Electroweak baryogenesis in the two Higgs doublet model

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1 Michael Seniuch Bielefeld University 1 Electroweak baryogenesis in the two Higgs doublet model M. Seniuch, Bielefeld University COSMO 05 Bonn August 2005 Work is done in collaboration with Lars Fromme and Stephan Huber Outline Introduction 2 Higgs doublet model Phase transition CP conserving case Phase transition CP violating case Baryon asymmetry Preliminary results Summary and Outlook

2 Michael Seniuch Bielefeld University 2 Introduction Aim: Explaining the BAU η = n B s = (8.9 ± 0.4) [Spergel et al. (2003)] Sakharov conditions i) B violation. ii) C and CP violation. iii) Deviation from thermal equilibrium. Electroweak baryogenesis Formation of bubbles of the Higgs field condensate at the electroweak phase transition (EWPT). Strong first order EWPT to avoid washout in the broken phase: ξ v c /T c 1

3 Michael Seniuch Bielefeld University 3 2 Higgs doublet model Zero-temperature potential: V 0 (Φ 1, Φ 2 ) = µ 2 1Φ 1 Φ 1 µ 2 2Φ 2 Φ 2 µ 2 3Φ 1 Φ 2 µ 2 3 Φ 2 Φ 1 + λ 1 2 (Φ 1 Φ 1) 2 + λ 2 2 (Φ 2 Φ 2) 2 + h 1 (Φ 1 Φ 2)(Φ 2 Φ 1) + h 2 (Φ 1 Φ 1)(Φ 2 Φ 2) + h 3 [(Φ 1 Φ 2) 2 + (Φ 2 Φ 1) 2 ] For the VEVs we choose: Φ 1 = 1 2 ( 0 v 1 ) and Φ2 = 1 2 ( 0 v 2 ) with the ratio v 2 /v 1 tan β = 1 and v = v v2 2 = 246 GeV. For simplification: µ 2 1 = µ 2 2, λ 1 = λ 2, and µ 2 3 = µ (CP violation for complex µ 2 3.) Particle spectrum: 3 Goldstone bosons: G +, G, G 0 4 heavy physical Higgs bosons: H +, H, A 0, H 0 1 light physical Higgs boson: h 0 Parameters of the potential: µ 2 1, µ 2 3, h 1, h 2, h 3, λ 1 Translation into physical parameters: m H ±, m A 0, m H 0, m h 0, v 1, µ 2 3 via minimum condition V 0 φ i VEV = 0 and mass matrix M 2 = 2 V 0 φ i φ j VEV.

4 Michael Seniuch Bielefeld University 4 Effective potential 1-loop finite temperature contribution: V eff,t = T 4 f B (m B /T ) + T 4 f F (m F /T ) 1 dx x 2 ln 2π 2 = T 4 B 1 2π 2 0 ( 1 exp( ) x 2 + m 2 B /T 2 ) ( ) 1 + exp( x 2 + m 2 F /T 2 ) T 4 dx x 2 ln F 0 Approximation of these integrals by high and low temperature expansion and a smooth interpolation in between. Effective potential: V eff (φ 1, φ 2 ) = V 0 + V eff,t Phase transition CP conserving case We explore the parameter region: 0 µ GeV GeV m light m h GeV 300 GeV m heavy m H 0 = m A 0 = m H ± 800 GeV [Turok, Zadrozny (1992)], [Davies, Froggatt, Jenkins, Moorhouse (1994)] Example: [Cline, Lemieux (1997)] µ 2 3 = GeV 2, m light = 120 GeV, m heavy = 600 GeV T c = GeV, v c = v c12 + v c22 = GeV ξ = 1.3 tan(β T ) = v c 2 v c1 = 0.97

5 Michael Seniuch Bielefeld University 5 V eff [GeV 4 ] φ = φ φ2 2 [GeV] φ 2 φ φ = φ φ2 2 [GeV]

6 Michael Seniuch Bielefeld University 6 Strength of the phase transition (µ 2 3 = GeV 2 ) ξ m light [GeV] m heavy [GeV] 1000 Phase transition CP violating case Complex µ 2 3 in V 0 =... µ 2 3Φ 1 Φ 2 µ 2 3 Φ 2 Φ with µ 2 3 = µ 2 3 e iϕ. VEVs: Φ 1 = 1 ( ) 0 2 v 1 e iθ 1 and Φ 2 = 1 ( ) 0 2 v 2 e iθ 2 We treat the CP violation as a small perturbation.

7 Michael Seniuch Bielefeld University 7 Minimizing the effective Potential V eff (φ 1, φ 2, θ θ 2 θ 1 ). Symmetric phase: v sym = 0, θ sym = ϕ Broken phase: v brk = v c > 0, θ brk ϕ θ = θ sym θ brk 0 Bubble wall profile: φ(z) = v c 2 ( 1 tanh z L W ) with L W =thickness of the bubble wall Restricting to the top quark, coupled only to Φ 2, in the limit tan(β T ) 1 we get: m top = m(z)e iθ t(z) with m(z) = y 2 φ(z) 2 and θ t (z) = 1 ( ( θ 1 + tanh z )) + θ brk 2 2 L W [Huber, John, Laine, Schmidt (1999)] Example: µ 2 3 = GeV 2, ϕ = 0.1, m light = 120 GeV, m heavy = 600 GeV T c = GeV, v c = GeV ξ = 1.2 tan(β T ) = 0.97 θ sym = ϕ = 0.1, θ brk = θ = 0.064

8 Michael Seniuch Bielefeld University 8 Results: θ becomes larger for increasing m heavy decreasing m light decreasing µ 2 3 increasing ϕ Baryon asymmetry Preliminary results We describe the evolution of the plasma by using classical Boltzmann equations with a fluid-type ansatz in the rest frame of the plasma. Expanding the transport equations in derivatives of the fermion mass. Taking into account source terms proportional to first order perturbations. Computing the asymmetry in the left-handed quark density. [Joyce, Prokopec, Turok (1995)], [Prokopec, Schmidt, Weinstock (2004)]

9 Michael Seniuch Bielefeld University 9 Example: µ 2 3 = GeV 2, ϕ = 0.1, m light = 120 GeV, m heavy = 600 GeV η log 10 (v W ) We can reach the right order of magnitude of the BAU.

10 Michael Seniuch Bielefeld University 10 Summary and Outlook Summary: Investigation of the EWPT in the 2 Higgs doublet model. Strong first order phase transition occurs for a wide parameter region. Introducing explicit CP violation in the potential. Treating the CP violation as a small perturbation. Enough CP violation is possible to generate the BAU. Parameters are in accord with the experimental electroweak constraints. Outlook: Testing the influence of different Higgs bosons. Computing the baryon asymmetry in the 2HDM. Analyzing the parameter region with regard to the BAU.