Neutrinos in the Early Universe, Dark Matter & Matter-Antimatter Asymmetry
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Transcript of Neutrinos in the Early Universe, Dark Matter & Matter-Antimatter Asymmetry
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Neutrinos in the Early Universe, Dark Matter & Matter-Antimatter
Asymmetry
Nick E. Mavromatos
King’s College London & CERN/PH-TH
London Centrefor TerauniverseStudies (LCTS)
AdV 267352
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Motivation: Neutrinos & Baryon Asymmetry in Universe
Right-handed Neutrinos in Torsionful Geometries
Interactions of Sterile Neutrinos & masses
OUTLINE
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Motivation: Neutrinos & Baryon Asymmetry in Universe
Right-handed Neutrinos in Torsionful Geometries
Interactions of Sterile Neutrinos & masses
OUTLINE
Role of (heavy) Majorana Right-handed NeutrinosIn Leptogenesis/Baryogenesis: extra CP Violation & Dark Matter
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Motivation: Neutrinos & Baryon Asymmetry in Universe
Right-handed Neutrinos in Torsionful Geometries
Interactions of Sterile Neutrinos & masses
OUTLINE
Field Theory of neutrinos in torsionful (Kalb-Ramond) GeometriesCPT Violation in Early Universe & particle/antiparticle asymmetries in thermal equilibrium. No need for extra CP Violationfor explanation of matter dominance?
Role of (heavy) Majorana Right-handed NeutrinosIn Leptogenesis/Baryogenesis: extra CP Violation & Dark Matter
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Motivation: Neutrinos & Baryon Asymmetry in Universe
Right-handed Neutrinos in Torsionful Geometries
Interactions of Sterile Neutrinos & masses
OUTLINE
Field Theory of neutrinos in torsionful (Kalb-Ramond) GeometriesCPT Violation in Early Universe & particle/antiparticle asymmetries in thermal equilibrium. No need for extra CP Violationfor explanation of matter dominance?
Role of (heavy) Majorana Right-handed NeutrinosIn Leptogenesis/Baryogenesis: extra CP Violation & Dark Matter
Kalb-Ramondpseudoscalar
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Motivation: Neutrinos & Baryon Asymmetry in Universe
Right-handed Neutrinos in Torsionful Geometries
Interactions of Sterile Neutrinos & masses
OUTLINE
Field Theory of neutrinos in torsionful (Kalb-Ramond) GeometriesCPT Violation in Early Universe & particle/antiparticle asymmetries in thermal equilibrium. No need for extra CP Violationfor explanation of matter dominance?
Beyond see-saw for Right-handed Majorana masses: Anomalous generation of neutrino mass due to Kalb-Ramond quantum torsion
Role of (heavy) Majorana Right-handed NeutrinosIn Leptogenesis/Baryogenesis: extra CP Violation & Dark Matter
Kalb-Ramondpseudoscalar
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Motivation: Neutrinos & Baryon Asymmetry in Universe
Right-handed Neutrinos in Torsionful Geometries
Interactions of Sterile Neutrinos & masses
OUTLINE
Field Theory of neutrinos in torsionful (Kalb-Ramond) GeometriesCPT Violation in Early Universe & particle/antiparticle asymmetries in thermal equilibrium. No need for extra CP Violationfor explanation of matter dominance?
Explanationsof mass hierarchyamong sterileneutrinos?
Beyond see-saw for Right-handed Majorana masses: Anomalous generation of neutrino mass due to Kalb-Ramond quantum torsion
Role of (heavy) Majorana Right-handed NeutrinosIn Leptogenesis/Baryogenesis: extra CP Violation & Dark Matter
Kalb-Ramondpseudoscalar
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PART INEUTRINOS
& MATTER-ANTIMATTER
ASYMMETRY INUNIVERSE
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OBSERVED BARYON ASYMMETRY
• Matter-Antimatter asymmetry in the Universe Violation of Baryon # (B), C & CP
• Tiny CP violation (O(10-3)) in Labs: e.g.
• But Universe consists only of matter
00KK
T > 1 GeV
Sakharov : Non-equilibrium physics of early Universe, B, C, CP violation but not quantitatively in SM, still a mystery
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OBSERVED BARYON ASYMMETRY
• Matter-Antimatter asymmetry in the Universe Violation of Baryon # (B), C & CP
• Tiny CP violation (O(10-3)) in Labs: e.g.
• But Universe consists only of matter
00KK
T > 1 GeV
Sakharov : Non-equilibrium physics of early Universe, B, C, CP violation but not quantitatively in SM, still a mystery
Assume CPT
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General Remarks on CP Violation
• Within Standard Model, CP Violation not enough to produce observed Baryon over antibaryon Asymmetry
• Several Ideas to go beyond the SM (e.g. GUT models, Supersymmetry, extra dimensional models etc.)
• Massive ν are simplest extension of SM
• 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
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SM Extension with N extra right-handed neutrinos
Paschos, Hill, Luty , Minkowski, Yanagida, Mohapatra, Senjanovic,de Gouvea…, Liao, Nelson, Buchmuller, Anisimov, di Bari…Akhmedov, Rubakov, Smirnov,Davidson, Giudice, Notari, Raidal, Riotto, Strumia, Pilaftsis, Underwood, Shaposhnikov … Hernandez, Giunti...
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SM Extension with N extra right-handed neutrinos
Boyarski, Ruchayskiy, ShaposhnikovNon SUSY
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SM Extension with N extra right-handed neutrinos
Right-handedMassive Majorananeutrinos
Leptons
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SM Extension with N extra right-handed neutrinos
Higgs scalar SU(2)Dual:
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SM Extension with N extra right-handed neutrinos
Yukawa couplingsMatrix (N=2 or 3 )
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SM Extension with N extra right-handed neutrinos
Yukawa couplingsMatrix (N=2 or 3 )
From Constraints (compiled ν oscillation data) on (light) sterile neutrinos:Giunti, Hernandez ...N=1 excluded by data
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SM Extension with N extra right-handed neutrinos
Yukawa couplingsMatrix (N=2 or 3 )
Majorana massesto (2 or 3) active neutrinos via seesaw
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SM Extension with N extra right-handed neutrinos
Yukawa couplingsMatrix (N=2 or 3 )
Majorana massesto (2 or 3) active neutrinos via seesaw
NB: Upon Symmetry Breaking <Φ> = v ≠ 0 Dirac mass term
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Light Neutrino Masses through see saw Minkowski,Yanagida, Mohapatra, SenjanovicSechter, Valle …
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SM Extension with N extra right-handed neutrinos
Yukawa couplingsMatrix (N=2 or 3 )
Model with 2 or 3 singlet fermions works well in reproducing Baryon Asymmetry and is consistent with Experimental Data on neutrino oscillations
Model with N=3 also works fine, and in fact it allows one of the Majorana fermions to almost decouple from the rest of the SM fields, thus providing candidates for light (keV region of mass) sterile neutrino Dark Matter.
From Constraints (compiled ν oscillation data) on (light) sterile neutrinos:Giunti, Hernandez ...N=1 excluded by data
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Model with N=3 also works fine, and in fact it allows one of the Majorana fermions to almost decouple from the rest of the SM fields, thus providing candidates for light (keV region of mass) sterile neutrino Dark Matter. It can also provide consistent model for Leptogenesis and, through,sphaleron processes, Baryogenesis.
SM Extension with N extra right-handed neutrinos
Yukawa couplingsMatrix (N=2 or 3 )
Model with 2 or 3 singlet fermions works well in reproducing Baryon Asymmetry and is consistent with Experimental Data on neutrino oscillations
From Constraints (compiled ν oscillation data) on (light) sterile neutrinos:Giunti, Hernandez ...N=1 excluded by data
Boyarski, Ruchayskiy, ShaposhnikovNon SUSY
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Thermal Properties
Two distinct physics cases: MI > MW & MI < MW
(i) MI > MW (electroweak scale), e.g. MI > O(100) GeV
If right-handed neutrinos non degenerate in Massthen problem with one loop Higgs stability breakdown of electroweak Higgs sector perturbationtheory
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Thermal Properties
Two distinct physics cases: MI > MW & MI < MW
(i) MI > MW (electroweak scale), e.g. MI > O(100) GeV
If right-handed neutrinos non degenerate in Massthen problem with one loop Higgs stability breakdown of electroweak Higgs sector perturbationtheory
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Thermal Properties
Two distinct physics cases: MI > MW & MI < MW
(i) MI > MW (electroweak scale), e.g. MI > O(100) GeV
If right-handed neutrinos non degenerate in Massthen problem with one loop Higgs stability breakdown of electroweak Higgs sector perturbationtheory
If two of neutrinos degenerate in mass, thenperturbation theory and Baryon asymmetry phenomenology works for Yukawaand
PilaftsisUnderwood
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Independent of Initial Conditions
@ T >>Teq
Heavy Right-handed Majorana neutrinos enter equilibrium at T = Teq > Tdecay
Thermal Leptogenesis
Fukugita, Yanagida,
Lepton number Violation
Produce Lepton asymmetry
Observed Baryon Asymmetry In the Universe (BAU)
Equilibrated electroweakB, L violating sphaleron interactions (B-L conserv)
Kuzmin, Rubakov,Shaposhinkov
Estimate BAU by solving Boltzmann equations for Heavy Neutrino Abundances
Pilafsis, Riotto…Buchmuller, di Bari et al.
Independent of Initial Conditions
Out of Equilibrium Decaysenhanced CP V.
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Independent of Initial Conditions
@ T >>Teq
Heavy Right-handed Majorana neutrinos enter equilibrium at T = Teq > Tdecay
Thermal Leptogenesis
Fukugita, Yanagida,
Lepton number Violation
Produce Lepton asymmetry
Observed Baryon Asymmetry In the Universe (BAU)
Equilibrated electroweakB, L violating sphaleron interactions (B-L conserv)
Kuzmin, Rubakov,Shaposhinkov
Estimate BAU by solving Boltzmann equations for Heavy Neutrino Abundances
Pilafsis, Riotto…Buchmuller, di Bari et al.
Independent of Initial Conditions
Out of Equilibrium Decaysenhanced CP V.
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Thermal PropertiesAshaka, Shaposhnikov…
(ii) MI < MW (electroweak scale), e.g. MI = O(1) GeV
Baryogenesis through coherent oscillations right-handed singlet fermions
Akhmedov, Rubakov, Smirnov
Two distinct physics cases: MI > MW & MI < MW
Keep light neutrino masses in right order , Yukawa couplings must be:
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Assume Mass degeneracy N2,3 , hence enhanced CP violationCoherent Oscillations between these singlet fermions
BAU ESTIMATES
FOR CP VIOLATION TO OCCUR MUST HAVE: Oscillation rate > Hubble rate H(T)
Baryogenesis occurs @: eg O(100) GeV
Quite effective Mechanism: Maximal Baryon asymmetry
for TB = Tsph = Teq
Assumption: Interactions with plasma of SM particles do not destroy quantum mechanical coherence of oscillations
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Assume Mass degeneracy N2,3 , hence enhanced CP violationCoherent Oscillations between these singlet fermions
BAU ESTIMATES
FOR CP VIOLATION TO OCCUR MUST HAVE: Oscillation rate > Hubble rate H(T)
Baryogenesis occurs @: eg O(100) GeV
Quite effective Mechanism: Maximal Baryon asymmetry
for TB = Tsph = Teq
Assumption: Interactions with plasma of SM particles do not destroy quantum mechanical coherence of oscillations
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Assume Mass degeneracy N2,3 , hence enhanced CP violationCoherent Oscillations between these singlet fermions
BAU ESTIMATES
FOR CP VIOLATION TO OCCUR MUST HAVE: Oscillation rate > Hubble rate H(T)
Baryogenesis occurs @: eg O(100) GeV
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Assume Mass degeneracy N2,3 , hence enhanced CP violationCoherent Oscillations between these singlet fermions
FOR CP VIOLATION TO OCCUR MUST HAVE: Oscillation rate > Hubble rate H(T)
Baryogenesis occurs @: eg O(100) GeV
Mass N2 (N3) / (Mass N1) = O(105 ) N1 Lightest Sterile nutrino is a natural DARK MATTER candidate
Higgs mass stability vs higher loops Mass degeneracy N2,3
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Light Sterile Neutrinos (mass > keV ) may provide good dark Matter Candidates
Boyarski, Ruchayskiy, Shaposhnikov…
Davidson, Widrow, Shi, Fuller, Dolgov, Hansen, Abazajian, Patel, Tucker …
Sterile neutrinos and DARK MATTER
νMSM Lightest of singlet fermions N1 plays thar role
Coupling with SM matter: superweak
To be DM : life time > age of Universe
Contributions to mass matrix of active neutrinos
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mass contribution smaller thansolar mass diff experimental error
Light Sterile Neutrinos (mass > keV ) may provide good dark Matter Candidates
Boyarski, Ruchayskiy, Shaposhnikov…
Davidson, Widrow, Shi, Fuller, Dolgov, Hansen, Abazajian, Patel, Tucker …
Sterile neutrinos and DARK MATTER
νMSM Lightest of singlet fermions N1 plays thar role
Coupling with SM matter: superweak
To be DM : life time > age of Universe
Contributions to mass matrix of active neutrinos
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mass contribution smaller thansolar mass diff experimental error
Light Sterile Neutrinos (mass > keV ) may provide good dark Matter Candidates
Boyarski, Ruchayskiy, Shaposhnikov…
Davidson, Widrow, Shi, Fuller, Dolgov, Hansen, Abazajian, Patel, Tucker …
Sterile neutrinos and DARK MATTER
νMSM Lightest of singlet fermions N1 plays thar role
Coupling with SM matter: superweak
To be DM : life time > age of Universe
Contributions to mass matrix of active neutrinos
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νMSMBoyarski, Ruchayskiy, Shaposhnikov…
MODEL CONSISTENT WITH BBN, STRUCTURE FORMATION DATA IN THE UNIVERSE & ALL OTHER ASTROPHYSICAL CONSTRAINTS
M1 << M2 ≈ M3
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νMSMBoyarski, Ruchayskiy, Shaposhnikov…
MODEL CONSISTENT WITH BBN, STRUCTURE FORMATION DATA IN THE UNIVERSE & ALL OTHER ASTROPHYSICAL CONSTRAINTS
Decaying N1 produces narrow spectral linein spectra of DM dominated astrophysical objects
M1 << M2 ≈ M3
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More than one sterile neutrino needed to reproduce Observed oscillations
νMSM Boyarski, Ruchayskiy, Shaposhnikov…
Constraints on two heavy degenerate singlet neutrinos
N1 DM production estimation in Early Universe must take into accountits interactions with N2,3 heavy neutrinos
M1 << M2 ≈ M3
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NB:Some Remarks on Right-HandedNeutrinos & CMB
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PLANCK
PLANCK + BAO
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PLANCK + WMAP+ BAO + high-multiple CMB data
PLANCK SATELLITE RESULTS ON STERILE NEUTRINOS
Effective number of excited neutrino species contributing to radiation content of the Universe as measured by CMB data within ΛCDM
still leaves room for almost an extra light neutrino species?
@ 68 % C.L.
Mirizzi et al. 1303.5368May be, with active-sterile mass squared splitting in the rangeΔm2
i4 = (10-5 – 102 ) eV2 and active/sterile mixing sin2θi4 < 10-2.5
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BUT…Subtle connection of Neff to real number of active plus keV sterile neutrinos
One warm (keV) dark matter sterile neutrino contributes to Neff at recombination (rc)
@ z=1094 (redshift of rc), one can estimate for, e.g. standard model
too small to be detected by CMB
Since (see previous slide) one sterile (Majorana) neutrino up to a few eV mass range is compatible with Planck important, since, in view of the above, this may imply also the existence of keV sterile neutrinosplaying the role of dark matter as in the νMSM extension of Standard Model
de Vega, Sanchez, 1304.0759
(entropy conservation requirements)
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CONCLUSIONS FO FAR:
PERTURBATIVELY CONSISTENT (STABLE) STANDARD MODEL HIGGS SECTORWHEN RIGHT-HANDED NEUTRINOS PRESENT SEEMS TO REQUIRE :THREE RIGHT-HANDED NEUTRINOSTWO DEGENERATE IN MASS (HEAVIER THAN GeV)ONE LIGHT (in keV region) dark matter candidate
CPT IS ASSUMED AN EXACT SYMMETRY OF THE EARLY UNIVERSECP Violation enhanced due to degeneracy but may not be sufficient to reproduce Baryon Asymmetry
Can we have alternatives to this CP Violation but with theimportant role of Right-handed Neutrinos maintained?
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CONCLUSIONS FO FAR:
PERTURBATIVELY CONSISTENT (STABLE) STANDARD MODEL HIGGS SECTORWHEN RIGHT-HANDED NEUTRINOS PRESENT SEEMS TO REQUIRE :THREE RIGHT-HANDED NEUTRINOSTWO DEGENERATE IN MASS (HEAVIER THAN GeV)ONE LIGHT (in keV region) dark matter candidate
CPT IS ASSUMED AN EXACT SYMMETRY OF THE EARLY UNIVERSECP Violation enhanced due to degeneracy but may not be sufficient to reproduce Baryon Asymmetry
Can we have alternatives to this CP Violation but with theimportant role of Right-handed Neutrinos maintained?
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PART IICPT VIOLATION IN
(TORSIONFUL) GEOMETRIES OF THE
EARLY UNIVERSE &
NEUTRINOS
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CPT VIOLATION IN THE EARLY UNIVERSE
GENERATE Baryon and/or Lepton ASYMMETRY without Heavy Sterile Neutrinos?
CPT Invariance Theorem :(i) Flat space-times(ii) Lorentz invariance(iii) Locality(iv) Unitarity
(ii)-(iv) Independent reasons for violation
Schwinger, Pauli,Luders, Jost, Bellrevisited by:Greenberg,Chaichian, Dolgov,Novikov…
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CPT VIOLATION IN THE EARLY UNIVERSE
GENERATE Baryon and/or Lepton ASYMMETRY without Heavy Sterile Neutrinos?
CPT Invariance Theorem :(i) Flat space-times(ii) Lorentz invariance(iii) Locality(iv) Unitarity
(ii)-(iv) Independent reasons for violation
Schwinger, Pauli,Luders, Jost, Bellrevisited by:Greenberg,Chaichian, Dolgov,Novikov…
Backgroundinduced
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GRAVITATIONAL BACKGROUNDS GENERATING CPT VIOLATING EFFECTSIN THE EARLY UNIVERSE: PARTICLE-ANTIPARTICLE DIFFERENCES IN DISPERSION RELATIONS Differences in populations freeze out Baryogenesis or Leptogenesis Baryogenesis
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GRAVITATIONAL BACKGROUNDS GENERATING CPT VIOLATING EFFECTSIN THE EARLY UNIVERSE: PARTICLE-ANTIPARTICLE DIFFERENCES IN DISPERSION RELATIONS Differences in populations freeze out Baryogenesis or Leptogenesis Baryogenesis
REVIEW VARIOUS SCENARIOS
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GRAVITATIONAL BACKGROUNDS GENERATING CPT VIOLATING EFFECTSIN THE EARLY UNIVERSE: PARTICLE-ANTIPARTICLE DIFFERENCES IN DISPERSION RELATIONS Differences in populations freeze out Baryogenesis or Leptogenesis Baryogenesis
REVIEW VARIOUS SCENARIOS
B-L conserving GUT or
Sphaleron
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CPTV Effects of different Space-Time-Curvature/Spin couplings between
neutrinos/antineutrinos
B. Mukhopadhyay, U. Debnath, N. Dadhich, M. SinhaLambiase, Mohanty
Curvature Coupling to fermion spin may lead to different dispersion relationsbetween neutrinos and antineutrinos (assumed dominant in the Early eras) in non-spherically symmetric geometries in the Early Universe.
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Dirac Lagrangian
Gravitational covariant derivativeincluding spin connection
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Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivativeincluding spin connection
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Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivativeincluding spin connection
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Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivativeincluding spin connection
Standard Model Extensiontype Lorentz-violating coupling (Kostelecky et al.)
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Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivativeincluding spin connection
For homogeneous and isotropic Friedman-Robertson-Walker geometries the resulting Bμ vanish
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Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivativeincluding spin connection
Can be constant in a givenlocal frame in Early Universeaxisymmetric (Bianchi) cosmologiesor near rotating Black holes
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DISPERSION RELATIONS OF NEUTRINOS ARE DIFFERENT FROM THOSE OF ANTINEUTRINOS IN SUCH GEOMETRIES
IF Ba = CONSTANT IN A LOCAL FRAME
± refers to chiral fields (here neutrino/antineutrino)
CPTV Dispersion relations
but (bare) masses are equal between particle/anti-particle sectors
Abundances of neutrinos in Early Universe, then, different from those of antineutrinosif B0 is non-trivial, ALREADY IN THERMAL EQUILIBRIUM
_
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Abundances of neutrinos in Early Universe different from those of antineutrinosif B0 ≠ 0 asnd constant in a local frame
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CPTV BARYOGENESIS through B-L conserving sphalerons? NO NEED FOR ENHANCED CP VIOLATION IN EARLY UNVIERSE?
DISPERSION RELATIONS OF NEUTRINOS ARE DIFFERENT FROM THOSE OF ANTINEUTRINOS IN SUCH GEOMETRIES
IF Ba = CONSTANT IN A LOCAL FRAME
± refers to chiral fields (here neutrino/antineutrino)
CPTV Dispersion relations
but (bare) masses are equal between particle/anti-particle sectors
Abundances of neutrinos in Early Universe, then, different from those of antineutrinosif B0 is non-trivial, ALREADY IN THERMAL EQUILIBRIUM
_
Lepton Asymmetry, e.g. for neutrinos
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A SPECIFIC KIND OF TORSION (KALB-RAMOND FIELD STRENGTH)INSPIRED FROM STRING THEORY (UV COMPLETE)CAN DO THE JOB OF PROVIDING A CONSTANT B0 AXIAL BACKGROUND IN A LOCAL FRAME OF FRW COSMOLOGY
Fermions in Gravity with TORSION
NEM & Sarben Sarkar, arXiv:1211.0968
Ellis, NEM, Sarkar 1304.5433
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Dirac Lagrangian (for concreteness, it can be extended to Majorana neutrinos)
Gravitational covariant derivativeincluding spin connection
If torsion then Γμν ≠ Γνμ
antisymmetric part is the contorsion tensor, contributes to
vielbeins (tetrads)independent fromspin connection ωμ
ab
now ….
Fermions in Gravity with TORSION
of interest to us here….cf below
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• Field Theories with (Kalb-Ramond) torsion & axion fields : String inspired models, loop quantum gravity effective field theories …
• Majorana Neutrino Masses from (three-loop) anomalous terms with axion-neutrino couplings
UV complete models
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Microscopic UV complete underlying theory of quantum gravity :
STRINGS
Effective field theories (low energy scale E << Ms) `` gauge’’ invariant
Depend only on field strength :
Bianchi identity :
KALB-RAMOND FIELD
Massless Gravitational multiplet of (closed) strings: spin 0 scalar (dilaton) spin 2 traceless symmetric rank 2 tensor (graviton) spin 1 antisymmetric rank 2 tensor
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Anomaly (gravitational vs gauge) cancellation in strings require redefinition of H so that Bianchi identity now is extended to :
Lorentz (L) & Gauge (V)Chern-Simons three forms
EXTENDED BIANCHI IDENTITY
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4-DIM PART
IN 4-DIM DEFINE DUAL OF H AS :
b(x) = Pseudoscalar (Kalb-Ramond (KR) axion)
ROLE OF Kalb-Ramond H-FIELD AS TORSION
EFFECTIVE GRAVITATIONAL ACTION IN STRING LOW-ENERGY LIMIT CAN BE EXPRESSED IN TERMS OF A GENERALIZED CURVATURE RIEMANN TENSOR WHERE THE CHRISTOFFEL CONNECTION INCLUDES H-FIELD TORSION
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FERMIONS COUPLE TO H –TORSION VIA GRAVITATIONAL COVARIANT DERIVATIVE
TORSIONFUL CONNECTION, FIRST-ORDER FORMALISM
gauge field contorsion
Non-trivial contributions to Bμ
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TORSIONFUL CONNECTION, FIRST-ORDER FORMALISM
gauge field contorsion
Non-trivial contributions to Bμ
FERMIONS COUPLE TO H –TORSION VIA GRAVITATIONAL COVARIANT DERIVATIVE
Constant H ?
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Exact (conformal Field Theories on World-sheet) Solutions from String theory
Antoniadis, Bachas, Ellis, Nanopoulos
In Einstein frame E (Scalar curvature term in gravitational effective action has canonical normalisation):
Cosmological Solutions, non-trivial time-dependent dilatons, axions
Central charge of uderlying world-sheet conformal field theory
Kac-Moodyalgebra level``internal’’ dims
central charge
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Exact (conformal Field Theories on World-sheet) Solutions from String theory
Antoniadis, Bachas, Ellis, Nanopoulos
In Einstein frame E (Scalar curvature term in gravitational effective action has canonical normalisation):
Cosmological Solutions, non-trivial time-dependent dilatons, axions
Central charge of uderlying world-sheet conformal field theory
Kac-Moodyalgebra level``internal’’ dims
central charge
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Conformal Invariance (world-sheet) Conditions for the string to O(α’) (lowest non-trivial order in derivatives in the effective target-space action):
= 0
= 0
= 0
Linear dilaton solution in string frame (or logarithmic in FRW time in Einstein-frame with conformally flat Einstein-frame target space time
exact (to all orders in α’)
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Exact (conformal Field Theories on World-sheet) Solutions from String theory
Antoniadis, Bachas, Ellis, Nanopoulos
In Einstein frame E (Scalar curvature term in gravitational effective action has canonical normalisation):
Cosmological Solutions, non-trivial time-dependent dilatons, axions
Central charge of uderlying world-sheet conformal field theory
Kac-Moodyalgebra level``internal’’ dims
central charge
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Covariant Torsion tensor
Constant
constant B0
Lepton Asymmetry as in previous cases , e.g. for neutrinos
NEM & Sarben Sarkar, arXiv:1211.0968 H-torsion & CPTV
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DISPERSION RELATIONS OF NEUTRINOS ARE DIFFERENT FROM THOSE OF ANTINEUTRINOS IN SUCH GEOMETRIES
± refers to chiral fields (here neutrino/antineutrino)
CPTV Dispersion relations
but (bare) masses are equal between particle/anti-particle sectors
Abundances of neutrinos in Early Universe, then, different from those of antineutrinosif B0 is non-trivial, ALREADY IN THERMAL EQUILIBRIUM
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Abundances of neutrinos in Early Universe different from those of antineutrinosif B0 ≠ 0
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CPTV BARYOGENESIS through B-L conserving sphalerons? NO NEED FOR ENHANCED CP VIOLATION IN EARLY UNVIERSE?
DISPERSION RELATIONS OF NEUTRINOS ARE DIFFERENT FROM THOSE OF ANTINEUTRINOS IN SUCH GEOMETRIES
± refers to chiral fields (here neutrino/antineutrino)
CPTV Dispersion relations
but (bare) masses are equal between particle/anti-particle sectors
Abundances of neutrinos in Early Universe, then, different from those of antineutrinosif B0 is non-trivial, ALREADY IN THERMAL EQUILIBRIUM
Lepton Asymmetry, e.g. for neutrinos
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CPTV neutrino/antineutrino mixing & oscillations
Assume Majorana neutrino in Weyl rep (Lepton number violation unavoidable)
M Sinha & B. MukhopadhyayarXiv: 0704.2593
Majorana mass termviolates L number
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CPTV neutrino/antineutrino mixing & oscillations
Assume Majorana neutrino in Weyl rep (Lepton number violation unavoidable)
M Sinha & B. MukhopadhyayarXiv: 0704.2593
Lead to neutrino/antineutrinomixing & oscillations
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neutrino/antineutrino mixing
oscillations
NB: neutrino CPTV mass shifts
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neutrino/antineutrino mixing
oscillations
oscilaltion length
NB: neutrino CPTV mass shifts
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SCENARIO: Phase transitions in the early string Universe may induce B0 = 0 @ T = Td
Ellis, NEM, Sarkar 1304.5433
T > Td : B0 ≠ 0 Majorana Neutrino-Antineutrino Oscillations (Pontecorvo-type)
4-component chiral Majoranaspinor
Mass eigenstates
with eigenvalues
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Neutrino/antineutrino Mixing & Oscillations
Number operators
≠ 0 for
Probability of Oscillation
Oscillation length
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Neutrino/Antineutrino oscillations are the local processesin the early Universe responsible for the CPT Violation
They occur provided the oscillation length is smaller than the Hubble horizon
For Td = O(109 GeV) the Hubble horizon size is 10-12 cm & for B0 = O(0.1) GeVthe oscillation length is 10-13 cm, i.e. smaller than Hubble Horizon, so oscilaltions can occur provide chemical equilibrium for T > Td
NB: If neutrinos have also Dirac mass, i.e. mass matrix in lagrangian of the form
with oscillation length depending on the neutrino energy E
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Neutrino/natineutrino oscillation processes are UNIQUE to Majorana neutrinos
Charged leptons and quarks of the Standard Model, which also couple to H-torsion, cannot exhibit such oscillationdue to electric charge conservation
Hence: above scenario for Leptogenesis @ T = 109 GeVand then Baryogenesis at T = O(100 GeV) through standard-model B-L conserving sphaleron processes appears unique to Majorana Neutrinos
Consistent with absence of observed CPTV today in neutrino sectorTorsion B0 = 0 (or very small) today
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MINOS Exp. RESULTS ON Potential Neutrino-Antineutrino OSCILLATION PARAMETER DIFFERENCES
vμ disapearance-Energy spectrum − vμ vs vμ Oscillation parameters −
νμ disappearance: Δm2=(2.32+0.12-0.08)x10-3 eV2 , sin2(2Θ) =1.00 (sin2(2Θ) > 0.90 @ 90% CL
νμ disappearance: Δm2=(2.62+0.31-0.28 (stat.) ±0.09 (syst.) )x10-3 eV2, sin2(2Θ)=0.95 +0.10-0.11 (stat.) ±0.01 (syst.).
−−
[arXiv:1108.1509] [arXiv:1104.0344] [arXiv1103.0340]
http://www-numi.fnal.gov
Consistent with equality of mass differences between particle/antiparticles
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MINOS Exp. RESULTS ON Potential Neutrino-Antineutrino OSCILLATION PARAMETER DIFFERENCES
vμ disapearance-Energy spectrum − vμ vs vμ Oscillation parameters −
νμ disappearance: Δm2=(2.32+0.12-0.08)x10-3 eV2 , sin2(2Θ) =1.00 (sin2(2Θ) > 0.90 @ 90% CL
νμ disappearance: Δm2=(2.62+0.31-0.28 (stat.) ±0.09 (syst.) )x10-3 eV2, sin2(2Θ)=0.95 +0.10-0.11 (stat.) ±0.01 (syst.).
−−
[arXiv:1108.1509] [arXiv:1104.0344] [arXiv1103.0340]
http://www-numi.fnal.gov
Consistent with equality of mass differences between particle/antiparticles
NO OBSERVED C
PTV T
ODAY
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Independent of Initial Conditions
@ T >>Teq
Heavy Right-handed Majorana neutrinos enter equilibrium at T = Teq > Tdecay
Standard Thermal Leptogenesis
Fukugita, Yanagida,
Lepton number Violation
Produce Lepton asymmetry
Observed Baryon Asymmetry In the Universe (BAU)
Equilibrated electroweakB+L violating sphaleron interactions
Kuzmin, Rubakov,Shaposhinkov
Estimate BAU by solving Boltzmann equations for Heavy Neutrino Abundances
Independent of Initial Conditions
Out of Equilibrium Decays
enhanced CP V
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Independent of Initial Conditions
@ T >>Teq
Heavy Right-handed Majorana neutrinos enter equilibrium at T = Teq > Tdecay
Standard Thermal Leptogenesis
Fukugita, Yanagida,
Lepton number Violation
Produce Lepton asymmetry
Observed Baryon Asymmetry In the Universe (BAU)
Equilibrated electroweakB+L violating sphaleron interactions
Kuzmin, Rubakov,Shaposhinkov
Estimate BAU by solving Boltzmann equations for Heavy Neutrino Abundances
Independent of Initial Conditions
Out of Equilibrium Decays
enhanced CP VX
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No need for enhanced CPV. Heavy Right-handedMajorana neutrino/antineutrino oscillations
CPT Violating Thermal Leptogenesis
Fukugita, Yanagida,
CPT Violation
Produce Lepton asymmetry
Observed Baryon Asymmetry In the Universe (BAU)
Equilibrated electroweakB+L violating sphaleron interactions
Kuzmin, Rubakov,Shaposhinkov
Estimate BAU by fixing CPTV background parametersIn some models this may imply fine tuning ….
Independent of Initial Conditions
Early UniverseT > Td = 109 GeV
particle/antiparticle populations difference
already in thermalequilibrium
T = O(100) GeV
Ellis, NEM, Sarkar 1304.5433
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B0 : (string) theory underwent a phase transition @ T = Td = 109 GeV, to :
(i) either B0 = 0 (ii) or B0 small today but non zero
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Standard Model Extension type coupling bμ If a small Ba ispresent today Kostelecky, Mewes, Russell, Lehnert …
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Standard Model Extension type coupling bμ If a small Ba ispresent today Kostelecky, Mewes, Russell, Lehnert …
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Standard Model Extension type coupling bμ If a small Ba ispresent today Kostelecky, Mewes, Russell, Lehnert …
If due to H-torsion, it should couple universally (gravity)to all particle species of the standard model (electrons etc)
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Standard Model Extension type coupling bμ If a small Ba ispresent today 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)
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bμ = Βμ
NB
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Standard Model Extension type coupling bμ If a small Ba ispresent today 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 it be connected smoothly with some form of temperature T dependence to the B0 of O(0.1 GeV) in our case, required for Leptogenesis at T=109 GeV ?
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Modifications in Neutrinoless 2Beta decay rate in 2 flavour mixing (due to CPTV modified effective mass)
Majorana neutrino
Amplitude
ignore neutrino/antineutrinomixing here:
M Sinha & B. MukhopadhyayarXiv: 0704.2593
If a small B0 ispresent today
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If a small Ba ispresent today …will also affect flavour oscillations
Sinha, Mukhopadhyay, 0704.2593
2-flavour toy example
neutrino-antineutrino mixing on top of flavour mixing
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FLAVOUR OSCILALTIONS IN THE PRESENCE OF GRAVITY
OSCILLATIONLENGTH
2 SETS OF FLAVOUR EIGENSTATES
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FLAVOUR OSCILALTIONS IN THE PRESENCE OF GRAVITY
OSCILLATIONLENGTH
2 SETS OF FLAVOUR EIGENSTATES
STRINGENT C
ONSTRAINTS T
ODAY
DUE TO N
ON-OBSERVATIO
N OF
NEUTRINO/A
NTINEUTRIN
O OSCIL
LATIO
NS?
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PART III: QUANTUM
H-TORSION-INDUCEDMASS HIERARCHY
FOR RIGHT-HANDEDNEUTRINO
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ABOVE: We have seen how a background of kalb-Ramond H-Torsion generates Matter-Antimatter Asymmetry via (Right-handed) neutrino/antineutrino oscillations in the Early Universe
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ABOVE: We have seen how a background of kalb-Ramond H-Torsion generates Matter-Antimatter Asymmetry via (Right-handed) neutrino/antineutrino oscillations in the Early Universe
What About the Quantum Fluctuations of the H-torsion ?
Physical Effect in Generating Majorana masses for neutrinos via coupling to ordinary axion fields
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ANOMALOUS GENERATIONOF RIGHT-HANDED MAJORANA NEUTRINO MASSES THROUGHTORSIONFUL QUANTUM GRAVITYUV complete string models ?
NEM & Pilaftsis 2012PRD 86, 124038 arXiv:1209.6387
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Fermionic Field Theories with H-TorsionEFFECTIVE ACTION AFTER INTEGRATING OUT
QUANTUM TORSION FLUCTUATIONS
+ standard Dirac terms without torsion
Fermions:
Bianchi identity
conserved ``torsion ‘’ charge
classical
Postulate conservation at quantum level by adding counterterms
Implement via constraint lagrange multiplier in Path integral b-field
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Fermionic Field Theories with H-TorsionEFFECTIVE ACTION AFTER INTEGRATING OUT
QUANTUM TORSION FLUCTUATIONS
+ standard Dirac terms without torsion
Fermions:
Bianchi identity
conserved ``torsion ‘’ charge
classical
Postulate conservation at quantum level by adding counterterms
Implement via constraint lagrange multiplier in Path integral b-field
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partial integrate
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partial integrate
Use chiral anomaly equation (one-loop) in curved space-time:
Hence, effective action of torsion-full QED
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partial integrate
Use chiral anomaly equation (one-loop) in curved space-time:
Hence, effective action of torsion-full QED coupling
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Fermionic Field Theories with H-TorsionEFFECTIVE ACTION AFTER INTEGRATING OUT
QUANTUM TORSION FLUCTUATIONS
+
+ Standard Model terms for fermions
SHIFT SYMMETRY b(x) b(x) + c
total derivatives
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ANOMALOUS MAJORANA NEUTRINO MASS TERMSfrom QUANTUM TORSION
SHIFT SYMMETRY b(x) b(x) + c
total derivatives
OUR SCENARIO Break such shift symmetry by coupling first b(x) to another pseudoscalar field such as QCD axion a(x) (or e.g. other string axions)
Mavromatos, Pilaftsis arXiv: 1209.6387
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ANOMALOUS MAJORANA NEUTRINO MASS TERMSfrom QUANTUM TORSION
SHIFT SYMMETRY b(x) b(x) + c
total derivatives
OUR SCENARIO Break such shift symmetry by coupling first b(x) to another pseudoscalar field such as QCD axion a(x) (or e.g. other string axions)
Mavromatos, Pilaftsis arXiv: 1209.6387
neutrino fields Yukawa
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Field redefinition
so, effective action becomes
must have otherwise axion field a(x) appears as a ghost canonically normalised kinetic terms
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Field redefinition
so, effective action becomes
CHIRALITY CHANGE
must have otherwise axion field a(x) appears as a ghost canonically normalised kinetic terms
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NEM, Pilaftsis arXiv: 1209.6387
bx
a = axionmixing with KR field b
b
axion field redefinition
GRAVITON
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THREE-LOOP ANOMALOUS FERMION MASS TERMS
ONE-LOOP
CHIRALITY CHANGE
GRAVITONGRAVITON AXION
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THREE-LOOP ANOMALOUS FERMION MASS TERMS
ONE-LOOP
CHIRALITY CHANGE
GRAVITONGRAVITON AXION
Λ = UV cutoff
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SOME NUMBERS
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SOME NUMBERS
INTERESTING WARM DARK MATTER
REGIME
Appropriate Hierarchy for the other two massive Right-handed neutrinos for Leptogenesis-Baryogenesis& Dark matter cosntraints can be arranged by choosing Yukawa couplings
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νMSMBoyarski, Ruchayskiy, Shaposhnikov…
MODEL CONSISTENT WITH BBN, STRUCTURE FORMATION DATA IN THE UNIVERSE & ALL OTHER ASTROPHYSICAL CONSTRAINTS
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More than one sterile neutrino needed to reproduce Observed oscillations
νMSM Boyarski, Ruchayskiy, Shaposhnikov…
Constraints on two heavy degenerate singlet neutrinos
N1 DM production estimation in Early Universe must take into accountits interactions with N2,3 heavy neutrinos
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FINITENESS OF THE MASS
MULTI-AXION SCENARIOS (e.g. string axiverse)
positive mass spectrum for all axions
simplifying all mixing equals
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MULTI-AXION SCENARIOS (e.g. string axiverse)
positive mass spectrum for all axions
simplifying all mixing equals
MR : UV finite for n=3 @ 2-loop independent of axion mass
FINITENESS OF THE MASS
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• nuMSM: Three Sterile neutrinos necessary for Higgs sector stability ?
• These Sterile Neutrinos may explain matter-antimatter origin in the Universe
• Lightest of them provide interesting Dark matter Candidates
• Gravitationally-induced anomalous Right-handed Majorana neutrino masses possible, without the need for see-saw…
• Interesting Physics for the Early Universe to be investigated, e.g. H-torsion-induced CPTV Leptogenesis/Baryogenesis
CONCLUSIONS
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ASTROPHYSICS
• keV dark matter (generic) may play important role in galactic structures (core & haloes)
• Right-handed neutrino matter with scalar and/or vector interactions may provide consistent galactic profiles for haloes and core structure core contains significant amounts of right-
handed neutrinos (rhn)
role of rhn condensates? (Ruffini, Arguelles, Rueda,…NEM)
OUTLOOK
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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.