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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 Change orientation rel. Lab during the day