Higgs Self-Coupling and Electroweak Baryogenesis Eibun Senaha(GUAS, KEK) Nov. 9-12, 2004 , 7th ACFA Workshop @NTU in collaboration with Shinya Kanemura(Osaka U) Yasuhiro Okada(GUAS, KEK) 1
Outline § 1. Introduction -Connection between collider physics and cosmology § 2. Conditions of baryogenesis -Electroweak phase transition in the THDM § 3. Radiative corrections to hhh coupling constant -Collider signal of electroweak baryogenesis? § 4. Summary 2
Introduction • Higgs physics at colliders -Discovery of the Higgs boson(s) (@Tevatron, LHC) � gauge bosons -Measurements of the Higgs couplings with ( mass generation ) fermions O (1)% accuracy (@ILC) ACFA Rep. TESLA TDR -Measurements of the Higgs self-couplings (reconstruction of the Higgs potential) O (10 − 20)% accuracy (@ILC) ACFA Higgs WG, Battaglia et al • Connection between collider physics and cosmology (1). B-L-gen. above EW phase transition (Leptogenesis, etc) -Baryon Asymmery of the Universe (2). B-gen. during EW phase transition (EW baryogenesis) -dark matter ✄ Since the EW baryogenesis depends on the dynamics of the phase transition, we can naively expect that a collider signal of it can appear in the Higgs self-coupling. ✄ We investigate the region where the EW baryogenesis is possible in the THDM, and calculate the deviation of the self-coupling constant from SM prediction in such a region. 3
Conditions of Baryogenesis Evidence of the BAU n B s ≡ n b − n ¯ b ≃ (8 . 7 +0 . 4 − 0 . 3 ) × 10 − 11 s • 3 requirements for generation of the BAU (Sakharov conditions) 1. baryon number violation 2. C and CP violation 3. out of equilibrium 2 scenarios (1) B-L-generation above EW phase transition. (Leptogenesis, etc) (2) B-generation at the electroweak phase transition. (Electroweak baryogenesis) -based on a testable model 4
Baryogenesis in the electroweak theory ✬ ✩ • baryon number violation sphaleron process • C violation chiral interation • CP violation KM-phase or other sources in the extension of the SM • out of equilibrium 1st order phase transition with expanding bubble walls ✫ ✪ In principle, SM fulfills the Sakharov conditions, BUT • Phase transition is not 1st order for the current Higgs mass bound ( m h > 114 GeV) • KM-phase is too small to generate the sufficient baryon asymmetry = ⇒ Extension of the minimal Higgs sector THDM, MSSM, Next-to-MSSM, etc. ✄ THDM is a simple viable model not so constrained 5
Two Higgs Doublet Model (THDM) Higgs potential 1 | Φ 1 | 2 + m 2 2 | Φ 2 | 2 − ( m 2 3 Φ † m 2 V THDM = 1 Φ 2 + h.c. ) + λ 1 2 | Φ 1 | 4 + λ 2 2 | Φ 2 | 4 + λ 3 | Φ 1 | 2 | Φ 2 | 2 + λ 4 | Φ † 1 Φ 2 | 2 � λ 5 � 1 Φ 2 ) 2 + h.c. 2 (Φ † + , � � φ + i ( x ) � � Φ i ( x ) = . ( i = 1 , 2) 1 v i + h i ( x ) + ia i ( x ) √ 2 discrete sym.( Φ 1 → Φ 1 , Φ 2 → − Φ 2 ) → FCNC suppression Yukawa interaction q L f ( d ) q L f ( u ) Φ 1 u R + ¯ ˜ l L f ( e ) L I Type I : Yukawa = ¯ 1 Φ 1 d R + ¯ 1 Φ 1 e R + h.c. , 1 q L f ( d ) q L f ( u ) Φ 2 u R + ¯ ˜ l L f ( e ) L II Type II : Yukawa = ¯ 1 Φ 1 d R + ¯ 1 Φ 1 e R + h.c. 2 6
To avoid complication, we consider [Cline et al PRD54 ’96] � � m 1 = m 2 ≡ m, λ 1 = λ 2 = λ, sin( β − α ) = tan β = 1 � � � Φ 1 � = � Φ 2 � = 1 0 • Higgs VEVs: ϕ 2 • Tree-level potential V tree ( ϕ ) = − µ 2 2 ϕ 2 + λ eff λ eff = 1 µ 2 = m 2 4 ϕ 4 , 3 − m 2 , 4( λ + λ 3 + λ 4 + λ 5 ) � �� � ≡ λ 345 ✄ Mass formulae of the Higgs bosons h = 1 m 2 2( λ + λ 345 ) v 2 , 2 ( λ − λ 345 ) v 2 + M 2 , m 2 H = 1 � c i λ i v 2 and M 2 . A = − λ 5 v 2 + M 2 , m 2 Two origins of the masses : i 2 ( λ 4 + λ 5 ) v 2 + M 2 m 2 H ± = − 1 m 2 where M 2 = 3 (soft breaking scale of the discrete symmetry) sin β cos β 7
1-loop effective potential • Zero temperature � � m 4 log m 2 i ( ϕ ) i ( ϕ ) − 3 V 1 ( ϕ ) = n i 64 π 2 Q 2 2 ( n W = 6 , n Z = 3 , n t = − 12 , n h = n H = n A = 1 , n H ± = 2) • Finite temperature V 1 ( ϕ, T ) = T 4 � � � n i I B ( a 2 ) + n t I F ( a ) 2 π 2 i = bosons dx x 2 log(1 ∓ e − √ � ∞ � � a ( ϕ ) = m ( ϕ ) where x 2 + a 2 ) , I B,F ( a 2 ) = T 0 ( a 2 � 1) ✄ High temperature expansion � � − π 4 45 + π 2 6( a 2 ) 3 / 2 − a 4 log a 2 12 a 2 − π − 3 I B ( a 2 ) + O ( a 6 ) , = 32 α B 2 � � 7 π 4 360 − π 2 24 a 2 − a 4 log a 2 − 3 � � I F ( a 2 ) + O ( a 6 ) , = log α F ( B ) = 2 log(4) π − 2 γ E 32 α F 2 ϕ 3 -term comes from the “bosonic”loop 8
Finite temperature Higgs potential Φ ( v ) ϕ 2 For m 2 Φ ( v ) � M 2 , m 2 m 2 Φ ( ϕ ) ≃ m 2 (Φ = H, A, H ± ) h ( v ) v 2 , 0 ) ϕ 2 − ETϕ 3 + λ T V eff ≃ D ( T 2 − T 2 4 ϕ 4 where 1 12 πv 3 (6 m 3 W + 3 m 3 m 3 H + m 3 A + 2 m 3 E = Z + ) H ± � �� � additional contributions Veff ϕ c = 2 ET c At T c , degenerate minima: λ T c • The magnitude of E is relevent for the strongly T>Tc 1st order phase transition T=Tc 0 ϕ c T<Tc > • Strongly 1st order phase transition: ∼ 1 0 50 100 150 200 250 300 T c ϕ (GeV) ⇒ Not wash out the baryon density after EW phase transition ✄ CP violation at the bubble wall ⇒ Asymmetry of the charge flow 9
Contour plot of ϕ c /T c in the m Φ - M plane sin 2 ( α − β ) = tan β = 1 , m h = 120 GeV , m Φ ≡ m A = m H = m H ± Contour plot of ϕ c/Tc in the m Φ -M plane 450 400 350 phase transition is strongly 1st order m Φ (GeV) 300 250 200 ϕ c/Tc = 1 150 sin( α - β ) = -1, tan β = 1 100 m h = 120 GeV m Φ = m H = m A = m H + - 50 0 0 20 40 60 80 100 120 140 M (GeV) • For m 2 Φ � M 2 , m 2 h , Strongly 1st order phase transition is possible due to the loop effect of the heavy Higgs bosons ( non-decoupling effect ). ( ϕ 3 -term is effectively large) • What the magnitude of the λ hhh coupling at T=0 in such a region? 10
Radiative corrections to λ hhh [S. Kanemura, S. Kiyoura, Y. Okada, E.S., C.-P. Yuan PL ’03] • hhh h h h φ f = h h + h φ f + counter terms φ f h h h ( φ = h, H, A, H ± , f = t, b ) • For sin( β − α ) = 1 , − 3 m 2 h λ tree = v , ( same form as in the SM ) hhh � � � 3 � − 3 m 2 m 4 1 − M 2 c h Φ (Φ = H, A, H ± ) λ hhh ∼ 1 + m 2 m 2 12 π 2 h v 2 v Φ ( c = 1 for neutral Higgs, c = 2 for charged Higgs ) h , the loop effect of the heavy Higgs bosons is enhanced by m 4 For m 2 Φ � M 2 , m 2 Φ , which does not decouple in the large mass limit. ( non-decoupling effect ) 11
Contour plots of ∆ λ hhh /λ hhh and ϕ c /T c in the m Φ - M plane sin 2 ( α − β ) = tan β = 1 , m h = 120 GeV , m Φ ≡ m A = m H = m H ± Contour plot of ∆λ hhh / λ hhh and ϕ c /T c in the m Φ -M plane Contour plot of ∆λ hhh / λ hhh and ϕ c /T c in the m Φ -M plane 450 450 100 % 400 400 350 350 50 % m Φ (GeV) m Φ (GeV) 300 300 30 % 20 % 250 250 10 % 200 200 ϕ c / T c = 1 150 150 ∆λ hhh / λ hhh = 5% 100 100 sin( α - β ) = -1, tan β = 1 m h = 120 GeV 50 m Φ = m H = m A = m H + - 0 0 0 20 20 40 40 60 60 80 80 100 100 120 120 140 140 M (GeV) M (GeV) For m 2 Φ � M 2 , m 2 h , • Phase transition is strongly 1st order, AND ( ∆ λ hhh /λ hhh > • Deviation of hhh coupling from SM value becomes large. ∼ 10% ) 12
Summary We have investigated the region where the ✓ ✏ electroweak phase transition is strongly 1st EW baryogenesis order, and calculate the radiative correction ✒ ✑ to the triple Higgs self-coupling constant in ⇓ the THDM. ✤ ✜ Strongly 1st order V eff ( ϕ, T ) For m 2 Φ � M 2 , m 2 phase transition h ✣ ✢ • Phase transition is strongly 1st order. ⇓ ✤ ✜ • Deviation of hhh coupling from SM value Large loop correction ( ∆ λ hhh /λ hhh > becomes large. ∼ 10% ) V eff ( ϕ, 0) to λ hhh ✣ ✢ due to the non-decoupling effect ⇓ of the heavy Higgs bosons ✎ ☞ Measurement of λ hhh @ILC ✍ ✌ Such deviation can be testable at a Linear Collider. 13
Definitions of the mass eigenstates � � � � � � � � − π h 1 cos α − sin α H = , 2 ≤ α ≤ 0 , h 2 sin α cos α h � � � � � � � � G 0 0 < β < π a 1 cos β − sin β = , a 2 sin β cos β A 2 � � � � � � φ ± G ± cos β − sin β 1 = φ ± H ± sin β cos β 2 14
Renormalized h and H � � � � � � � � H B cos α B sin α B h 1 B h 1 B = = R ( − δα ) R ( − α R ) h B − sin α B cos α B h 2 B h 2 B � �� � ≡ R ( − α B ) � � h 1 R R ( − δα ) R ( − α R ) ˜ = Z h 2 R � � � � h 1 R Z ≡ R ( − α R ) ˜ = R ( − δα ) ZR ( − α R ) ZR ( α R ) h 2 R � � H R = R ( − δα ) Z h R � � � � � � Z 1 / 2 1 δα δA H R H ≡ Z 1 / 2 − δα 1 h R δA h � � � � 1 + 1 2 δZ H δA + δα H R = , 1 + 1 h R δA − δα 2 δZ h 15
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