wave annihilation in antiprotonic atom
coherent decays of
neutral kaons
have been considered
in the past as
a way of measurement
of CP ε’/ε
Βernabeu, Botella, Roldan (89)
In view of recent T Reversal Violation measurements
exploiting the EPR nature of entangled Kaons
we may use antiprotonic atoms to
measure directly T violation, independently of CPT,
via coherent decays of Kaons from the annihilation?
But there are subtleties
associated with
Quantum Gravity & EPR
CPTV & EPR-correlations modification
Other beyond Local EFT EffectsQG-induced ecoherence
Neutral Kaon Entangled States
• Complete Positivity
of Decoherence matrix
(KLOE)
Different parametrization
(Benatti-Floreanini)
Gravity with Torsion contains
Antisymmetric parts in the spin connection:
Contorsion tensor
Torsion decomposes in vector, Tμ , axial vector Sμ and tensor qμνρ parts
Curvature tensor in first order torsionful formalism
Tensor-LV-background induced EDMs
Bolokhov, Pospelov, Romalis 0609.153
tensor background  EFT terms
 corection to spin precession frequency
 signature in EDM expt
for paramagnetic
atoms ≈ O(1/10) CP-odd
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