[PPT] - Triplet seesaw model: from inflation to asymmetric DM and PowerPoint Presentation

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Triplet seesaw model: from inflation to asymmetric DM and leptogenesis

C.A., J.O.Gong and N.Sahu, arXiv:1206.0009 [hep-ph]
C.A. and N.Sahu, Nucl.Phys.B854, arXiv:1108.3967

[hep-ph]

Chiara Arina

PASCOS 2012 Mérida, Mexico June 3rd - 8th

Institute for Theoretical Particle Physics and Cosmology

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µ(GeV)

0.05

0.1 0.2 0.3 Λ

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The heavy triplet scalar model: under + SM + Dark Matter

Neutrino/Visible matter sector Higgs physics constraint

µ < M∆ → Λ = λH − 1

2

µ†

HµH

M 2

∆

,

µ ≥ M∆ → Λ = λH ,

type II seesaw, i.e.: Valle, Schechter ’80; Cheng, Li ’80; Lazarides, Shafi, Wetterich ’81.

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Asymmetric Dark Matter: Inert doublet with Z2 flavour symmetry

(2, −1)

Scalar DM Fermionic DM

coupling is complex, CP net asymmetry generated

via out of equilibrium process

No wash out processes, asymmetry is not erased
Hierarchy between Majorana masses of DM and

neutrinos

V (∆, H, χ) = M 2

χχ†χ + λχ(χ†χ)2 +

µχ∆†χχ + h.c.
+λ3|H|2|χ|2 + λ4|H†χ|2 + λ5

2

(H†χ)2 + h.c.
U(1) global symmetry (Peccei-Quinn like) for
small mass splitting (keV)
coupling is complex, CP net asymmetry generated

via out of equilibrium process

Wash out processes, asymmetry may get erased

λ5 → 0 ∆M 2 ≡ M 2

S − M 2 A = λ5v2 .

∆ → χχ

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Direct detection constraints on DM

S (ψ1) A (ψ2)

n n

excluded by Z boson decay width Xenon100 CDMS-Ge (i) the DM has non zero hypercharge, the interaction with the Z should be off diagonal not to be excluded by direct detection (ii) inelastic scattering off nucleus

Scalar DM candidate excluded as explanation of DAMA by Xenon100
Fermionic candidate allowed between 45 GeV and ~ 250 GeV

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Scalar potential for inflation

Jordan frame Einstein frame (i) conformal transformation (ii) redefinition of the three degrees of freedom (h, δ and θ) -> (φ, r and θ) (iii) large field limit (i) the quartic term is dominant for , because the mass terms are already suppressed by an additional exponential factor (ii) note that a similar constraint on the lepton number violating term arises from Higgs physics (iii) r is an heavy field, it does not contribute to inflation but sets quickly to its minimum (iv) study of the minimum of the potential depending only on r

M∆ µH < 10−6

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C. Arina (RWTH-Aachen) - PASCOS 2012

Scalar potential for inflation

Jordan frame Einstein frame (i) conformal transformation (ii) redefinition of the three degrees of freedom (h, δ and θ) -> (φ, r and θ) (iii) large field limit (i) the quartic term is dominant for , because the mass terms are already suppressed by an additional exponential factor (ii) note that a similar constraint on the lepton number violating term arises from Higgs physics (iii) r is an heavy field, it does not contribute to inflation but sets quickly to its minimum (iv) study of the minimum of the potential depending only on r

M∆ µH < 10−6

non minimal couplings to gravity Salopek, Bond and Bardeen ’89

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C. Arina (RWTH-Aachen) - PASCOS 2012

Scalar potential for inflation

Jordan frame Einstein frame (i) conformal transformation (ii) redefinition of the three degrees of freedom (h, δ and θ) -> (φ, r and θ) (iii) large field limit (i) the quartic term is dominant for , because the mass terms are already suppressed by an additional exponential factor (ii) note that a similar constraint on the lepton number violating term arises from Higgs physics (iii) r is an heavy field, it does not contribute to inflation but sets quickly to its minimum (iv) study of the minimum of the potential depending only on r

M∆ µH < 10−6

non minimal couplings to gravity Salopek, Bond and Bardeen ’89

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C. Arina (RWTH-Aachen) - PASCOS 2012

Scalar potential for inflation

Jordan frame Einstein frame (i) conformal transformation (ii) redefinition of the three degrees of freedom (h, δ and θ) -> (φ, r and θ) (iii) large field limit (i) the quartic term is dominant for , because the mass terms are already suppressed by an additional exponential factor (ii) note that a similar constraint on the lepton number violating term arises from Higgs physics (iii) r is an heavy field, it does not contribute to inflation but sets quickly to its minimum (iv) study of the minimum of the potential depending only on r

M∆ µH < 10−6

non minimal couplings to gravity Salopek, Bond and Bardeen ’89

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Slow-roll inflationary phase

Mixed Inflaton Pure Higgs Inflaton Pure Triplet Inflaton

Effective final potential is equivalent to Higgs inflation

(Bezrukov and Shaposnikov ‘07)

V0 depends on the minimum in which rolls

2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 1.2 j VeffHjLêHMplL4

V0 normalized at the pivot scale of WMAP7

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Constraints on the couplings (RGes from EW to Unitarity scale)

Mixed Higgs Triplet All three cases lead to same constraints on matter sector Mixed and Triplet cases Higgs

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Generation of the asymmetries

5 free parameters, considering the DM mass, while the triplet mass is fixed at 108 GeV and the neutrino mass at

0.05 eV

tree level decay channels

triplet leptogenesis: Hambye, Radial, Strumia ’05 and Chun, Scopel ’07

to generate CP asymmetries needed at least 2 triplets -> decay of the lightest mass eigenstate: ,

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Boltzmann equations for out of equilibrium decay

Asymmetry transferred to baryon sector via SU(2) sphalerons
Parameter space sampled via Markov-Chain Monte Carlo techniques, with a likelihood demanding:
Defining the triplet number density and the asymmetries (efficiency factors) as:

ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1

L

¯ L

H H

The relevant processes contributing to triplet leptogenesis consist in:

(i) decays and inverse decays (ii) scattering such as (iii) scattering such as:

∆ζ1 = 2 ∆L = 2

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Results

excluded by Xe100

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Summary

Presented phenomenology of a heavy triplet extension of the SM

triplet at 108 GeV scale prevents vacuum instability due to Higgs quartic coupling running negative with a Higgs at 125 GeV; allowing non minimal couplings to gravity, the triplet mixed with the Higgs behaves as inflaton; the low energy effective theory generates neutrino masses via type-II seesaw; fermionic asymmetric DM candidate is allowed, with inelastic scattering of nucleus as direct detection signature;

ut of equilibrium decay of the triplet generates both the baryon and DM

asymmetries via leptogenesis route.

Future prospects

the triplet is heavy, therefore the quartic couplings are not measurable at LHC; to distinguish between the 3 cases of inflation a proper numerical treatment is due, including the multi field dynamics; the scale of the triplet can be lowered at TeV scale in order to lead to visible signatures at LHC, i.e. via dilepton signals. careful study of oscillations - gauge interactions interplay for arising the asymmetry Thanks for your attention!

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Back-up slides

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Wash-out processes

(1) DM number violating processes

For these processes remain out of equilibrium

(2) Oscillations

To preserve the asymmetry the DM should freeze out before it starts

scillate:

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Renormalization group equations with heavy triplet (I)

Schmidt ’07; Gogoladze, Okada and Shafi ’08 Our contribution is the addition of the RG for the DM and for the non minimal couplings to gravity

Above the mass scale of the triplet:
Below the mass scale of the triplet, the triplet is integrated out, effective theory with

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Renormalization group equations with heavy triplet (II)

the triplet is a singlet under SU(3) therefore the running of g3 and Yt are not modified
non minimal coupling to gravity

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Relevant Boltzmann equations (I)

Transfer the asymmetry from the lepton sector to the baryon sector

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Relevant Boltzmann equations (II)

Scattering interaction that produce a wash out of the asymmetry mainly due to gauge interactions Triplet mass eigenstates

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Details on the inflationary potential (I)

Transformation due to the conformal factor Field redefinition Slow roll inflation

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Details on the inflationary potential (II)

1. Case mixed inflation
2. Case pure Higgs inflation
3. Case pure triplet inflation

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Details on the inflationary potential (III)

Assuming quartic dominant, the quadratic term is negligible: Assuming quartic dominant, the other term is made negligible demanding positivity of the potential: Numerical estimation:

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More on the model

Scalar DM Fermionic DM Triplet VEV

Covariant derivative with GUT charge normalization

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C. Arina (RWTH-Aachen) - PASCOS 2012

Triplet seesaw model: from inflation to asymmetric DM and leptogenesis

[hep-ph]

Chiara Arina

PASCOS 2012 Mérida, Mexico June 3rd - 8th

Institute for Theoretical Particle Physics and Cosmology

The heavy triplet scalar model: under + SM + Dark Matter

Neutrino/Visible matter sector Higgs physics constraint

µ ≥ M∆ → Λ = λH ,

type II seesaw, i.e.: Valle, Schechter ’80; Cheng, Li ’80; Lazarides, Shafi, Wetterich ’81.

Asymmetric Dark Matter: Inert doublet with Z2 flavour symmetry

(2, −1)

Scalar DM Fermionic DM

via out of equilibrium process

neutrinos

V (∆, H, χ) = M 2

2

via out of equilibrium process

λ5 → 0 ∆M 2 ≡ M 2

∆ → χχ

Direct detection constraints on DM

S (ψ1) A (ψ2)

n n

excluded by Z boson decay width Xenon100 CDMS-Ge (i) the DM has non zero hypercharge, the interaction with the Z should be off diagonal not to be excluded by direct detection (ii) inelastic scattering off nucleus

Scalar potential for inflation

M∆ µH < 10−6

Scalar potential for inflation

M∆ µH < 10−6

non minimal couplings to gravity Salopek, Bond and Bardeen ’89

Scalar potential for inflation

M∆ µH < 10−6

non minimal couplings to gravity Salopek, Bond and Bardeen ’89

Scalar potential for inflation

M∆ µH < 10−6

non minimal couplings to gravity Salopek, Bond and Bardeen ’89

Slow-roll inflationary phase

Mixed Inflaton Pure Higgs Inflaton Pure Triplet Inflaton

(Bezrukov and Shaposnikov ‘07)

2 4 6 8 10 0.0 0.2 0.4 0.6 0.8 1.0 1.2 j VeffHjLêHMplL4

V0 normalized at the pivot scale of WMAP7

Constraints on the couplings (RGes from EW to Unitarity scale)

Mixed Higgs Triplet All three cases lead to same constraints on matter sector Mixed and Triplet cases Higgs

Generation of the asymmetries

0.05 eV

triplet leptogenesis: Hambye, Radial, Strumia ’05 and Chun, Scopel ’07

Boltzmann equations for out of equilibrium decay

ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1 ζ1

(i) decays and inverse decays (ii) scattering such as (iii) scattering such as:

∆ζ1 = 2 ∆L = 2

Results

excluded by Xe100

Summary

asymmetries via leptogenesis route.

Back-up slides

Wash-out processes

(1) DM number violating processes

For these processes remain out of equilibrium

(2) Oscillations

To preserve the asymmetry the DM should freeze out before it starts

Renormalization group equations with heavy triplet (I)

Schmidt ’07; Gogoladze, Okada and Shafi ’08 Our contribution is the addition of the RG for the DM and for the non minimal couplings to gravity

Renormalization group equations with heavy triplet (II)

Relevant Boltzmann equations (I)

Transfer the asymmetry from the lepton sector to the baryon sector

Relevant Boltzmann equations (II)

Scattering interaction that produce a wash out of the asymmetry mainly due to gauge interactions Triplet mass eigenstates

Details on the inflationary potential (I)

Transformation due to the conformal factor Field redefinition Slow roll inflation

Details on the inflationary potential (II)

Details on the inflationary potential (III)

Assuming quartic dominant, the quadratic term is negligible: Assuming quartic dominant, the other term is made negligible demanding positivity of the potential: Numerical estimation:

More on the model

Scalar DM Fermionic DM Triplet VEV

Covariant derivative with GUT charge normalization

The wash out processes for scalar DM

(1) DM number violating processes (2) Oscillations