Update on the post-sphaleron baryogenesis model prediction for neutron-antineutron oscillation time Bhupal Dev Washington University in St. Louis Theoretical Innovations for Future Experiments Regarding B Violation University of Massachusetts, Amherst August 4, 2020 Outline Post-Sphaleron Baryogenesis [Babu, Mohapatra, Nasri (PRL ’06)] A UV-complete model [Babu, BD, Mohapatra (PRD ’08)] Low-energy constraints (Neutrino masses and mixing, FCNC, BAU) Upper limit on n − n¯ oscillation time [Babu, BD, Fortes, Mohapatra (PRD ’13)] 2020 update (in light of recent lattice, neutrino and LHC results) [Babu, Chauhan, BD, Mohapatra, Thapa (work in progress)] Conclusion 2 Post-sphaleron baryogenesis: Deep connection between BAU and n − n¯ oscillation. BAU is generated below 100 GeV, after the EW sphalerons go out-of-equilibrium. [Babu, Mohapatra, Nasri (PRL ’06)] Low reheating temperature consistent with wide range of inflation models. More compelling than EW baryogenesis. [Ann Nelson (INT Workshop ’17)] Why PSB is Compelling? BAU requires B violation. [Sakharov (JETP Lett. ’67)] 16 ∆B = 1: Proton decay constraints require very high scale ∼ 10 GeV. [Nath, Fileviez Perez (Phys. Rept. ’07)] ∆B = 2: Induced by dimension-9 operator 1 L = qqqqqq eff Λ5 High-dimension implies scale can be as low as Λ ∼ 106 GeV. Observable signature: n − n¯ oscillation. [Phillips, Snow, Babu et al. (Phys. Rept. ’16)] 3 Why PSB is Compelling? BAU requires B violation. [Sakharov (JETP Lett. ’67)] 16 ∆B = 1: Proton decay constraints require very high scale ∼ 10 GeV. [Nath, Fileviez Perez (Phys. Rept. ’07)] ∆B = 2: Induced by dimension-9 operator 1 L = qqqqqq eff Λ5 High-dimension implies scale can be as low as Λ ∼ 106 GeV. Observable signature: n − n¯ oscillation. [Phillips, Snow, Babu et al. (Phys. Rept. ’16)] Post-sphaleron baryogenesis: Deep connection between BAU and n − n¯ oscillation. BAU is generated below 100 GeV, after the EW sphalerons go out-of-equilibrium. [Babu, Mohapatra, Nasri (PRL ’06)] Low reheating temperature consistent with wide range of inflation models. More compelling than EW baryogenesis. [Ann Nelson (INT Workshop ’17)] 3 Naturally realized in quark-lepton unified models, with S identified as the Higgs boson of B − L breaking. Yukawa couplings that affect PSB and n − n¯ are the same as the ones that generate neutrino masses via seesaw. Requiring successful BAU and observed neutrino oscillation parameters lead to a concrete, quantitative prediction for n − n¯ amplitude. Basic Idea of PSB A (pseudo)scalar S decays to baryons, violating B. ∆B = 1 is strongly constrained by proton decay and cannot lead to successful PSB. ∆B = 2 decay of S, if violates CP and occurs out-of-equilibrium, can generate BAU below T = 100 GeV. The same ∆B = 2 operator leads to n − n¯. 4 Basic Idea of PSB A (pseudo)scalar S decays to baryons, violating B. ∆B = 1 is strongly constrained by proton decay and cannot lead to successful PSB. ∆B = 2 decay of S, if violates CP and occurs out-of-equilibrium, can generate BAU below T = 100 GeV. The same ∆B = 2 operator leads to n − n¯. Naturally realized in quark-lepton unified models, with S identified as the Higgs boson of B − L breaking. Yukawa couplings that affect PSB and n − n¯ are the same as the ones that generate neutrino masses via seesaw. Requiring successful BAU and observed neutrino oscillation parameters lead to a concrete, quantitative prediction for n − n¯ amplitude. 4 w w w w 0 ± ∓ (1,1,15)wMc & 1400 TeV (from KL → µ e ) w w [Valencia, Willenbrock (PRD ’94)] SU(2)L × SU(2)R × U(1)B−L × SU(3)c [Mohapatra, Pati (PRD ’75)] w [Senjanović, Mohapatra (PRD ’75)] w w w (1, 3, 10)wvBL (& 200 TeV) [Mohapatra, Marshak (PRL ’80)] w w SU(2)L × U(1)Y × SU(3)c No ∆B = 1 processes since B − L is broken by two units. Quark-Lepton Symmetric Model SU(2)L × SU(2)R × SU(4)c [Pati, Salam (PRD ’74)] 5 w w w w (1, 3, 10)wvBL (& 200 TeV) [Mohapatra, Marshak (PRL ’80)] w w SU(2)L × U(1)Y × SU(3)c No ∆B = 1 processes since B − L is broken by two units. Quark-Lepton Symmetric Model SU(2)L × SU(2)R × SU(4)c [Pati, Salam (PRD ’74)] w w w w 0 ± ∓ (1,1,15)wMc & 1400 TeV (from KL → µ e ) w w [Valencia, Willenbrock (PRD ’94)] SU(2)L × SU(2)R × U(1)B−L × SU(3)c [Mohapatra, Pati (PRD ’75)] [Senjanović, Mohapatra (PRD ’75)] 5 Quark-Lepton Symmetric Model SU(2)L × SU(2)R × SU(4)c [Pati, Salam (PRD ’74)] w w w w 0 ± ∓ (1,1,15)wMc & 1400 TeV (from KL → µ e ) w w [Valencia, Willenbrock (PRD ’94)] SU(2)L × SU(2)R × U(1)B−L × SU(3)c [Mohapatra, Pati (PRD ’75)] w [Senjanović, Mohapatra (PRD ’75)] w w w (1, 3, 10)wvBL (& 200 TeV) [Mohapatra, Marshak (PRL ’80)] w w SU(2)L × U(1)Y × SU(3)c No ∆B = 1 processes since B − L is broken by two units. 5 (B − L)-breaking Scalars Under SU(2)L × U(1)Y × SU(3)c , 8 2 4 ∆(1, 3, 10) = ∆ (1, − , 6∗) ⊕ ∆ (1, − , 6∗) ⊕ ∆ (1, + , 6∗) uu 3 ud 3 dd 3 2 4 ⊕ ∆ (1, , 3∗) ⊕ ∆ (1, − , 3∗) ue 3 uν 3 8 2 ⊕ ∆ (1, , 3∗) ⊕ ∆ (1, , 3∗) de 3 dν 3 ⊕ ∆ee (1, 4, 1) ⊕ ∆νe (1, 2, 1) ⊕ ∆νν (1, 0, 1) . ∆uu, ∆ud , ∆dd (diquarks) generate B violation. ∆νν (singlet) breaks the B − L symmetry and provides a real scalar field S for PSB: 1 0 ∆νν = vBL + √ (S + iG ) 2 6 The real scalar field S can decay into 6q and 6q¯, thus violating B by two units. S must be the lightest of the (1, 3, 10) multiplet to forbid its B-conserving decays involving on-shell ∆qq. Diquark Interactions and B-violating Decay of S Interactions of color-sextet diquarks and B-violating couplings: fij hij gij LI = ∆dd di dj + ∆uuui uj + √ ∆ud (ui dj + uj di ) 2 2 2 2 λ + ∆ ∆ ∆ ∆ + λ0∆ ∆ ∆ ∆ + H.c. 2 νν dd ud ud νν uu dd dd 0 Boundary conditions: fij = gij = hij and λ = λ in the PS symmetry limit. Couplings only to RH quarks due to L-R embedding. In general, ∆ud could couple to both LH and RH quark bilinears, leading to EDM. [Bell, Corbett, Nee, Ramsey-Musolf (PRD ’19)] 7 Diquark Interactions and B-violating Decay of S Interactions of color-sextet diquarks and B-violating couplings: fij hij gij LI = ∆dd di dj + ∆uuui uj + √ ∆ud (ui dj + uj di ) 2 2 2 2 λ + ∆ ∆ ∆ ∆ + λ0∆ ∆ ∆ ∆ + H.c. 2 νν dd ud ud νν uu dd dd 0 Boundary conditions: fij = gij = hij and λ = λ in the PS symmetry limit. Couplings only to RH quarks due to L-R embedding. In general, ∆ud could couple to both LH and RH quark bilinears, leading to EDM. [Bell, Corbett, Nee, Ramsey-Musolf (PRD ’19)] The real scalar field S can decay into 6q and 6q¯, thus violating B by two units. S must be the lightest of the (1, 3, 10) multiplet to forbid its B-conserving decays involving on-shell ∆qq. 7 Conditions for PSB: ΓS→6q ≤ H(TEW), and ΛQCD ≤ Td ≤ TEW. S → 6q must be the dominant decay mode (over S → Zf f¯, ZZ) =⇒ v 100 TeV. √ BL & Vacuum stability restricts vBL from being arbitrarily large: λvBL . 2 πM∆. −1/4 √ sbefore g∗ 0.6 ΓS MPl Td Not too much dilution: d ≡ ' ∼ =⇒ MS 17 TeV. safter nS MS /s(Td ) MS . Thermal History of S Decay P 12 M13 Γ ≡ Γ(S → 6q) + Γ(S → 6q¯) = |λ|2Tr(f †f )[Tr(ˆg †gˆ)]2 S S π9 · 225 · 45 4 M8 M4 ∆ud ∆dd −4 where P = 1.13 × 10 is a phase space factor (for M∆ud /MS , M∆dd /MS 1). 8 Thermal History of S Decay P 12 M13 Γ ≡ Γ(S → 6q) + Γ(S → 6q¯) = |λ|2Tr(f †f )[Tr(ˆg †gˆ)]2 S S π9 · 225 · 45 4 M8 M4 ∆ud ∆dd −4 where P = 1.13 × 10 is a phase space factor (for M∆ud /MS , M∆dd /MS 1). Conditions for PSB: ΓS→6q ≤ H(TEW), and ΛQCD ≤ Td ≤ TEW. S → 6q must be the dominant decay mode (over S → Zf f¯, ZZ) =⇒ v 100 TeV. √ BL & Vacuum stability restricts vBL from being arbitrarily large: λvBL . 2 πM∆. −1/4 √ sbefore g∗ 0.6 ΓS MPl Td Not too much dilution: d ≡ ' ∼ =⇒ MS 17 TeV. safter nS MS /s(Td ) MS . 8 CP Asymmetry W ui ui dβ dβ ∆ud ∆ud uj W uj dα dα s 2 2 m2 2 m2 8g ∗ ∗ mt mj mW β β wave ' − † δi3=(ˆgiαgˆjαVjβ Viβ ) 2 2 1 − 2 + 2 − 4 2 64π Tr(f f ) mt − mj mt mt mt 2 2 2 2 2 2 mW mβ mβ mβ mt mβ × 2 1 − 2 + 2 − 4 2 + 1 + 2 2 + 2 − 1 mt mt mW mt mW mW 2 2 (i,j6=3) 8g ∗ ∗ mβ mj 3mW 2hp1 · p2i vertex ' − † =(ˆgiαgˆjβ Viβ Vjα) 2 1 + ln 1 + 2 32π Tr(f f ) mW 2hp1 · p2i mW 2 2 (i=3,j6=3) 8g δi3 ∗ ∗ mβ mj 3mW 2hp1 · p2i vertex ' − † =(ˆgiαgˆjβ Viβ Vjα) 2 1 + ln 1 + 2 32π Tr(f f ) mW 2hp1 · p2i mt (Updated calculation) 9 Flavor Violation Diquark fields lead to flavor violation, both at tree and loop levels. ∗ † † † † 1 fi`f α β 1 [(ff ) (ff ) + (ff ) (ff ) ] H = − kj (d γ d α )(d γµd β ) + ij `k ik `j ∆dd 8 M2 kR µ iR jR `R 256π2 M2 ∆dd ∆dd h α α β µ β α β β µ α i × (d jR γµdiR )(d kR γ d`R ) + 5(d jR γµdiR )(d kR γ d`R ) .