Electroweak baryogenesis from a dark sector with K. Kainulainen and D. Tucker-Smith Jim Cline, McGill U. Moriond Electroweak, 24 Mar., 2017 J. Cline, McGill U. p. 1
Outline Has electroweak baryogenesis been ruled out? How adding a singlet scalar to Higgs sector helps orking model with dark matter producing the baryon asymmetry LHC constraints from MSSM searches J. Cline, McGill U. p. 2
Electroweak Baryogenesis EBG relies on a strongly 1st order electroweak phase transition, and CP violating interactions of fermions at the bubble walls, <H> = 0 <H> = v baryon # baryon conserved violation by sphalerons L R L R Needs new physics at the electroweak scale to get both ingredients. A highly testable model of baryogenesis. Has it been tested out of existence? J. Cline, McGill U. p. 3
EBG in the MSSM Strong EPT (with m h = 125GeV) needs light right-handed stop, m t R m h and heavy left-handed stop, m t L 100TeV Such a light stop increases hgg fusion production; essentially ruled out g g ~ t R h Getting large enough baryon asymmetry requires too much CP violation and too light charginos/neutralinos: sin = 1 000000 111111 000000 111111 000000 111111 000000 111111 Cline & Kainulainen, PRL 85 (2000) 5519 (hep ph/000272) observed BAU maximal CP phase ruled out by neutron EDM, need even lighter sparticles J. Cline, McGill U. p. 4
EBG in two Higgs doublet models MSSM is a two Higgs doublet model. More general 2HDMs have the needed ingredients for EBG. But the parameter space that works is extremely small. Results from MCMC scan of 10,000 models (JC, Kainulainen, Trott, 1107.3559). Only a handful give big enough asymmetry. J. Cline, McGill U. p. 5
Difficult to get strong phase transition First order phase transition requires potential barrier, 2nd Order 1st Order V(H) Higgs Field, H H Traditionally, the barrier came from finite-temperature cubic correction to potential, V = T 12π (m 2 i(h)) 3/2 = T (m 2 i,0 g 2 12π ih 2 c i T 2 ) 3/2 i It is typically not very cubic, and not big enough. Tends to give only a 2nd order or weak 1st order phase transition, v/t < 1. i J. Cline, McGill U. p. 6
Tree-level barrier with a singlet scalar A more robust way is to use a scalar singlet s. Choi & Volkas, hep-ph/9308234; Espinosa, Konstandin, Riva, 1107.5441 V high T T=0 s At T = 0, ESB vacuum is deepest, but at higher T, the h = 0, s 0 vacuum is lower energy. h The transition is controlled by the leading T 2 2 i finite-t potential. corrections in the Phase transition can easily be very strong. J. Cline, McGill U. p. 7
Singlet can help with CP violation JC, K. Kainulainen (1210.4196) introduce dimension-6 coupling to top quark, i(s/λ) 2 Q L Ht R, to give complex mass in the bubble wall, This gives the CP-violating interactions of t in the wall, producing CP asymmetry between t L and t R. MCMC no longer needed to find good models, a random scan suffices. But need Λ TeV to get large enough BAU. hat is the new physics at this scale? *Dimension-5 also works, but with dim-6, S can be stable dark matter candidate. J. Cline, McGill U. p. 8
Singlet can be dark matter candidate λ m h 2 S 2 coupling provides tree-level barrier, and Higgs portal interaction. λ m determines both relic density and cross section σ for s scattering on nucleons. For strong EPT, λ m 0.25, singlet can only constitute fraction f rel 0.01 of the total DM density, but still detectable JC & KK, 1210.4196 Define σ eff = f rel σ Blue: allowed by XENON100 (and mostly LUX) with λ m < 1 Orange: marginally excluded, depending on astrophysical uncertainty in local DM density. Yellow: allowed, with 1 < λ m < 1.5 J. Cline, McGill U. p. 9
Can we do better? EBG with singlet to facilitate EPT is less constrained, but needs additional new physics below the TeV scale. Can we find reasonable UV-complete (renormalizable) models that satisfy all criteria? Need to couple singlet to new fermions, with CP-violating couplings. CP asymmetry in new fermions must be communicated to sphalerons. J. Cline, McGill U. p. 10
Introduce Majorana fermion, A working model 1 2 [m S(ηP L η P R )] with Im(m η) 0. Creates CP asymmetry between helicities at bubble wall. Bonus: is a dark matter candidate To transfer CP asymmetry to SM leptons, need an inert Higgs doublet and coupling ( CP portal interaction ) y L Asymmetry is transferred by (inverse) decays, L, L, New coupling also controls the DM relic density, _ Note Z 2 symmetry,. DM must be rather than because of direct detection constraints. J. Cline, McGill U. p. 11
Scalar potential For simplicity we impose S S symmetry on the potential, V = 1 4 λ h(h 2 v 2 ) 2 1 4 λ s(s 2 w 2 ) 2 1 2 λ mh 2 S 2 and take (CP-conserving) pseudoscalar coupling to, 1 2 (m iηγ 5 S) giving no S or S 3 terms from fermion loop. (Must break S S slightly to avoid domain walls.) CP violation is spontaneous, due to S, disappears at T = 0: No constraints from EDMs At finite temperature, we just need leading O(T 2 ) correction. V can be written as V = λ h 4 ( h 2 v 2 c v2 c w 2 c S 2 ) 2 κ 4 S2 h 2 1 2 (T2 T 2 c )(c hh 2 c s S 2 ) where T c = [(λ h /c h )(v 2 v 2 c)] 1/2 = critical temperature, v c,w c = critical VEVs. J. Cline, McGill U. p. 12
The baryon asymmetry e need chemical potentials for helicity, and near the bubble wall: µ, µ, µ Baryon production via sphalerons depends only on µ, η B = 405Γ sph 4π 2 v w g T dzµ f sph (z)e 45Γ sphz/(4v w ) with Γ sph f sph (z) = local sphaleron rate in wall. µ comes from network of diffusion equations together with µ, µ, and velocity potentials u i, Γ d = decay rate for Γ hf = rate of helicity flips Γ el,i = elastic scattering rate for particle i Γ K i = thermal kinematic coefficients,i = rate of due to mass insertions S = source term from semiclassical force v w (m 2 θ ) J. Cline, McGill U. p. 13
Decay and scattering rates These processes govern the rates appearing in the diffusion equations. a Γ d Γ, el Γ, el Γ, el (Γ ) hf S a S f S f a H H S S a a x x * Γ x f f * * J. Cline, McGill U. p. 14
Decay and scattering rates Scattering is dominated by IR divergent processes a Γ d Γ, el Γ, el Γ, el (Γ ) hf S a S f S f a H H Intermediate fermion can go on shell S S a (Due to decay followed by inverse decay) x x * a Γ x Thermal width of t channel particle renders cross section finite f f * * J. Cline, McGill U. p. 15
Solution of diffusion equations Example: (subscript c = critical, n = nucleation) λ m y η m m m S w c w n v c v n T c T n η B η B,obs Ω dm h 2 0.45 0.66 0.51 56 124 102 85 111 82 140 129 112 0.9 0.12 J. Cline, McGill U. p. 16
Dark matter relic density e get thermal relic abundance from annihilations, ν ν Cross section is p-wave suppressed, e get right relic density for reasonable values of parameters, m m 50GeV, Ω dm h 2 DM allowed y m 100 150GeV, y = 0.6 0.7 y J. Cline, McGill U. p. 17
Direct detection: signal is small Higgs portal at one loop gives strongest interaction with nuclei: h s s h Cross section is 0.3 σ 2 η 4 λ 2 mm 2 m 4 N = = 16 2 π 5 m 4 10 48 cm 2 m4 h ell below LUX bound of 10 45 cm 2 Anapole moment γ 5 γ µ ν F µν is also induced at one loop, γ Cross section is velocity-suppressed, σ p v 2α2 y 4 m 2 p 16π 3 m 4 even smaller = 10 51 cm 2 Small S VEV would give tree-level Higgs portal: s h s h Cross section is suppressed by higgs-scalar mixing angle, σ 10 46 cm 2 ( θhs 0.03 ) 2 assuming scalar coupling ηs J. Cline, McGill U. p. 18
Sample models A region of parameter space that gives relic density and baryon asymmetry of right order of magnitude: y [0.6,0.8], η [0.1,0.9], λ m [0.3,0.6] m [40,60], m [100,140], v 0 v c [1,10], v c w c [0.01,2] log 10 Ω dm h 2 log 10 η Β /η obs (600 good models out of 380,000 tries in random scan) J. Cline, McGill U. p. 19
Sample models A region of parameter space that gives relic density and baryon asymmetry of right order of magnitude: y [0.6,0.8], η [0.1,0.9], λ m [0.3,0.6] m [40,60], m [100,140], v 0 v c [1,10], v c w c [0.01,2] Recall 2HDM result: Now we have good overlap J. Cline, McGill U. p. 20
Sample models A region of parameter space that gives relic density and baryon asymmetry of right order of magnitude: y [0.6,0.8], η [0.1,0.9], λ m [0.3,0.6] m [40,60], m [100,140], v 0 v c [1,10], v c w c [0.01,2] Couplings are reasonably small, we succeed in being UV complete J. Cline, McGill U. p. 21
LHC constraints Drell-Yan production of followed by ± ± is main collider signature. This resembles pp, 0 1 in the MSSM. ATLAS (1407.0350) has constrained this in Run 1, Limits are still weak, but could improve significantly in Run 2. Analysis has not yet been redone! J. Cline, McGill U. p. 22
Conclusions Singlet Higgs field can significantly enhance allowed parameter space for electroweak baryogenesis First example of EBG where CP asymmetry is generated by the dark matter. New CP portal mechanism to transport CP asymmetry into SM sector e find renormalizable example without fine tuning or too large couplings Potential for discovery in Run 2 of LHC (though not by direct DM detection) J. Cline, McGill U. p. 23
Backup slides J. Cline, McGill U. p. 24
EPT & observable gravity waves A strongly first order transition can produce gravity waves, potentially observable by elisa experiment. Huang, Long, ang (1608.06619) find elisa sensitivity Orange: 1st order; blue: strongly 1st order (EBG); green: very strongly 1st order (gravity waves) Small perturbation to hzz coupling may be observable at future colliders J. Cline, McGill U. p. 25
Nucleation temperature,t n T c For not too strong phase transitions, bubbles nucleate near the critical temperature. For stronger PTs, T n can be significantly < T c. Criterion to avoid sphaleron washout inside bubbles is T n v n T n > 1.1, not v c T c > 1.1 Must compute bubble action S 3 S 3 = 4π 0 drr 2( 1 2 (h 2 s 2 )V(h,s) V(0,s T ) ) and solve exp( S 3 /T n ) = 3 4π ( ) H(Tn ) 4 ( 2πTn T n S 3 ) 3/2 for T n. But finding bubble wall solution at T < T c is numerically tricky. J. Cline, McGill U. p. 26
Diffusion equations Formalism developed by JC, Joyce, Kainulainen hep-ph/0006119, refined by Fromme, Huber hep-ph/0604159 Split distribution function into two pieces, with d 3 pδf i 0, deviation from deviation from chemical equilibrium kinetic equilibrium encoded in µ i d 3 p(p z /ω)δf i u i : velocity potential To leading order in small quantities, Boltzmann eq. is i wall velocity Semiclassical force, Then take first two moments to derive diffusion equations, d 3 p(b.e.), d 3 p p z ω (B.E.) J. Cline, McGill U. p. 27