Is electroweak baryogenesis dead? with K. Kainulainen and D. Tucker-Smith Jim Cline, McGill U. Higgs cosmology meeting, 28 March, 2017 J. Cline, McGill U. – p. 1
J. Cline, McGill U. – p. 2 See also G. Servant’s talk . . .
The SM BEH? J. Cline, McGill U. – p. 3
Englert & Brout No mention of the dynamics of the scalar whose VEV breaks the symmetry . . . J. Cline, McGill U. – p. 4
Higgs Equation of motion and mass of the Higgs field are front and center J. Cline, McGill U. – p. 5
Outline • Has electroweak baryogenesis been ruled out? • How adding a singlet scalar to Higgs sector helps • Working model with dark matter producing the baryon asymmetry • LHC constraints from MSSM ˜ τ searches J. Cline, McGill U. – p. 6
Why Electroweak Baryogenesis? Why is there more baryonic matter than antimatter in the universe? n B − n ¯ ∼ B = 6 × 10 − 10 n γ from CBM and BBN. Standard model cannot explain it. Leptogenesis is an elegant solution, but might never be testable. Electroweak baryogenesis relies on minimal new physics near the weak scale; it is the most testable framework. Is there still room for it to work after LHC Run 1? J. Cline, McGill U. – p. 7
Electroweak Baryogenesis EWBG relies on a strongly 1st order electroweak phase transition, and CP violating interactions of fermions at the bubble walls, <H> = 0 〈 〉 <H> = v 〈 〉 L R baryon # L baryon conserved R violation by sphalerons Needs new physics at the electroweak scale to get both ingredients. It is practially ruled out in MSSM and two Higgs doublet models. J. Cline, McGill U. – p. 8
EWBG in the MSSM Strong EWPT (with m h = 125 GeV ) needs light right-handed stop, m ˜ t R � m h and heavy left-handed stop, m ˜ t L � 100 TeV g Such a light stop increases hgg fusion production; h ~ t R essentially ruled out g Getting large enough baryon asymmetry requires too much CP violation and too light charginos/neutralinos: φ |sin | = 1 ������ ������ Cline & Kainulainen, ������ ������ ������ ������ ������ ������ PRL 85 (2000) 5519 (hep−ph/000272) maximal CP phase ruled out by neutron EDM, need even lighter observed sparticles BAU J. Cline, McGill U. – p. 9
EWBG in two Higgs doublet models MSSM is a two Higgs doublet model. More general 2HDMs have the needed ingredients for EWBG. 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. Demanding no Landau pole below 1 TeV is a crucial constraint! J. Cline, McGill U. – p. 10
Difficult to get strong phase transition First order phase transition requires potential barrier, 2nd Order 1st Order V(H) H Higgs Field, H Traditionally, the barrier came from finite-temperature cubic correction to potential, ∆ V = − T i ( h )) 3 / 2 = − T i h 2 + c i T 2 ) 3 / 2 � � ( m 2 ( m 2 i, 0 + g 2 12 π 12 π i 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 . J. Cline, McGill U. – p. 11
Tree-level barrier with a singlet scalar A more robust way is to couple a scalar singlet s to SM Higgs h . Choi & Volkas, hep-ph/9308234; Espinosa, Konstandin, Riva, 1107.5441 high T V T=0 h s At T = 0 , EWSB vacuum is deepest, but at higher T , the h = 0 , s � = 0 vacuum has lower energy. The transition is controlled by the leading T 2 φ 2 i corrections in the finite- T potential. Phase transition can easily be very strong. J. Cline, McGill U. – p. 12
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. What 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. 13
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 EWPT, λ m � 0 . 25 , singlet can only constitute fraction f rel � 0 . 01 of the total DM density, but still detectable 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 JC & KK, 1210.4196 J. Cline, McGill U. – p. 14
Can we do better? EWBG with singlet to facilitate EWPT 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. 15
Heavy top partners A simple UV completion is a vector-like top partner T R,L coupling to singlet, T L T R + y ′ ¯ t R ST L + M ¯ η ¯ T R Ht L Integrate out heavy state: H S x t L t R T Generates desired coupling ηy ′ ¯ t R SHt L M which can be CP-violating and large enough. ATLAS limit M � 900 GeV might be weakened by T → St decays. Here we consider a different model . . . J. Cline, McGill U. – p. 16
A working model with dark matter Introduce Majorana fermion χ , 1 χ [ m χ + S ( η P L + η ∗ P R )] χ 2 ¯ with Im( m χ η ) � = 0 . Creates CP asymmetry between χ helicities at bubble wall. Bonus: χ is a dark matter candidate To transfer CP asymmetry to SM leptons, need an inert Higgs doublet φ and coupling (“CP portal interaction”) y ¯ χφL τ χ χ Asymmetry is transferred by (inverse) decays, φ φ τ τ χ ¯ φ → ¯ L τ → φ, L τ χ, χ τ New coupling also controls the DM relic density, φ _ χ τ Note Z 2 symmetry φ → − φ , χ → − χ . DM must be χ rather than φ because of direct detection constraints. J. Cline, McGill U. – p. 17
Scalar potential For simplicity we impose S → − S symmetry on the potential, 4 λ h ( h 2 − v 2 ) 2 + 1 4 λ s ( S 2 − w 2 ) 2 + 1 V = 1 2 λ m h 2 S 2 and take (CP-conserving) pseudoscalar coupling to χ , 1 2 ¯ χ ( m χ + i η γ 5 S ) χ 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 � 2 c + v 2 V = λ h � + κ 4 S 2 h 2 + 1 c )( c h h 2 + c s S 2 ) h 2 − v 2 2 ( T 2 − T 2 c S 2 w 2 4 c c )] 1 / 2 = critical temperature, where T c = [( λ h /c h )( v 2 − v 2 v c , w c = critical VEVs. J. Cline, McGill U. – p. 18
Nucleation temperature, T n T c T n 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 v n v c > 1 . 1 , not > 1 . 1 T n T c Must compute bubble action S 3 � ∞ 2 ( h ′ 2 + s ′ 2 ) + V ( h, s ) − V (0 , s T ) dr r 2 � 1 � S 3 = 4 π 0 and solve � 4 � 2 πT n � 3 / 2 exp( − S 3 /T n ) = 3 � H ( T n ) 4 π T n S 3 for T n . Finding bubble wall solution at T < T c is numerically tricky. J. Cline, McGill U. – p. 19
Shape of the bubble wall h s / T n s h / T n Small wall width L w = ⇒ larger baryon asymmetry, but we need L w > few /T to justify semiclassical approximation for diffusion eqs. 1 ∼ 8 √ λ h v c L w ∼ for our working models. We find T n J. Cline, McGill U. – p. 20
The baryon asymmetry We need chemical potentials for χ helicity, φ and τ near the bubble wall: µ χ , µ φ , µ τ Baryon production via sphalerons depends only on µ τ , � ∞ 405 Γ sph dz µ τ f sph ( z ) e − 45 Γ sph z/ (4 v w ) η B = 4 π 2 v w g ∗ T −∞ with Γ sph f sph ( z ) = local sphaleron rate in wall. µ τ comes from network of diffusion equations together with µ χ , µ φ , and velocity potentials u i , Γ d = decay rate for φ → χτ Γ hf = rate of χ helicity flips Γ el ,i = elastic scattering rate for particle i τ → φ ∗ τ Γ × ,i = rate of φ ¯ K i = thermal kinematic coefficients due to χ mass insertions S χ = source term from semiclassical force ∼ v w ( m 2 χ θ ′ ) ′ J. Cline, McGill U. – p. 21
Diffusion equations Formalism developed by JC, Joyce, Kainulainen hep-ph/0006119, refined by Fromme, Huber hep-ph/0604159 Split distribution function into two pieces, deviation from deviation from chemical equilibrium kinetic equilibrium µ i encoded in d 3 p δf i ≡ 0 , d 3 p ( p z /ω ) δf i ∝ u i : “velocity potential” � � with 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 p z d 3 p (B . E . ) , ω (B . E . ) J. Cline, McGill U. – p. 22
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