Electroweak Baryogenesis - PDF Free Download

Electroweak Baryogenesis Eibun Senaha (KIAS) Feb. 13, 2013 HPNP2013 @U. of Toyama

Outline Motivation Electroweak baryogenesis (EWBG) sphaleron decoupling condition strong 1 st order EW phase transition (PT) Triple Higgs bosons coupling as a probe of EWBG 2HDM, MSSM Summary

Baryon Asymmetry of the Universe (BAU) Our Universe is baryon-asymmetric. /0(+ /0(* /0//) ' "# 356789%>#9?=;7%Ω @! ( /0/. /0/( /0/! /0() η n B n γ = n b n b n γ =(5.1 6.5) 10 10 (95% CL) D & BBB A " /0(' /0(!./!./ ' A$"% & 334 123 If the BAU is generated before T O(1) MeV, the light element abundances (D, 3 He, 4 He, 7 Li) can be explained by the standard Big-Bang cosmology. + C=$"%&./ )./ - )! "#$"% & Baryogenesis = generate right η (././. (! ' ) * +, -./ 356789:;8:&<8;89%65;=8%η././ gure 20.1: The abundances of He, D, He, and Li as predicted by the standa [PDG 2012]

Sakharov s criteria To get the BAU from initially baryon symmetric Universe, the following conditions must be satisfied. [Sakharov, 67] (1) Baryon number (B) violation (2) C and CP violation (3) Out of equilibrium BAU must arise After inflation (scale is model-dependent) Before Big-Bang Nucleosynthesis (T 1 MeV). What kind of model can satisfy these conditions?

Many possibilities [Shaposhnikov, J.Phys.Conf.Ser.171:012005,2009.] 1. GUT baryogenesis. 2. GUT baryogenesis after preheating. 3. Baryogenesis from primordial black holes. 4. String scale baryogenesis. 5. Affleck-Dine (AD) baryogenesis. 6. Hybridized AD baryogenesis. 7. No-scale AD baryogenesis. 8. Single field baryogenesis. 9. Electroweak (EW) baryogenesis. 10. Local EW baryogenesis. 11. Non-local EW baryogenesis. 12. EW baryogenesis at preheating. 13. SUSY EW baryogenesis. 14. String mediated EW baryogenesis. 15. Baryogenesis via leptogenesis. 16. Inflationary baryogenesis. 17. Resonant leptogenesis. 18. Spontaneous baryogenesis. 19. Coherent baryogenesis. 20. Gravitational baryogenesis. 21. Defect mediated baryogenesis. 22. Baryogenesis from long cosmic strings. 23. Baryogenesis from short cosmic strings. 24. Baryogenesis from collapsing loops. 25. Baryogenesis through collapse of vortons. 26. Baryogenesis through axion domain walls. 27. Baryogenesis through QCD domain walls. 28. Baryogenesis through unstable domain walls. 29. Baryogenesis from classical force. 30. Baryogenesis from electrogenesis. 31. B-ball baryogenesis. 32. Baryogenesis from CPT breaking. 33. Baryogenesis through quantum gravity. 34. Baryogenesis via neutrino oscillations. 35. Monopole baryogenesis. 36. Axino induced baryogenesis. 37. Gravitino induced baryogenesis. 38. Radion induced baryogenesis. 39. Baryogenesis in large extra dimensions. 40. Baryogenesis by brane collision. 41. Baryogenesis via density fluctuations. 42. Baryogenesis from hadronic jets. 43. Thermal leptogenesis. 44. Nonthermal leptogenesis. Electroweak baryogenesis (EWBG) is testable. directly linked to the low energy observables, e.g. Higgs physics.

Electroweak baryogenesis B violation: anomalous process (sphaleron) C violation: chiral gauge interaction [Kuzmin, Rubakov, Shaposhnikov, PLB155,36 ( 85) ] Sakharov s conditions CP violation: Kobayashi-Maskawa (KM) phase and other complex phases in the beyond the SM Out of equilibrium: 1 st order EW phase transition (EWPT) with expanding bubble walls symmetric phase broken phase BAU can arise by the growing bubbles.

Esph Energy sphaleron rates (/time/volume): (B+L) transition (B+L) current is violated by the quantum anomaly. But (B-L) is conserved. N CS (t) = 1 32π 2 sphaleron instanton -1 0 1 Tunneling probability: Γ instanton e 2S instanton = e 16π2 /g 2 2 10 162. sphaleron = static saddle point solution with finite energy of the gauge-higgs system. broken phase : thermal activation tunneling Ncs d 3 x ijk g 2Tr F 2 ij A k 23 g 2A i A j A k g 21B ij B k Γ (b) sph T 4 e E sph/t, symmetric phase : Γ (s) sph κ(α W T ) 4, 1 gen., 0 u L d L d L ν el N g N g gen., 0 (3qL i + ll) i unobservable! [N.S. Manton, PRD28 ( 83) 2019] α W = g 2 2/(4π), κ= O(1) (B+L)-violating process is active at finite T but is suppressed at T=0. e.g. Δ(B+L) 0 low T: tunneling high T: thermal activation i=1 left-handed fermion only

Baryogenesis mechanism (3) (1) (2) H:Hubble constant n B 0 start with zero baryon number. n B =0 n B (1) (2) (3) Φ =0 CP n B Φ =0 B+L n B Φ =0 n R b n R b n R b n R b n B =0 n B = n L b n L b =0 n L b n L b + n R b n R b =0 =0 n B = n L b n L b n L b n L b by Γ (s) B (>H) + n R b n R b n B =0 changed B =+1 e.g.,1 gen. ū L d L d L ν el L =+1 Γ (b) B <H is needed. If Γ (b) B >H n B 0

Γ (b) B <H B-changing rate in the broken phase is E sph is a sphaleron energy which is proportional to Higgs VEV Γ (b) B (T ) (prefactor)γ(b) sph T 3 (prefactor)e E sph/t, E sph v what we need: large Higgs VEV after the EWPT -> EWPT should be strongly 1 st order. sphaleron decoupling condition gives strong constraints on Higgs sector. In most cases, collider signals of EWBG is consequence of this condition.

More on Γ (b) B <H After the EWPT, the sphaleron process must be decoupled. Γ (b) B (T ) (prefactor)e E sph/t <H(T ) 1.66 g T 2 /m P g massless dof, 106.75 (SM) m P Planck mass 1.22x10 19 GeV E sph =4πvE/g 2 (g 2 : SU(2) gauge coupling), v T > g 2 42.97 + log corrections 4πE sphaleron energy gives the dominant effect. log corrections are subleading. Commonly, the sphaleron decoupling condition is evaluated at a critical temperature (Tc.).

Sphaleron energy For simplicity, we evaluate sphaleron energy at T=0. We take SM as an example. (U(1) Y is neglected) L = 1 4 F a µνf aµν +(D µ Φ) D µ Φ V 0 (Φ) V 0 (Φ) = λ Φ Φ v2 sphaleron energy: 2 2 E sph = 4πv g 2 E 3 2.5 2 1.5 1 0.5 [Klinkhammer and Manton, PRD30, ( 84) 2212] Higgs mass (λ) -> E sph 0 0.001 0.01 0.1 1 1 0 100 1000 For m h = 126 GeV (λ =0.13), E1.92 v T > 1.16

SM EWBG It turned out that the SM EWBG was ruled out. KM phase is too small to generate the observed BAU. [Gavela et al, NPB430,382 ( 94); Huet and Sather, PRD51,379 ( 95).] 130 The Standard Model crossover i EWPT is a crossover for m H >73 GeV. 120 symmetric phase f..." [Kajantie at al, PRL77,2887 ( 96); Rummukainen et al, NPB532,283 ( 98); Csikor et al, PRL82, 21 ( 99); Aoki et al, PRD60,013001 ( 99), Laine et al, NPB73,180( 99)] (LHC exp., m H =126GeV) > [.~ ll0 100 90 1 st order... 2nd order endpoint 2 nd order end point -> New Physics is required. 80 50 i L i 60 70 80 90 mh/gev Many directions to go: SUSY models or non-susy models etc.

1 st and 2 nd order EWPTs This is what the 1 st and 2 nd order PTs look like. order parameter = Higgs VEV EWBG requires 1 st order PT [From K. Funakubo s slide]

1 st and 2 nd order EWPTs This is what the 1 st and 2 nd order PTs look like. order parameter = Higgs VEV EWBG requires 1 st order PT A negative contributions is necessary. [From K. Funakubo s slide]

1 st and 2 nd order EWPTs This is what the 1 st and 2 nd order PTs look like. order parameter = Higgs VEV EWBG requires 1 st order PT A negative contributions is necessary. e.g. Bosonic thermal loop [From K. Funakubo s slide] V (boson) 1 const m(v) 3/2 T

SM EWPT at 1-loop order Veff V eff D(T 2 T 2 0 )ϕ 2 ET ϕ 3 + λ T 4 ϕ4 T =TC λ TC 4 ϕ2 (ϕ v C ) 2 0 T>Tc T=Tc T<Tc 0 50 100 150 200 250 300 (GeV) sphaleron decoupling condition T C is defined at which V eff has two degerate minima. 1 st order EWPT is realized by the boson loops E SM 1 4πv 3 (2m3 W + m 3 Z) 0.01 v C = 2ET C λ TC v C T C = 2E λ TC λ TC λ = m 2 h SM /(2v 2 ) Γ (b) B <H v C T C > 1 = m h SM < 48 GeV excluded by LEP way out: enhance E by adding new bosons. = cubic coeff. quartic coeff.

Caveat Scalar does not always play a roll. Suppose the scalar mass is given by m 2 = M 2 + λv 2 M : M 2 λv 2 nondecoupling decoupling λ : V eff λ 3/2 T v 3 M 2 λv 2 V eff M 3 T mass parameter in the Lagrangian coupling between Higgs and a scalar 3/2 1+ M 2 λv 2 1+ λv2 M 2 3/2 contribute does not requirements: 1. large coupling λ, 2. small M nondecoupling scalar E = E SM + E v C T C

Triple Higgs boson coupling as a probe of EWBG EWBG signal can appear in the triple Higgs boson coupling.

2 Higgs doublet model (2HDM) Additional Higgs doublet is added to the SM Higgs sector. To suppress the FCNC processes, Z 2 symmetry is imposed Higgs potential Φ 1 Φ 1, Φ 2 Φ 2 (Type I, II etc) V 2HDM = m 2 1Φ 1 Φ 1 + m 2 2Φ 2 Φ 2 (m 2 3Φ 1 Φ 2 + h.c.) + λ 1 2 (Φ 1 Φ 1) 2 + λ 2 2 (Φ 2 Φ 2) 2 + λ 3 (Φ 1 Φ 1) 2 (Φ 2 Φ 2) 2 + λ 4 (Φ 1 Φ 2) 2 (Φ 2 Φ 1) 2 λ5 + 2 (Φ 1 Φ 2) 2 charged Higgs + h.c., φ + i Φ 1,2 (x) = (x) 1. 2 v i + h i (x)+ia i (x) m 2 3,λ 5 C Higgs VEV 6 free parameters (v and m h are known.) m h, m H, m A, m H ± α : mixing angle between h and H tan β = v 2 /v 1, (v = v 2 1 + v2 2 246 GeV) CP-even Higgs CP-odd Higgs M 2 = m 2 3/(sin β cos β)

Quantum corrections to hhh coupling Loop corrections of heavy Higgs bosons [S. Kanemura, S. Kiyoura, Y. Okada, E.S., C.-P. Yuan, PLB558 (2003) 157] h h h For sin(β α) = 1 λ 2HDM hhh 3m2 h v 1+ (SM-like limit) Φ=H,A,H ± c 12π 2 m 4 Φ m 2 h v2 1 M 2 m 2 Φ 3 c=1(2) for neutral (charged Higgs bosons) 2 kinds of large mass limits m 2 Φ M 2 + λ i v 2. For M 2 λ i v 2 (m 2 Φ λ iv 2 ), the quantum corrections would grow with m 4 Φ. nondecoupling limit (coupling constants get large) For M 2 λ i v 2 (m 2 Φ M 2 ), the quantum corrections would be suppressed. ordinary decoupling limit (1/mass) Loop corrections are sizable if the heavy Higgs bosons have nondecoupling property. (Successful EWBG enforces the former limit.)

Correlation between Δλhhh/λ SM hhh and vc/tc [S. Kanemura, Y. Okada, E.S.,PLB606 (2005) 361] 450 400 Contour plot of hhh / hhh and c /T c in the m -M plane 100 % 350 50 % EWPT is strongly m (GeV) 300 250 200 10 % 20 % 30 % 1 st order 150 100 hhh/ hhh = 5% sin( - ) = -1, tan = 1 50 mh = 120 GeV m = mh = ma = mh +- 0 0 20 40 60 80 100 120 140 M (GeV) c/tc = 1 Heavy Higgs boson loops enhance the 1 st order EWPT E 2HDM For vc/tc>1, Δλhhh/λ SM hhh is greater than (10-20)%.

How about the MSSM?

Light stop scenario [Carena, Quiros, Wagner, PLB380 ( 96) 81] requirements: 1. large coupling λ, 2. small M top Yukawa small soft SUSY mass LEP bound on m H ρ parameter stop mass m 2 t 2 m 2 t 1 = m 2 q + y2 t sin 2 β 2 = m 2 t R + y2 t sin 2 β 2 m 2 q m 2 t R,X 2 t, X t = A t µ/ tan β. 1+ X t 2 v 2 + O(g 2 ) m 2 q, m 2 q 1 X t 2 v 2 + O(g 2 ). m 2 q At finite T, there is a thermal correction, T m 2 t R O(T 2 ) > 0. To have a large loop effect, m 2 t R + T m 2 t R m 2 t R (T ) m 2 t R + T m 2 t R =0 m 2 t R < 0 must be small. Charge-Color-Breaking vacuum m t 1 <m t light stop is needed!! X t = 0 (no-mixing) maximizes the loop effect

Δλhhh/λ SM hhh Coefficient of cubic term in Veff(T) V eff (E SM + E t 1 )Tv 3 E t 1 + y3 t sin 3 β 4 2π Deviation of hhh coupling λ MSSM hhh λ SM hhh m 4 t 2π 2 v 2 m 2 h 1 X t 2 1 X t 2 m 2 q For m h = 126 GeV, tan β = 10, X t =0 m 2 q 3 = 3/2. 2v4 m 2 t m 2 h (E t 1 ) 2 λ MSSM hhh λ SM hhh 0.05 Size of the loop effect is fixed by the top Yukawa coupling. SUSY models based on the strong dynamics can have a larger coupling constant, so the deviation can be larger. (Toshifumi Yamada s talk)

Current status of MSSM EWBG t 1 = mostly right-handed. EWPT can be strong 1 st order if m H < 127 GeV, m t 1 < 120 GeV [M. Carena, G. Nardini, M. Quiros, CEM. Wagner, NPB812, (2009) 243] This light stop scenario is now in tension with the current LHC data. In this scenario, σ(gg -> H), Γ(H->γγ), Γ(H->VV) has no drastic change. Enhanced σ(gg -> H -> VV) is not favored by the LHC data. [D. Curtin, P. Jaiswall, P. Meade., arxiv:1203.2932] For mh 125 GeV, MSSM EWBG is ruled out at greater than 98% CL (ma>1 TeV), at least 90% CL for light value of ma (~300 GeV) loophole [M. Carena, G. Nardini, M. Quiros, CEM. Wagner, arxiv:1207.6330] If m χ 0 1 < 60 GeV, Higgs invisible decay mode is open. reduce σ(gg -> H -> VV) tension may be loosen. MSSM EWBG is not fully excluded but is more and more unlikely.

Beyond the MSSM Next-to-MSSM (NMSSM) nearly-mssm (nmssm) W NMSSM λsh u H d + κ 3 S3 W nmssm λsh u H d + m2 12 λ S U(1) -extended-mssm (UMSSM) W UMSSM λsh u H d 1 st order EWPT is driven by singlet Higgs 4 Higgs doublets+singlets-extended MSSM (Toshifumi Yamada s talk) W = λ H d Φ u ζ + H u Φ d η H u Φ u Ω H d Φ d Ω + + n Φ Φ u Φ d + n Ω (Ω + Ω ζη) µ(h u H d n Φ n Ω ) µ Φ Φ u Φ d µ Ω (Ω + Ω ζη). 1 st order EWPT is driven by extra charged Higgs In the beyond the MSSM, the light stop is not necessarily required to have the strong 1 st order EWPT.

SM EWBG was ruled out. Summary Nondecoupling scalar is one of the possibilities to overcome the issue. Triple Higgs boson coupling is useful for probing the signal of EWBG. 2HDM: Δλhhh/λ SM hhh is greater than (10-20)% if the EWTP is strong 1st order. symmetric phase broken phase EW baryogenesis Large corrections to λ hhh MSSM EWBG is not fully excluded but is more and more unlikely due to the recent LHC data. (light stop scenario is not favored.) In the beyond the MSSM (e.g. NMSSM etc.), the light stop is not necessarily required to have the strong 1 st order EWPT.

Outlook To have the strong 1st order EWPT, the Higgs sector must be modified. Most of the EWBG scenarios would be tested by the LHC data., especially by σ Br (σ Br) SM Tree-level mixing driven 1 st order PT scenarios driven by (S inert) -> universal reduction of signal strengths. λ HS S 2 H 2 Thermal cubic term driven scenarios -colored scalar loop -> enhancement of σ(gg -> H) -charged scalar loop -> reduction of Γ(H->γγ)