Introduction The Model Conclusion Baryogenesis and Late-Decaying Moduli Kuver Sinha Mitchell Institute for Fundamental Physics Texas A M University College Station, TX PHENO 2010, University of Wisconsin, Madison arXiv:0912.2324, work in progress Rouzbeh Allahverdi, Bhaskar Dutta, KS
Introduction The Model Conclusion Introduction String moduli play interesting roles in cosmology and particle phenomenology 1. A modulus of mass ∼ 1000 TeV m 3 c 2. Gravitational coupling to matter Γ T = σ 2 π M 2 P ⇒ � T reheat ∼ Γ T M P ∼ 200 MeV Affects dark matter physics, baryon asymmetry, etc. arXiv:0904.3773 [hep-ph]
Introduction The Model Conclusion The most well-studied moduli stabilization models have such moduli... In KKLT, W flux ≃ ( 2 Re T ) 3 / 2 ∼ 30 TeV , m 3 / 2 ¯ T m σ ≃ F , T ≃ a Re T m 3 / 2 ∼ 1000 TeV , Re T ∼ m 3 / 2 F T m soft ≃ a ReT ,
Introduction The Model Conclusion Standard processes of baryogenesis may be affected by late production of entropy... Dilution roughly ( T EW / T reheat ) 3 ∼ 10 7 Baryogenesis is a challenge at low temperatures...
Introduction The Model Conclusion May invoke Affleck-Dine baryogenesis scenarios λ M P σ u c d c d c Or consider operators like W ⊃ hep-ph/9507453, hep-ph/9506274 Result in constraints on modulus sector We will consider MSSM extension, leaving modulus sector unconstrained.
Introduction The Model Conclusion The Model Basic idea: 1. Modulus decays, produces MSSM + extra matter ( X ) non-thermally 2. Extra matter X has baryon violating couplings to MSSM 3. Decay violates CP Sakharov conditions are satisfied.
Introduction The Model Conclusion Estimates: Net baryon asymmetry 6 × 10 − 10 = η = n B − n B ∼ ǫ Y X n γ Yield Y X = 2 Y T ( Br ) X = 3 T r ( Br ) X ∼ 10 − 7 ( Br ) X 2 m T ( Br ) X ∼ 0 . 1 ⇒ Need ǫ ∼ 10 − 3 λ 4 Typically, ǫ ∼ Tr λ 2 Yukawas O ( 0 . 1 )
Introduction The Model Conclusion MSSM extension: Two flavors of X = ( 3 , 1 , 4 / 3 ) , X = ( 3 , 1 , − 4 / 3 ) Singlet N hep-ph/0612357, arXiv:0908.2998 λ i α Nu c ij α d c i d c i X α + λ ′ W extra = j X α (1) M N + 2 NN + M X , ( α ) X α X α . M ∼ 500 GeV. Can be obtained by the Giudice-Masiero mechanism if the modulus has non-zero F -term.
Introduction The Model Conclusion d c ψ 1 ˜ d c N d c ψ 1 ψ 2 ψ 2 ψ 1 ˜ d c u c ∆ B = + 2 / 3
Introduction The Model Conclusion N ψ 1 ψ 1 u c d c N ψ 2 ψ 1 ψ 2 d c ˜ u c ∆ B = − 1 / 3
Introduction The Model Conclusion ˜ ψ 1 → ˜ ¯ ¯ ψ 1 → d c ∗ d c ∗ Nu c k , N ˜ u c and i j i � � � λ ∗ k 1 λ k 2 λ ′∗ ij 1 λ ′ i , j , k Im � � M 2 ǫ 1 = 1 ij 2 2 F S � ij 1 + � M 2 8 π i , j λ ′∗ ij 1 λ ′ k λ ∗ k 1 λ k 1 1 where, for M 2 − M 1 > Γ ¯ ψ 1 , we have F S ( x ) = 2 √ x x − 1 .
Introduction The Model Conclusion 1 decays since ¯ ψ 1 and ψ c Same asymmetry from ψ 1 and ψ ∗ 1 form a four-component fermion with hypercharge quantum number − 4 / 3. In the limit of unbroken supersymmetry, we get exactly the same asymmetry from the decay of scalars X 1 , ¯ X 1 and their 1 , ¯ antiparticles X ∗ X ∗ 1 . In the presence of supersymmetry breaking the asymmetries from fermion and scalar decays will be similar provided that m 1 , 2 ∼ M 1 , 2 Similarly, the decay of the scalar and fermionic components of X 2 , ¯ X 2 will result in an asymmetry ǫ 2 , with 1 ↔ 2.
Introduction The Model Conclusion � � M 1 M 2 η B = 7 . 04 × 10 − 6 1 � λ ∗ k 1 λ k 2 λ ′∗ ij 1 λ ′ i , j , k Im ij 2 8 π M 2 2 − M 2 1 � � Br 1 Br 2 × k 1 λ k 1 + . i , j λ ′∗ ij 1 λ ′ k λ ∗ i , j λ ′∗ ij 2 λ ′ k λ ∗ � ij 1 + � � ij 2 + � k 2 λ k 2 Want: 4 × 10 − 10 ≤ η B ≤ 7 × 10 − 10 . Assume similar couplings to all flavors of (s)quarks where | λ i 1 | ∼ | λ i 2 | ≫ | λ ′ ij 1 | ∼ | λ ′ ij 2 | (1 ≤ i , j ≤ 3), and CP -violating phases of O ( 1 ) in λ and λ ′ . | λ i 1 | ∼ | λ i 2 | ∼ 1 , | λ ′ ij 1 | ∼ | λ ′ ij 2 | ∼ 0 . 04 .
Introduction The Model Conclusion Can consider variations of the model Single flavor of X , two flavors of singlets N λ i α N α u c ij d c i d c i X + λ ′ W extra = j X (2) M N αβ + N α N β + M X XX 2
Introduction The Model Conclusion u c N α X u c X N β N α u c X X N α N β u c X u c
Introduction The Model Conclusion � � � λ i α λ ∗ i β λ ∗ j β λ j α i , j ,β Im � � M 2 � � M 2 �� β β ǫ α = F S + F V 24 π � M 2 M 2 i λ ∗ i α λ i α α α where F S ( x ) = 2 √ x √ � 1 + 1 � x − 1 , F V = x ln x Choose λ s, can get required BAU
Introduction The Model Conclusion Other variations: singlets replaced by iso-doublet color triplet fields Y , Y with charges ∓ 5 / 3. ij α d c i d c = λ i α YQ i X α + λ ′ W extra j X α (3) + M Y YY + M X , ( α ) X α X α
Introduction The Model Conclusion No parity-violating terms in the superpotential, the LSP is absolutely stable. Dark matter is produced non-thermally. Annihilation cross-section must be enhanced. The enhancement factor is given by ( T f / T r ) ∼ 50, where T f ∼ 10 GeV is the freeze-out temperature of the LSP , and T r ∼ 200 MeV is the reheat temperature.
Introduction The Model Conclusion Conclusion String moduli play interesting roles in cosmology and particle phenomenology We looked at non-thermal production of baryon asymmetry Constructed a model which satisfies the Sakharov conditions. Stable LSP dark matter
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