Neutron-Antineutron Oscillation, Low-scale Baryogenesis, Dark Matter - PowerPoint PPT Presentation

Neutron-Antineutron Oscillation, Low-scale Baryogenesis, Dark Matter and LHC Physics B HUPAL D EV Washington University in St. Louis R. Allahverdi, BD and B. Dutta, arXiv:1711.xxxxx. BD and R. N. Mohapatra, Phys. Rev. D 92 , 016007 (2015) [arXiv:1504.07196]. INT Workshop on Neutron-Antineutron Oscillations University of Washington, Seattle October 26, 2017

Proton Decay vs n − ¯ n Selection rules for ∆ B ∆ B = 1 ∆ B = 2 Di-nucleon decay and n − ¯ Proton decay n Induced by dimension-6 operator Induced by dimension-9 operator. (also dimension-5 in SUSY). Amplitude ∝ Λ − 5 . Amplitude ∝ Λ − 2 . Λ � 100 TeV enough to satisfy τ p � 10 34 yr implies Λ � 10 15 GeV. experimental constraints. Proton decay requires GUT-scale n − ¯ n oscillation could come from physics. a TeV-scale new physics. ∆ B � = 0 could be linked to baryogenesis (Sakharov).

Highlights of this Talk A simple TeV-scale SM-extension with baryogenesis, dark matter and n − ¯ n . Introduces / B -interactions via TeV-scale color-triplet scalars ( X α ) and a singlet Majorana fermion ( ψ ) that couple only to the RH quarks. ψ is stable, and hence, a DM candidate, if m ψ ≃ m p . Baryogenesis occurs via out-of-equilibrium decays of X α . Common origin for both baryon and DM abundance. Requirements of successful baryogenesis and Ω DM / Ω b ≈ 5 put meaningful constraints on the model parameter space. Observable n − ¯ n in the allowed parameter space. Complementarity with monojet/monotop signals at the LHC.

Highlights of this Talk A simple TeV-scale SM-extension with baryogenesis, dark matter and n − ¯ n . Introduces / B -interactions via TeV-scale color-triplet scalars ( X α ) and a singlet Majorana fermion ( ψ ) that couple only to the RH quarks. ψ is stable, and hence, a DM candidate, if m ψ ≃ m p . Baryogenesis occurs via out-of-equilibrium decays of X α . Common origin for both baryon and DM abundance. Requirements of successful baryogenesis and Ω DM / Ω b ≈ 5 put meaningful constraints on the model parameter space. Observable n − ¯ n in the allowed parameter space. Complementarity with monojet/monotop signals at the LHC.

The Model Start with the SM gauge group and add renormalizable terms that violate baryon number. Gauge invariance requires introduction of new colored fields. A minimal setup: Iso-singlet, color-triplet scalars X α with Y = + 4 / 3 . Allows X α d c d c terms in the Lagrangian. Need at least two ( α = 1 , 2 ) to produce baryon asymmetry from X decay. Total baryon asymmetry vanishes after summing over all flavors of d c . [Kolb, Wolfram (NPB ’80)] Need additional / B interactions. Introduce a SM-singlet Majorana fermion ψ (also plays the role of DM). � � j + 1 2 m ψ ¯ α ψ u c α ij X α d c i d c ψ c ψ + H . c . λ α i X ∗ i + λ ′ L ⊃ . [Allahverdi, Dutta (PRD ’13); BD, Mohapatra (PRD ’15); Davoudiasl, Zhang (PRD ’15)]

The Model Start with the SM gauge group and add renormalizable terms that violate baryon number. Gauge invariance requires introduction of new colored fields. A minimal setup: Iso-singlet, color-triplet scalars X α with Y = + 4 / 3 . Allows X α d c d c terms in the Lagrangian. Need at least two ( α = 1 , 2 ) to produce baryon asymmetry from X decay. Total baryon asymmetry vanishes after summing over all flavors of d c . [Kolb, Wolfram (NPB ’80)] Need additional / B interactions. Introduce a SM-singlet Majorana fermion ψ (also plays the role of DM). � � j + 1 2 m ψ ¯ α ψ u c α ij X α d c i d c ψ c ψ + H . c . λ α i X ∗ i + λ ′ L ⊃ . [Allahverdi, Dutta (PRD ’13); BD, Mohapatra (PRD ’15); Davoudiasl, Zhang (PRD ’15)]

Dark Matter Integrate out X α to obtain ψ u c i d c j d c k interaction (assuming m ψ ≪ m X ). ψ decays to three quarks (baryons) if m ψ ≫ GeV. Also ψ → p + e − + ¯ ν e if m ψ > m p + m e . Absolutely stable for m ψ < m p + m e (no discrete symmetry required). In addition, need m p > m ψ + m e to avoid p → ψ + e + + ν e . So the viable scenario for ψ to be the DM candidate is (see also A. Nelson’s talk) m p − m e ≤ m ψ ≤ m p + m e . ψ cannot give mass to light neutrinos through H ψ L term, because this with X ψ u c and Xd c d c terms will induce the dimension-7 operator HLu c d c d c for rapid proton decay. Stability of DM is linked to the stability of proton.

Dark Matter Integrate out X α to obtain ψ u c i d c j d c k interaction (assuming m ψ ≪ m X ). ψ decays to three quarks (baryons) if m ψ ≫ GeV. Also ψ → p + e − + ¯ ν e if m ψ > m p + m e . Absolutely stable for m ψ < m p + m e (no discrete symmetry required). In addition, need m p > m ψ + m e to avoid p → ψ + e + + ν e . So the viable scenario for ψ to be the DM candidate is (see also A. Nelson’s talk) m p − m e ≤ m ψ ≤ m p + m e . ψ cannot give mass to light neutrinos through H ψ L term, because this with X ψ u c and Xd c d c terms will induce the dimension-7 operator HLu c d c d c for rapid proton decay. Stability of DM is linked to the stability of proton.

DM Relic Density For m ψ ≈ m p , only annihilation channel is ψψ → u c u c . | λ α 1 | 4 m 2 ψ � σ ann v � ∼ . 8 π m 4 X For m X ∼ O (1 TeV), even λ ∼ O ( 1 ) gives � σ ann v � ≪ 3 × 10 − 26 cm 3 s − 1 . Thermal overproduction of ψ (as expected). [Lee, Weinberg (PRL ’77]] Need a non-thermal mechanism to obtain the correct relic density. Late decay of a scalar (moduli) field φ with a low reheating temperature T R ≤ GeV. [Moroi, Randall (NPB ’00); Allahverdi, Dutta, Sinha (PRD ’10)] n ψ s = Y φ Br φ → ψ , where Y φ = 3 T R 4 m φ is the entropy dilution due to the φ decay.

DM Relic Density For m ψ ≈ m p , only annihilation channel is ψψ → u c u c . | λ α 1 | 4 m 2 ψ � σ ann v � ∼ . 8 π m 4 X For m X ∼ O (1 TeV), even λ ∼ O ( 1 ) gives � σ ann v � ≪ 3 × 10 − 26 cm 3 s − 1 . Thermal overproduction of ψ (as expected). [Lee, Weinberg (PRL ’77]] Need a non-thermal mechanism to obtain the correct relic density. Late decay of a scalar (moduli) field φ with a low reheating temperature T R ≤ GeV. [Moroi, Randall (NPB ’00); Allahverdi, Dutta, Sinha (PRD ’10)] n ψ s = Y φ Br φ → ψ , where Y φ = 3 T R 4 m φ is the entropy dilution due to the φ decay.

Baryogenesis Via direct decays of X α → ψ u c i , d c i d c j . Independent of sphaleron processes. Example of post-sphaleron baryogenesis. [Babu, Mohapatra, Nasri (PRL ’06)] For complex λ α i or λ ′ α ij , interference of tree and one-loop contributions produces a non-zero CP asymmetry. In principle, either self-energy or vertex diagrams or both could contribute. In the non-thermal scenario, final baryon asymmetry also depends on the moduli decay rate: � η B ≃ 7 . 04 Y φ Br φ → X α ǫ α . α

Moduli Decay Naturally long-lived due to gravitationally suppressed couplings. Dominates the energy density of the universe before decaying. Must decay well before BBN ( T BBN ∼ MeV). m 3 Decay rate: Γ φ = c φ φ Pl , where c φ ∼ 0 . 01 − 1 (in typical string 2 π M 2 compactification scenarios, e.g. KKLT). Moduli decay occurs when Γ φ ∼ H ≃ 1 . 66 √ g ∗ T 2 M Pl . Reheat temperature: � 1 / 4 � � 10 . 75 � 3 / 2 m φ T R ≃ c 1 / 2 3 . 5 MeV . φ g ∗ 100 TeV Requiring MeV � T R � GeV implies 200 TeV � m φ � 4500 TeV , or 10 − 9 � Y φ ≡ 3 T R 4 m φ � 10 − 7 . Need ǫ ∼ 10 − 3 − 10 − 1 .

Moduli Decay Naturally long-lived due to gravitationally suppressed couplings. Dominates the energy density of the universe before decaying. Must decay well before BBN ( T BBN ∼ MeV). m 3 Decay rate: Γ φ = c φ φ Pl , where c φ ∼ 0 . 01 − 1 (in typical string 2 π M 2 compactification scenarios, e.g. KKLT). Moduli decay occurs when Γ φ ∼ H ≃ 1 . 66 √ g ∗ T 2 M Pl . Reheat temperature: � 1 / 4 � � 10 . 75 � 3 / 2 m φ T R ≃ c 1 / 2 3 . 5 MeV . φ g ∗ 100 TeV Requiring MeV � T R � GeV implies 200 TeV � m φ � 4500 TeV , or 10 − 9 � Y φ ≡ 3 T R 4 m φ � 10 − 7 . Need ǫ ∼ 10 − 3 − 10 − 1 .

Resonant Baryogenesis Similar in spirit to resonant leptogenesis. [Pilaftsis (PRD ’97); Pilaftsis, Underwood (NPB ’03; PRD ’05); BD, Pilaftsis, Millington, Teresi (NPB ’14)] Self-energy graphs dominate the CP -asymmetry for quasi-degenerate X α ’s. Resonantly enhanced [up to O ( 0 . 1 ) ] for ∆ m X � Γ X / 2 . ( m 2 X α − m 2 � ijk Im ( λ ∗ α k λ β k λ ′∗ α ij λ ′ β ij ) X β ) m X α m X β ǫ α = 1 k | λ α k | 2 + � X β ) 2 + m 2 8 π � ij | λ ′ α ij | 2 ( m 2 X α − m 2 X α Γ 2 X β In the resonance limit, regulator goes as m X / Γ X . CP -asymmetry becomes insensitive to the mass scale m X , as well as the overall scaling of the coupling constants.

Free Parameters and Constraints Free parameters: m X , λ α i , λ ′ α ij (with α = 1 , 2 and i , j , k = 1 , 2 , 3 ). Color antisymmetry requires that λ ′ ij = 0 for i = j . Similarly, color conservation does not allow tree-level contributions to quark FCNCs. Only major constraint comes from di-nucleon decay (like pp → KK ): α 12 | � 10 − 6 ( m X / 1 TeV ) 2 . | λ α 1 λ ′ We assume λ ′ 12 small, while leave λ α 1 as a free parameter. For simplicity, also assume | λ 1 i | = | λ 2 i | ≡ | λ | ∀ i = 1 , 2 , 3 . Similarly, take | λ ′ 1 ij | = | λ ′ 2 ij | ≡ | λ ′ ij | . Left with only four parameters m X , λ, λ ′ 13 , 23 .