Z-ino-driven electroweak baryogenesis Eibun Senaha (Nagoya U, E-ken) - PowerPoint PPT Presentation

Z’-ino-driven electroweak baryogenesis Eibun Senaha (Nagoya U, E-ken) Oct 6, 2013 @7th Toyama Higgs meeting Ref. PRD88,055014 (2013) [arXiv:1308.3389]

Higgs physics and cosmology ❒ 126 GeV Higgs boson was discovered. What’ s the cosmological implication? ❒ Higgs-cosmology connections - cosmic baryon asymmetry ⟺ EW baryogenesis - dark matter ⟺ inert Higgs, Higgs portal etc. - etc It is possible to get the baryon asymmetry at the EW scale. However, the region where the baryon asymmetry can arise within the SM was excluded due to “no strong 1st-order PT, no sufficient CPV . ”

Current status ❒ SM EWBG was excluded. SUSY: MSSM EWBG (light stop scenario) looks dead. Next-to-MSSM (NMSSM), nearly-MSSM (nMSSM), U(1)’-MSSM (UMSSM), triplet-MSSM (TMSSM) etc. strong 1 st -order EWPT is OK, CPV is OK SM+extended Higgs sector: strong 1 st -order PT CPV(Higgs sector) real singlet OK X complex singlet OK OK MHDM (M ≥ 2) OK OK real triplet OK X complex triplet OK X In this talk, we discuss a possibility of the EWBG in the UMSSM.

Outline Introduction EWBG in the U(1)’-extended MSSM (UMSSM) strong 1 st -order EW phase transition (PT) sphaleron decoupling condition (baryon asymmetry) Summary

U(1)’-extended MSSM (UMSSM) D.Suematsu et al, Int.J.Mod.Phys.A10 (‘95) 4521. M.Cvetic et al, PRD56:2861 (’97) superpotential: u H j W UMSSM � � ij � SH i d 2 Higgs doublets (H d , H u ) + 1 Higgs singlet (S) Higgs potential V 0 = V F + V D + V soft , u | 2 + | S | 2 ( Φ † V F = | � | 2 � | � ij Φ i d Φ j d Φ d + Φ † � u Φ u ) , V D = g 2 2 + g 2 u Φ u ) 2 + g 2 ( Φ † 2 ( Φ † 1 2 d Φ d − Φ † d Φ u )( Φ † u Φ d ) 8 + g � 2 2 ( Q H d Φ † 1 d Φ d + Q H u Φ † u Φ u + Q S | S | 2 ) 2 , 1 Φ † V soft = m 2 d Φ d + m 2 2 Φ † u Φ u + m 2 S | S | 2 − ( � ij � A λ S Φ i d Φ j u + h . c . ) . � Q’ s: U(1)’ charges, Q Hd + Q Hu + Q S = 0. g � 5 / 3 g 1 1 = 1 φ + � 2 ( v d + h d + ia d ) � � � √ u Φ u = e i θ Φ d = , , 1 2 ( v u + h u + ia u ) φ − √ d 1 S = 2( v S + h S + ia S ) . √

U(1)’-extended MSSM (UMSSM) D.Suematsu et al, Int.J.Mod.Phys.A10 (‘95) 4521. M.Cvetic et al, PRD56:2861 (’97) superpotential: u H j W UMSSM � � ij � SH i d 2 Higgs doublets (H d , H u ) + 1 Higgs singlet (S) Higgs potential V 0 = V F + V D + V soft , u | 2 + | S | 2 ( Φ † V F = | � | 2 � | � ij Φ i d Φ j d Φ d + Φ † � u Φ u ) , V D = g 2 2 + g 2 u Φ u ) 2 + g 2 ( Φ † 2 ( Φ † 1 2 d Φ d − Φ † d Φ u )( Φ † u Φ d ) 8 + g � 2 U(1)’-D term 2 ( Q H d Φ † 1 d Φ d + Q H u Φ † u Φ u + Q S | S | 2 ) 2 , 1 Φ † V soft = m 2 d Φ d + m 2 2 Φ † u Φ u + m 2 S | S | 2 − ( � ij � A λ S Φ i d Φ j u + h . c . ) . � Q’ s: U(1)’ charges, Q Hd + Q Hu + Q S = 0. g � 5 / 3 g 1 1 = 1 φ + � 2 ( v d + h d + ia d ) � � � √ u Φ u = e i θ Φ d = , , 1 2 ( v u + h u + ia u ) φ − √ d 1 S = 2( v S + h S + ia S ) . √

Tadpole (minimization) conditions 1 + g 2 2 + g 2 + | λ | 2 S ) + g � 2 1 � ∂ V 0 v u v S � 1 1 = m 2 ( v 2 d − v 2 2 ( v 2 u + v 2 u ) − R λ 2 Q H d ∆ = 0 , 8 v d ∂ h d v d � ∂ V 0 2 − g 2 2 + g 2 + | λ | 2 S ) + g � 2 1 v d v S � = m 2 1 ( v 2 d − v 2 2 ( v 2 d + v 2 1 u ) − R λ 2 Q H u ∆ = 0 , ∂ h u 8 v u v u � ∂ V 0 + | λ | 2 u ) + g � 2 1 v d v u � 1 = m 2 2 ( v 2 d + v 2 2 Q S ∆ = 0 , S − R λ v S ∂ h S v S 1 = 1 � ∂ V 0 � ∂ V 0 � � = I λ v S = 0 , ∂ a d ∂ a u v u v d � ∂ V 0 1 v d v u � where v d = v u = v S � = 0 is assumed. = I λ = 0 , v S ∂ a S v S ∆ = Q H d v 2 d + Q H u v 2 u + Q S v 2 S , R λ = Re( λ A λ e i θ ) = | λ A λ | cos( δ A λ + δ λ + θ ) ≡ | λ A λ | cos( δ A λ + δ � λ ) , √ √ √ 2 2 2 I λ = Im( λ A λ e i θ ) = | λ A λ | sin( δ A λ + δ λ + θ ) ≡ | λ A λ | sin( δ A λ + δ � λ ) . √ √ √ 2 2 2 CP is conserved at the tree level. I λ = 0 .

Tadpole (minimization) conditions 1 + g 2 2 + g 2 + | λ | 2 S ) + g � 2 1 � ∂ V 0 v u v S � 1 1 = m 2 ( v 2 d − v 2 2 ( v 2 u + v 2 u ) − R λ 2 Q H d ∆ = 0 , 8 v d ∂ h d v d � ∂ V 0 2 − g 2 2 + g 2 + | λ | 2 S ) + g � 2 1 v d v S � = m 2 1 ( v 2 d − v 2 2 ( v 2 d + v 2 1 u ) − R λ 2 Q H u ∆ = 0 , ∂ h u 8 v u v u � ∂ V 0 + | λ | 2 u ) + g � 2 1 v d v u � 1 = m 2 2 ( v 2 d + v 2 2 Q S ∆ = 0 , S − R λ v S ∂ h S v S 1 = 1 � ∂ V 0 � ∂ V 0 � � = I λ v S = 0 , ∂ a d ∂ a u v u v d � ∂ V 0 1 v d v u � where v d = v u = v S � = 0 is assumed. = I λ = 0 , v S ∂ a S v S ∆ = Q H d v 2 d + Q H u v 2 u + Q S v 2 S , R λ = Re( λ A λ e i θ ) = | λ A λ | cos( δ A λ + δ λ + θ ) ≡ | λ A λ | cos( δ A λ + δ � λ ) , √ √ √ 2 2 2 I λ = Im( λ A λ e i θ ) = | λ A λ | sin( δ A λ + δ λ + θ ) ≡ | λ A λ | sin( δ A λ + δ � λ ) . √ √ √ 2 2 2 CP is conserved at the tree level. I λ = 0 .

Higgs boson masses At the tree level, the lightest Higgs mass is bounded as Z cos 2 2 β + | λ | 2 2 v 2 sin 2 2 β + g � 2 1 v 2 ( Q H d cos 2 β + Q H u sin 2 β ) 2 . m 2 H 1 ≤ m 2 CP-even Higgs: In the limit Q H d = Q H u ≡ Q , tan β = 1, one gets H 1 , 2 = 1 � S + | λ | 2 v 2 + 6 g � 2 m 2 m 2 1 Q 2 v 2 S 2 � �� � 2 + 4 v 2 � � 2 m 2 S + 2 g � 2 1 Q 2 (3 v 2 R λ � ( | λ | 2 � 2 g � 2 S � v 2 ) 1 Q 2 ) v S , � Z � | λ | 2 2 v 2 + 2 R λ v S , m 2 H 3 = m 2 1 + v 2 � � A = 2 R λ v S sin 2 2 β CP-odd Higgs: m 2 4 v 2 sin 2 β S sin 2 β v S − | λ | 2 W + 2 R λ charged Higgs: m 2 H ± = m 2 2 v 2 . Heavy Higgs boson masses are controlled by R λ (A λ ).

Higgs boson masses At the tree level, the lightest Higgs mass is bounded as Z cos 2 2 β + | λ | 2 2 v 2 sin 2 2 β + g � 2 1 v 2 ( Q H d cos 2 β + Q H u sin 2 β ) 2 . m 2 H 1 ≤ m 2 CP-even Higgs: In the limit Q H d = Q H u ≡ Q , tan β = 1, one gets H 1 , 2 = 1 � S + | λ | 2 v 2 + 6 g � 2 m 2 m 2 1 Q 2 v 2 S 2 � �� � 2 + 4 v 2 � � 2 m 2 S + 2 g � 2 1 Q 2 (3 v 2 R λ � ( | λ | 2 � 2 g � 2 S � v 2 ) 1 Q 2 ) v S , � Z � | λ | 2 2 v 2 + 2 R λ v S , m 2 H 3 = m 2 1 + v 2 � � A = 2 R λ v S sin 2 2 β CP-odd Higgs: m 2 4 v 2 sin 2 β S sin 2 β v S − | λ | 2 W + 2 R λ charged Higgs: m 2 H ± = m 2 2 v 2 . Heavy Higgs boson masses are controlled by R λ (A λ ).

Higgs boson masses At the tree level, the lightest Higgs mass is bounded as Z cos 2 2 β + | λ | 2 2 v 2 sin 2 2 β + g � 2 1 v 2 ( Q H d cos 2 β + Q H u sin 2 β ) 2 . m 2 H 1 ≤ m 2 CP-even Higgs: In the limit Q H d = Q H u ≡ Q , tan β = 1, one gets H 1 , 2 = 1 � S + | λ | 2 v 2 + 6 g � 2 m 2 m 2 1 Q 2 v 2 S 2 � �� � 2 + 4 v 2 � � 2 m 2 S + 2 g � 2 1 Q 2 (3 v 2 R λ � ( | λ | 2 � 2 g � 2 S � v 2 ) 1 Q 2 ) v S , � Z � | λ | 2 2 v 2 + 2 R λ v S , m 2 H 3 = m 2 1 + v 2 � � A = 2 R λ v S sin 2 2 β CP-odd Higgs: m 2 4 v 2 sin 2 β S sin 2 β v S − | λ | 2 W + 2 R λ charged Higgs: m 2 H ± = m 2 2 v 2 . Heavy Higgs boson masses are controlled by R λ (A λ ).

Vacuum structures Tree-level effective potential S − R λ ϕ d ϕ u ϕ S + g 2 2 + g 2 V 0 ( ϕ d , ϕ u , ϑ , ϕ S ) = 1 d + 1 u + 1 1 2 m 2 1 ϕ 2 2 m 2 2 ϕ 2 2 m 2 S ϕ 2 ( ϕ 2 d − ϕ 2 u ) 2 32 + | λ | 2 S ) + g � 2 1 4 ( ϕ 2 d ϕ 2 u + ϕ 2 d ϕ 2 S + ϕ 2 u ϕ 2 8 ( Q H d ϕ 2 d + Q H u ϕ 2 u + Q S ϕ 2 S ) 2 . EW : v = 246 GeV , v S � = 0; I : v = 0 , v S � = 0; various vacua: II : v � = 0 , v S = 0; SYM : v = v S = 0 . Energy of EW vacuum is ( v d , v u , θ , v S ) = − g 2 2 + g 2 2 R λ v d v u v S − | λ | 2 S ) − g � 2 u ) 2 + 1 V (EW) 1 ( v 2 d − v 2 4 ( v 2 d v 2 u + v 2 d v 2 S + v 2 u v 2 8 ∆ 2 , 1 0 32 We require V 0 ( ϕ = v EW ) < V 0 ( ϕ � = v EW ) , V (EW) ( v d , v u , θ , v S ) < 0 gives an upper bound on m H ± 0 Z cot 2 2 β + 2 | λ | 2 v 2 g � 2 1 ∆ 2 m 2 H ± < m 2 W + m 2 S v 2 sin 2 2 β ≡ ( m max H ± ) 2 . sin 2 2 β +

m max H ± | λ | = 0 . 8, Q H d = − 0 . 5, Q H u = Q H d / tan 2 β 6000 5000 4000 3000 2000 1000 0 200 400 600 800 1000 - Smallest m max H ± is realized for tan β = 1 . - In this case, m H ± � 1 TeV for v S � 640 GeV.

Neutral gauge boson masses � � g � � 1 4 ( g 2 2 + g 2 1 ) v 2 1 ( Q H d v 2 d − Q H u v 2 g 2 2 + g 2 u ) 1 M 2 ZZ � = 2 . g � � g 2 2 + g 2 1 ( Q H d v 2 d − Q H u v 2 g � 2 1 ( Q 2 H d v 2 d + Q 2 H u v 2 u + Q 2 S v 2 u ) S ) 1 2 � Q H d From EW precision tests, α ZZ � < O (10 − 3 ) = tan β = ⇒ Q H u m 2 Z � = g � 2 1 ( Q 2 H d v 2 d + Q 2 H u v 2 u + Q 2 S v 2 S ) . Z’ boson mass: Input parameters tan β tree level: A λ Q H d Q H u v S λ Q H d = Q H u = − 0 . 5 � m H 1 = 126 GeV m Z � Q H d m H ± ( Q S = − Q H d − Q H d = 1) Q H u 1-loop level: stop loop √ m ˜ q = m ˜ t R = 1 . 5 TeV, A t = m ˜ q + | µ e ff | / tan β , ( µ e ff = λ v S / 2).