Electroweak Baryogenesis and the triple Higgs boson coupling

Transcription

1 Electroweak Baryogenesis and te triple Higgs boson coupling Eibun Senaa (Grad. Univ. Advanced Studies, KEK) Mar , 2005, LCWS U. in collaboration wit Sinya Kanemura (Osaka U) Yasuiro Okada (GUAS, KEK) Reference: PLB (2005) 1

2 Outline Introduction -Higgs pysics/cosmology interface Electroweak baryogenesis -Electroweak pase transition in te 2HDM Quantum corrections to te coupling constant -Collider signals of electroweak baryogenesis? Summary 2

3 Higgs pysics/cosmology interface Higgs pysics at colliders -Discovery of te Higgs boson(s) LHC) { gauge bosons -Measurements of te Higgs couplings wit (mass generation) fermions O(1)% accuracy (@ILC) ACFA Rep. TESLA TDR -Measurements of te Higgs self-couplings (reconstruction of te Higgs potential) O(10 20)% accuracy (@ILC) ACFA Higgs WG, Battaglia et al. Cosmology -Baryon Asymmery of te Universe (BAU) Attempts: n B /s GUTs, Affleck-Dine, Leptogenesis, EW baryogenesis, etc... Connection wit collider pysics Electroweak baryogenesis based on te Higgs potential at T 0 collider signals?? Higgs self-couplings Higgs potential at T = 0 We evaluate te coupling in te possible region of EW baryogenesis. 3

4 Conditions for Baryogenesis 3 requirements for generation of te BAU (Sakarov conditions) 1. baryon number violation 2. C and CP violation 3. out of equilibrium Baryogenesis in te electroweak teory -B violation spaleron process -C violation ciral gauge interation -CP violation -out of equilibrium KM-pase or oter sources in te extension of te SM 1st order pase transition 4

5 Spaleron process A saddle point solution of 4d SU(2) gauge-higgs system [Manton, PRD28 ( 83)] Energy spaleron instanton Transition rate Γ (b) sp (α W T ) 4 e E sp/t Ncs ( B = N f N CS ) (broken pase) Γ (s) sp (α W T ) 4 (symmetric pase) B violation process is effective at finite temperature, but is suppressed at T = 0 5

6 Baryogenesis mecanism ϕ vwall (b) Γsp < H broken pase CP f, f f,f (s) Γ sp >> H B+L symmetric pase Z Asymmetry of te carge flow of te particle ( due to CP violation) Accumulation of te carge in te symmetric pase B generation via spaleron process Decoupling of spaleron process in te broken pase Strongly 1st order pase transition Decoupling of te spaleron process at T < T c : Γ (b) sp /T 3 c < H(T c ) = ϕ c T c > 1 6

7 In principle, te SM fulfills all te tree Sakarov conditions, BUT Pase transition is not 1st order (for m > 114 GeV) out of equilibrium KM-pase is too small to generate sufficient BAU Extension of te minimal SM Higgs sector Two Higgs Doublet Model (2HDM) Minimal Supersymmetric Standard Model (MSSM) Next-to-Minimal Supersymmetric Standard Model (NMSSM) etc... In tis talk we consider 2HDM MSSM simple viable model 7

8 Two Higgs Doublet Model (2HDM) Introduce te additional Higgs doublet Φ FCNC suppression Φ 1 Φ 1, Φ 2 Φ 2 (Type I, II Yukawa int.) V THDM = m 2 1 Φ m 2 2 Φ 2 2 (m 2 3Φ 1 Φ 2 +.c.) + λ 1 2 Φ λ 2 2 Φ λ 3 Φ 1 2 Φ λ 4 Φ 1 Φ 2 2 [ ] ( λ5 + 2 (Φ 1 Φ φ + 2) 2 i +.c., Φ i=1,2 (x) = (x) ) 1 2 (v i + i (x) + ia i (x) ). m 2 3, λ 5 C (sources of explicit CP violation) In te MSSM: λ 1 = λ 2 = (g2 2 + g1)/4, 2 λ 3 = (g2 2 g1)/4, 2 λ 4 = g2/2, 2 λ 5 = 0 7 independent parameters m, m H, m A, m H ±: CP-even, CP-odd and carged Higgs boson masses α: mixing angle between and H, tan β = v 2 /v 1, (v= v v2 2 M = m 3 sin β cos β (soft-breaking scale of te Z 2 symmetry) 246 GeV) 8

9 Setup 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 Higgs VEVs: Φ 1 = Φ 2 = 1 ( ) 0 2 ϕ Tree-level potential V tree (ϕ) = µ2 2 ϕ2 + λ eff 4 ϕ4, µ 2 = m 2 3 m 2, λ eff = 1 4 (λ + λ 3 + λ 4 + λ 5 ) Field dependent masses of te Higgs bosons m 2 (ϕ) = 3 ( ϕ 2 2 m2 (v) v 2 1 ), 3 m 2 H(ϕ) = [m 2H(v) + 12 ] ϕ m2(v) M 2 2 v m2 (v) + M 2, m 2 A(ϕ) = [m 2A(v) + 12 ] ϕ m2(v) M 2 2 v m2 (v) + M 2, m 2 H ± (ϕ) = [m 2H± (v) + 12 ] ϕ m2(v) M 2 2 v m2 (v) + M 2. 9

10 Zero temperature 1-loop effective potential V 1 (ϕ) = n i m 4 i (ϕ) 64π 2 ( log m2 i (ϕ) Q 2 3 ) 2 (n W = 6, n Z = 3, n t = 12, n = n H = n A = 1, n H ± = 2) Finite temperature were IB,F (a 2 ) = V 1 (ϕ, T ) = T 4 [ 2π 2 0 dx x 2 log i=bosons (1 e ] n i I B (a 2 ) + n t I F (a) x 2 +a 2), ( a(ϕ) = m(ϕ) ) T Hig temperature expansion (a 2 1) I B (a 2 ) = π π2 12 a2 π ( 6 (a2 ) 3/2 a4 log a2 3 ) + O(a 6 ), 32 α B 2 ( I F (a 2 ) = 7π4 360 π2 24 a2 a4 log a2 3 ) ( ) + O(a 6 ), log α F (B) = 2 log(4)π 2γ E 32 α F 2 ϕ 3 -term comes from boson loops 10

11 Finite temperature Higgs potential For m 2 Φ (v) M 2, m 2 (v) m2 Φ (ϕ) m2 Φ (v)ϕ2 v 2, (Φ = H, A, H ± ) V eff D(T 2 T 2 0 )ϕ 2 ET ϕ 3 + λ T 4 ϕ4 were E = 1 12πv 3(6m3 W + 3m 3 Z + m 3 H + m 3 A + 2m }{{ 3 H ± ) } additional contributions Veff At T c, degenerate minima: ϕ c = 0, 2ET c λ Tc Te magnitude of E is relevent for te strongly 1st order pase transition We examine te strengt of te pase transition witout te ig temperature expansion. 0 T>Tc T=Tc T<Tc ϕ (GeV) 11

12 T c and ϕ c vs eavy Higgs boson mass m = 120 GeV, m Φ = m H = m A = m H ±, sin(β α) = tan β = M = M = 50 GeV (GeV) ϕ c Tc (GeV) ϕ c Tc m Φ (GeV) m Φ (GeV) 200 M = 100 GeV 200 M = 150 GeV (GeV) ϕ c Tc (GeV) ϕ c Tc m Φ (GeV) m Φ (GeV) 12

13 Contours of ϕ c /T c in te m Φ -M plane sin 2 (α β) = tan β = 1, m = 120 GeV, m Φ m A = m H = m H ± 450 Contour plot of ϕc/tc in te mφ-m plane mφ (GeV) pase transition is strongly 1st order ϕc/tc = 1 sin(α-β) = -1, tanβ = 1 m = 120 GeV mφ = mh = ma = mh M (GeV) For m 2 Φ M2, m 2, Strongly 1st order pase transition is possible due to te loop effect of te eavy Higgs bosons (ϕ 3 -term is effectively large) How large is te magnitude of te λ coupling at T = 0 in suc a region? 13

14 Quantum corrections to te coupling [S. Kanemura, S. Kiyoura, Y. Okada, E.S., C.-P. Yuan PL 03] φ f = + φ f + counter terms φ f (φ =, H, A, H ±, G 0, G ±, f = t, b) For sin(β α) = 1, λ tree = 3m2, (same form as in te SM) v [ λ 3m2 1 + c m 4 Φ (1 v 12π 2 m 2 M 2 ) 3 ] v2 m 2 Φ (Φ = H, A, H ± ) (c = 1 for neutral Higgs, c = 2 for carged Higgs) For m 2 Φ M2, m 2, te loop effect of te eavy Higgs bosons is enanced by m4 Φ, wic does not decouple in te large mass limit. (nondecoupling effect) 14

15 Contour plots of λ /λ in te m Φ -M plane sin 2 (α β) = tan β = 1, m = 120 GeV, m Φ m A = m H = m H ± Contour plot of λ /λ and ϕ c /T c in te m Φ -M plane 100 % 50 % m Φ (GeV) % 20 % 30 % For m 2 Φ M 2, m 2, λ/λ = 5% sin(α-β) = -1, tanβ = 1 50 m = 120 GeV mφ = mh = ma = mh M (GeV) Deviation of te coupling constant from te SM value becomes large. 15

16 Contour plots of λ /λ and ϕ c /T c in te m Φ -M plane sin 2 (α β) = tan β = 1, m = 120 GeV, m Φ m A = m H = m H ± [S.Kanemura, Y.Okada, E.S.] Contour plot of λ /λ and ϕ c /T c in te m Φ -M plane 100 % m Φ (GeV) % 20 % 30 % 50 % 100 λ/λ = 5% sin(α-β) = -1, tanβ = 1 50 m = 120 GeV mφ = mh = ma = mh M (GeV) ϕc/tc = 1 For m 2 Φ M 2, m 2, Pase transition is strongly 1st order, AND Deviation of coupling from SM value becomes large. ( λ /λ > 10%) 16

17 Contour plots of λ /λ and ϕ c /T c in te m Φ -M plane sin 2 (α β) = tan β = 1, m = 160 GeV, m Φ m A = m H = m H ± 450 Contour plot of λ /λ and ϕ c /T c in te m Φ -M plane % m Φ (GeV) % 20 % ϕc/tc = 1 λ/λ = 10 % sin(α-β) = -1, tanβ = 1 m = 160 GeV mφ = mh = ma = mh M (GeV) Te correlation between ϕ c /T c and λ /λ is almost same as te ligter m case. 17

18 Electroweak pase transition in te MSSM Ligt stop scenario [Carena, Quiros, Wagner, PLB380 ( 96)] M 2 Q M 2 U, m2 t, m 2 A m2 Z (sin(β α) 1) m 2 t 1 (ϕ, β) M 2 U + O(m 2 Z) + y2 t sin 2 β 2 Hig termperature expansion For M 2 U 0, (m t 1 m t ) E t 1 1 m 3 t 2π v 3 (1 X t 2 M 2 Q (1 X t 2 M 2 Q ) ϕ 2, (X t = A t µ cot β) ) 3/2 Stop contribution make te pase transition stronger enoug for successful electroweak baryogenesis. Collider signals = m t 1 < m t, m < 120 GeV In tis scenario, ow large is te magnitude of te λ coupling? 18

19 Deviation of te λ from te SM value Leading contribution of stop loop λ (MSSM) λ (SM) m 4 t (1 2π 2 v 2 m 2 X t 2 ) 3 MQ 2 = 3v4 m 2 tm 2 ( E t 1 ) 2. ϕ c /T c = 2E/λ Tc > 1 gives λ (MSSM) λ (SM) 6%. (for m = 120 GeV) In te MSSM, te condition of strongly 1st order pase transition also leads to large quantum corrections to te coupling constant. Numerical evaluation witout te ig temperature expansion work in progress 19

20 Summary We ave studied te collider signature of te successful electroweak baryogenesis. In te 2HDM For m 2 Φ M2, m 2 Pase transition is strongly 1st order. Te deviation of te λ coupling from te SM prediction becomes large. ( λ /λ > 10%) due to te nondecoupling effect of te eavy Higgs bosons In te MSSM wit ligt stop scenario λ /λ several % Suc deviations can be testable at a future e + e Linear Collider. EW baryogenesis Strongly 1st order pase transition Large loop correction to te λ coupling V eff (ϕ, T ) V eff (ϕ, 0) Measurement of 20

21 Sensitivity of te coupling at Linear Colliders δλ 3 /λ 3 [%] 60 Higgs self coupling sensitivity Int(L)=1 ab 1 e Z 100% efficiency e + Z λ 40 1 TeV e + e >νν e + e >Z combined 1.5TeV 500GeV e e + W W ν e λ ν e 20 1 TeV 1.5 TeV Higgs mass [GeV] [Y.Yasui et al ACFA WG] 21

22 Ring-improved Higgs boson masses were m 2 (ϕ, T ) = 3 2 m2 (v) ϕ2 v m2 (v) + at 2, m 2 H(ϕ, T ) = [m 2H(v) + 12 ] ϕ m2(v) M 2 2 v m2 (v) + M 2 + at 2, m 2 A(ϕ, T ) = [m 2A(v) + 12 ] ϕ m2(v) M 2 2 v m2 (v) + M 2 + at 2, m 2 H ± (ϕ, T ) = [m 2H± (v) + 12 ] ϕ m2(v) M 2 2 v m2 (v) + M 2 + at 2, m 2 G 0 (ϕ, T ) = m 2 G ± (ϕ, T ) = 1 2 m2 (v) ϕ2 v m2 (v) + at 2. a = 1 [ 12v0 2 6m 2 W (v) + 3m 2 Z(v) + 5m 2 (v) + m 2 H(v) + m 2 A(v) + 2m 2 H ± (v) 4M 2]. 22

23 Magnitude of te self-couplings λ i 3 Te magnitude of te self-couplings (sin(β-α)=tanβ=1, m =120 GeV) λ 1 /4π=λ 2 /4π=λ 3 /4π λ 4 /4π=λ 5 /4π m Φ (GeV) 23