Signals from a scalar singlet electroweak baryogenesis

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1 Signals from a scalar singlet electroweak baryogenesis Ankit Beniwal Based on: CoEPP and CSSM, Department of Physics, University of Adelaide, Australia A. Beniwal, M. Lewicki, J. D. Wells, M. White and A. G. Williams, JHEP 08 (2017) 108, [arxiv: ]; Ongoing work with M. Lewicki, M. White and A. G. Williams. Theory Seminar, University of Oslo, Norway September 8, 2017 Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 1/31

2 Outline 1 Background Motivation Electroweak baryogenesis (EWBG) Electroweak phase transition (EWPT) 2 Recent work Scalar singlet model Collider signals Gravitational wave signals Dark Matter signals Cosmological modification Summary 3 Ongoing work Extended scalar singlet model Preliminary results Future plans Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 2/31

3 1 Background Motivation Electroweak baryogenesis (EWBG) Electroweak phase transition (EWPT) 2 Recent work Scalar singlet model Collider signals Gravitational wave signals Dark Matter signals Cosmological modification Summary 3 Ongoing work Extended scalar singlet model Preliminary results Future plans Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 3/31

4 Motivation An imbalance between matter (baryons) and antimatter (antibaryons). A homogeneous and symmetric Universe = no net asymmetry, however η n B n B s Asymmetry must be generated dynamically require Sakharov conditions [1] C and CP violation; Baryon number (B) violation; Departure from thermal equilibrium. Electroweak baryogenesis (EWBG) is an attractive possibility generation of asymmetry via a strong first-order electroweak phase transition (EWPT). All ingredients for EWBG are present in the Standard Model (SM). The SM alone is not enough to explain the asymmetry require new physics beyond the SM (BSM). Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 4/31

5 Electroweak baryogenesis (EWBG) A hot, radiation-dominated early Universe with zero baryon charge and full EW symmetry, i.e., ϕ = 0. When T 100 GeV (EW scale), ϕ develops a VEV EW symmetry is broken. Baryon asymmetry is generated when the Universe transitions from ϕ = 0 to ϕ = 0. Fig. 1: Left: Expanding bubbles of the broken phase around the plasma in the symmetric phase. Right: Baryon production in front of the bubble walls. Figure from Ref. [2]. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 5/31

6 Electroweak phase transition (EWPT) Key ingredient is the effective potential V eff (h, T ) = V tree(h) + V 1-loop (h) + V T (h, T ). At T = T c (critical temperature), both h = 0 and h = 0 minima are degenerate. If a barrier exists between the two minima a first-order phase transition, i.e., v c T c 1. In the SM, v c/t c 1 only if m h 70 GeV [3] require new BSM physics. Fig. 2: Evolution of V eff (h, T ) with T for a first- (left) and second- (right) order phase transition. Figure from Ref. [4]. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 6/31

7 1 Background Motivation Electroweak baryogenesis (EWBG) Electroweak phase transition (EWPT) 2 Recent work Scalar singlet model Collider signals Gravitational wave signals Dark Matter signals Cosmological modification Summary 3 Ongoing work Extended scalar singlet model Preliminary results Future plans Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 7/31

8 Scalar singlet model Add a new scalar singlet S with Z 2 symmetry S S = a DM candidate. Tree-level potential after EWSB is V tree(h, S) = 1 2 µ2 h λh λ HSh 2 S µ2 S S λ SS 4. The physical S mass is m 2 S = µ2 S + λ HSv 2 0, where v 0 = µ/ λ 246 GeV = SM Higgs VEV at T = 0. Large λ HS generates a barrier between h = 0 and h = 0 minima a strong first-order phase transition. Consider m S > m h /2 and λ HS [0.2, 4π] with λ S = 1 [5]. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 8/31

9 Scalar singlet model In this model, the EWPT can proceed in two ways: If µ 2 S > 0 = a one-step phase transition, i.e., first ( h, S ) = (0, 0) (v 0, 0). order If µ 2 S < 0 = a two-step phase transition, i.e., ( h, S ) = (0, 0) second (0, 0) order first order (v 0, 0). Fig. 3: Parameter space of the model relevant for EWBG. Above (below) the red curve, µ 2 S (Tc) < 0 (> 0). Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 9/31

10 Collider signals Indirect collider searches provide a far better probe for EWBG than direct searches. 1 Modification of the triple Higgs coupling Given by λ 3 = 1 3 V (h, S = 0, T = 0) 6 h 3 m2 h + λ3 HS v3 0 2v 0 24π 2 m 2. h=v0 S Only measurable at the HL-LHC in hh production events difficult due to a small cross section. Estimated precision is 30% [6]. Estimated precision at 1 TeV ILC is 13% with 2.5 ab 1 [7]. 100 TeV collider can offer a much better precision ignored in our analysis due to its long time frame. 2 Modification of the Zh production at lepton colliders Fraction change relative to the SM value is σ Zh = 1 [ λ 2 HS v π 2 m F h ( )] m 2 h 4m 2, S where ( ) 1 1 2τ 2 τ(τ 1) F (τ) = 4 τ(τ 1) log 1 2τ + 2. τ(τ 1) Estimated precision at the ILC is 2%. FCC-ee/TLEP will probe it with 0.6% accuracy at 95% C.L [8]. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 10/31

11 Collider signals Fig. 4: Parameter space of the model relevant for EWBG along with the reach of various collider experiments. Regions above the dotted and dashed lines will be accessible at colliders. Here λ 3 = (λ SM 3 λ 3 )/λ SM 3 and T is the transition temperature. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 11/31

12 Gravitational wave signals Three main sources of gravitational waves (GWs) from a first-order phase transition: 1 Collision of the bubble walls [9]; 2 Sound waves generated after the transition [10]; 3 Magneto-hydrodynamical (MHD) turbulence in the plasma [11]. All three sources depend on the following two parameters. 1 Ratio of the released latent heat to the plasma background: Defined as [12] α = 1 [ ( dvew (V EW V f ) + T dv )] f, ρ R dt dt T =T where V f = value of the potential in the unstable vacuum and T = transition (nucleation) temperature, i.e., when the first bubbles start to form. 2 Inverse time of the phase transition: Defined as [ β H = T d ( )] S3 (T ) dt T T =T, where S 3 = O(3) symmetric action and H = Hubble rate. Using α and β, the combined GW spectra as as a function of the frequency (f) is Ω GW h 2 (f) = Ωh 2 col (f) + Ωh2 sw (f) + Ωh2 turb (f). Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 12/31

13 Gravitational wave signals + x + x Fig. 5: Parameter space of the model relevant for EWBG along with the regions accessible at future GW detectors. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 13/31

14 Gravitational wave signals + x + x Fig. 6: Spectra of GWs from the EWPT for a few example points shown in Fig. 5. Projected sensitivities of the current and future GW detectors are also shown. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 14/31

15 Dark Matter signals With Z 2 symmetry S S, S is a stable DM candidate. The S relic density must be consistent with the Planck measured value [13] The SI DM-nucleon cross section is Ω DM h 2 = σ SI = λ2 HS f 2 N 4π µ 2 m 2 n m 2, S m4 h where µ = m S m n/(m S + m n), m n = MeV and f N = 0.3 [14]. Constraints from the LUX (2016) experiment are imposed by requiring Ω S Ω DM σ SI σ LUX, where σ LUX = 90% C.L. upper limit from LUX (2016) [15]. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 15/31

16 Dark Matter signals Fig. 7: Parameter space of the model relevant for EWBG along with the constraints from the DM abundance and LUX (2016) experiment. Constraints from the vacuum structure are also taken into account, hence the green and red curves do not enter into the grey and yellow shaded regions. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 16/31

17 Cosmological modification Add a new component to the energy density of the early Universe modified Friedmann equation is H 2 ( ) ȧ 2 = 8π ( ρr a 3Mp 2 a 4 + ρ ) N a n, where a a(t) = scale factor and n > 4 dilutes before it modifies any cosmological measurements. First important measurement comes from the Big Bang Nucleosynthesis (BBN) the Hubble rate can be measured around that time. Observed expansion is consistent with a Universe filled with the SM radiation within experimental uncertainties, one can add a small fraction of ρ N. Translate the effective number of neutrino species into a modification of the Hubble rate H H = R BBN 43 Nν, eff where H R = H in the standard case and N νeff = (N νeff + 2σ) N SM ν eff = ( ) = Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 17/31

18 Cosmological modification Assume the new component has no direct interaction with the SM, i.e., ρ R a 4 = π2 30 gt 4, where g = number of d.o.f. in the SM usual result for the Hubble rate in the radiationdominated case 4π H R = 45 g T 2. M p Upper bound on the expansion rate at an earlier time is ( ) H H 2 = H R H 1 R BBN [ ( ) ] n 4 g 1/4 2 T, g BBN T BBN Fig. 8: Maximal modification of the Hubble rate without any conflicts with the experimental bounds. where T BBN = 1 MeV. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 18/31

19 Cosmological modification A non-standard cosmological history can have important consequences. Sphaleron bound: Simplest criterion for the decoupling of sphalerons Γ Sph = T 4 g ( v ) ( 7 B 0 exp 4π ) v H, 4π T g T where B 0 encapsulate the details of the SU(2) sphaleron calculation. Fig. 9: Values of v/t at T = T needed to avoid the washout of baryon asymmetry after the EWPT as function of n. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 19/31

20 Cosmological modification Dark Matter: Increased Hubble rate early freeze-out of S than in the standard case = larger abundance of S in the Universe today. Fig. 10: Parameter space of the model relevant for EWBG along with the DM abundance and direct detection constraints due to the cosmological modification. The direct detection limits shown are based on the S abundance with n = 6. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 20/31

21 Summary Studied the viability and detection prospects of the scalar singlet model. Focused on two attractive features, namely the possibility to facilitate EWBG and a DM candidate. Discussed various experimental probes and their reach in parts of the model parameter space, i.e., collider, gravitational and dark matter signals. Future gravitational wave detectors will have a better reach in accessible the parameter space relevant for EWBG than the future collider experiments. Correct DM abundance cannot be obtained simultaneously with a first-order phase transition. Only two regions allowing EWBG remains viable, the Higgs resonance region m S m h /2 and the high mass region, m S 700 GeV. Employed a simple cosmological model which redshifts faster than radiation (i.e., ρ N a n where n > 4). Increased DM abundance from the cosmological modification is followed by severe constraints from the direct DM searches. All the DM constraints can be avoided if the scalar S only serves as a mediator between a new DM candidate and the SM. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 21/31

22 1 Background Motivation Electroweak baryogenesis (EWBG) Electroweak phase transition (EWPT) 2 Recent work Scalar singlet model Collider signals Gravitational wave signals Dark Matter signals Cosmological modification Summary 3 Ongoing work Extended scalar singlet model Preliminary results Future plans Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 22/31

23 Extended scalar singlet model Model Lagrangian is where L = L SM + L S + L ψ + L int, L S = 1 2 ( µs)( µ S) µ2 S S µ 3S λ SS 4, L ψ = ψ(i/ µ ψ )ψ g S ψψs, L int = µ ΦS Φ ΦS 1 2 λ ΦSΦ ΦS 2. Remove µ 3 1S term by the shift symmetry S S + σ. If µ 3 = µ ΦS = g S = 0 = S is Z 2 symmetric scalar Higgs portal. Tree-level scalar potential is modified to V = V SM + V S + V int, where and V SM = µ 2 Φ Φ Φ + λ Φ (Φ Φ) 2 ( ) G + Φ = ( 1 φ + ig 0 ). 2 Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 23/31

24 Extended scalar singlet model Both φ and S can develop non-zero VEVs. At T = 0, φ T =0 = v 0, S T =0 = s 0 such that After EWSB, we get ( ) Φ = 1 0, S = s 0 + s. 2 v 0 + ϕ µ 2 Φ = λ Φv µ ΦS s λ ΦSs 2 0, µ 2 S = µ 3s 0 + λ S s µ ΦSv 2 0 2s λ ΦSv 2 0. L int leads to a mixing between ϕ and s rotate to mass-eigenstate basis ( ) ( ) ( ) h cos α sin α ϕ =, H sin α cos α s where α is the mixing angle. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 24/31

25 Extended scalar singlet model The physical h and H masses are m 2 h = M2 ϕϕ cos 2 α + M 2 ss sin 2 α 2M 2 ϕs sin α cos α, m 2 H = M2 ϕϕ sin 2 α + M 2 ss cos 2 α + 2M 2 ϕs sin α cos α. Tree-level potential must be bounded from below require λ Φ > 0, λ S > 0, λ ΦS > 2 λ Φ λ S. After EWSB, the fermion DM Lagrangian is L ψ = ψ(i/ m ψ )ψ g S ψψs, where m ψ = µ ψ + g S s 0 is the physical fermion DM mass. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 25/31

26 Extended scalar singlet model With m h = 125 GeV and v 0 = GeV, the model contains 7 free parameters m H, s 0, µ 3, λ S, α, m ψ, g S. Remaining parameters can be expressed as λ Φ = 1 ( m 2 2v0 2 h cos 2 α + m 2 H sin2 α ), µ ΦS = 2s 0 v 2 0 ( m 2 h sin 2 α + m 2 H cos2 α + µ 3 s 0 2λ S s 2 ) 0, λ ΦS = 1 v 0 s 0 [ (m 2 H m2 h ) sin α cos α µ ΦSv 0 ], µ 2 Φ = λ Φv µ ΦS s λ ΦSs 2 0, µ 2 S = µ 3s 0 + λ S s µ ΦSv 2 0 2s λ ΦSv 2 0. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 26/31

27 Preliminary results Use micromegas-v4.3.5 [16] to compute the fermion DM relic density and match with the Planck measured value [13], i.e., Ω DM h 2 = Fermion DM annihilates into SM particles via an h/h exchange. 1.0 Ωψh 2 = pippi v2.0 (NP: 3k, convthresh: 1e-2) 1.0 log 10 gs log 10 (mψ/gev) log 10 gs Best fit Diver Prof. likelihood mψ(gev) Profile likelihood ratio Λ = L/Lmax Fig. 11: Left: Fixed relic density contour in the (m ψ, g S ) plane for the full mass range. Right: A parameter space scan of the model using Diver-v1.0.2 [17]. In both plots, the remaining free parameters are set to m H = 250 GeV, s 0 = µ 3 = 300 GeV, λ S = 1 and α = π/4. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 27/31

28 Preliminary results Fermion DM-nucleon interaction occurs via an h/h exchange in t-channel a SI interaction. The SI DM-nucleon cross section is σ ψn SI = µ2 π G2 N, where N (p, n), µ = m ψ m N /(m ψ + m N ) and G N = g S sin α cos α v 0 ( 1 m 2 h ) 1 m 2 m N f N. H Impose limits from XENON1T (2017) [18] by requiring Ω ψ σ ψn SI σ XENON1T. Ω DM log 10 gs Best fit pippi v2.0 (NP: 2000, convthresh: 0.2) Diver Prof. likelihood Ωψh 2 = m ψ(gev) Fig. 12: Parts of the model parameter space that are consistent with the XENON1T (2017) experiment. The remaining free parameter values are same as in Fig Profile likelihood ratio Λ = L/Lmax Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 28/31

29 Preliminary results Find regions in the model parameter space where v c/t c 0.6 subject to the following constraints: V min (T = 0) V EW excluded; λ ΦS 2 λ Φ λ S potential unbounded from below; λ S 4π, λ Φ 4π, λ ΦS 4π non-perturbative couplings. pippi v2.0 (NP: 1000, convthresh: 0.3) s0(gev) Profile likelihood ratio Λ = L/Lmax m H(GeV) Vmin(T = 0) VEW λφs 2 λφλs λφs 4π pippi v2.0 (NP: 1000, convthresh: 0.3) µ3(gev) Profile likelihood ratio Λ = L/Lmax m H(GeV) Vmin(T = 0) VEW λφs 2 λφλs λφs 4π Fig. 13: Regions in the 2D parameter space where v c/t c 0.6 (blue shaded). Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 29/31

30 Preliminary results pippi v2.0 (NP: 1000, convthresh: 0.3) λs Profile likelihood ratio Λ = L/Lmax m H(GeV) Vmin(T = 0) VEW λφs 2 λφλs λφs 4π pippi v2.0 (NP: 2000, convthresh: 0.2) α(rad.) Profile likelihood ratio Λ = L/Lmax m H(GeV) Vmin(T = 0) VEW λφs 2 λφλs λφs 4π Fig. 14: Regions in the 2D parameter space where v c/t c 0.6 (blue shaded). Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 30/31

31 Future plans Imposed constraints from the relic density, direct detection and electroweak baryogenesis. Yet to implement constraints from Electroweak precision observables (EWPO) The new scalar modifies the gauge boson self-energy diagrams affects the oblique parameters S, T and U. Collider searches A mixing between ϕ and S leads to a modification in the signal strengths µ h = µ H = Γ SM h cos4 α Γ SM, h cos2 α + Γ h ψψ + Γ h HH Γ SM H sin4 α Γ SM. H sin2 α + Γ H ψψ + Γ H hh Goal: Perform a full 7D scan of the model parameter space using Diver-v1.0.2 [17] with these constraints. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 31/31

32 Backup slides Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 1/10

33 Effective potential One-loop correction to the T = 0 potential using the cutoff regularisation and on-shell scheme [19] V 1-loop (h, S) = i=h,χ,w,z,t,s [ ( n i 64π 2 m 4 i log m2 i m 2 3 ) ] + 2m 2 i 0i 2 m2 0i, where n {h,χ,w,z,t,s} = {1, 3, 6, 3, 12, 1} and m 0 = particle masses at the EW VEV h = v 0, S = 0. The field-dependent masses are m 2 W = g2 4 h2, m 2 Z = g2 + g 2 h 2, 4 m 2 t = y2 t 2 h2, m 2 χ = µ2 + λh 2 + λ HS S 2. The h and S masses are the eigenvalues of ( ) µ 2 + 3λh 2 + λ HS S 2 2λ HS hs M HS = 2λ HS hs µ 2 S + 3λ SS 2 + λ HS h 2. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 2/10

34 Effective potential The finite temperature corrections are V T (h, S, T ) = i=h,χ,w,z,s n i T 4 ( m 2 ) 2π 2 J i b T 2 + n i T 4 ( m 2 ) 2π i=t 2 J i f T 2, where ( m 2 ) J i b/f T 2 = dk k 2 log 1 exp 0 k 2 + m 2 i T 2. Resum the multi-loop infrared divergent contributions to boson longitudinal polarisation by adding thermal corrections to masses [20] ( g Π h (T ) = Π χ(t ) = T g 16 + λ 2 + y2 t Π S (T ) = T 2 ( λhs 3 + λ S λ S 12 ), Π W (T ) = 11 6 g2 T 2. ), Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 3/10

35 Effective potential For the two scalars, the thermally corrected masses are the eigenvalues of ( ) Π h (T ) 0 M HS +, 0 Π S (T ) whereas for Z and γ, they are In all other cases, we substitute The effective potential is ( 1 4 g2 h g2 T g gh g gh g 2 h g 2 T 2 m 2 i m2 i + Π i. V eff (h, S, T ) = V tree(h, S) + V 1-loop (h, S) + V T (h, S, T ). ). Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 4/10

36 Two-step phase transition Finding T probability of finding a field configuration with action S 3 within a volume V [21] ( Γ V T 4 exp S ) 3(T ), T where S 3 = 4π dr r 2 { 1 2 ( ) dh dr 2 ( ) ds 2 + V eff(h, S, T )}. dr Parametrise the path by φ(t) = (h(t), S(t)) which connects the initial and final vacuum [22]. Set d φ 2 ( ) dh 2 ( ) ds 2 = + = 1 dt dt dt such that d φ/dt path and d 2 φ/dt 2 path equations of motion (EOMs) are dφ ( d 2 t dt dr ) dt = ( V ), r dr ) 2 = ( V ). d 2 φ dt 2 ( dt dr Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 5/10

37 Two-step phase transition For a given path, finding the bubble profile means solving d 2 t dr dt r dr = dv dt to find t(r) subject to the boundary conditions dt dr = 0, t(r ) = V f. r=0 Choose a certain initial path, obtain dt/dr along the path and calculate N = d2 φ dt 2 ( ) dt 2 ( V ). dr Modify the path to obtain N = 0. After a few modifications, the action stabilises. Phase transition proceeds when at least one bubble is nucleated in every horizon volume, i.e., T dt T ( 1 H ΓV dt 1 H = T T 2π 45 M p πg eff T ) 4 ( exp S ) 3(T ) = 1, T where H = Hubble rate, V H d.o.f. at temperature T. = horizon volume and g eff = effective number of Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 6/10

38 Gravitational wave sources Bubble collisions Peak frequency is [9] The energy density is f col = β T ( g ) 1/6 Hz. vb 2 0.1v b H Ωh 2 col (f) = ( β H ) v 3 b v 2 b where the efficiency factor κ and the bubble wall velocity v b is ( ) κ = α α α , α + α v b = 1/ 3 + α 2 + 2α/ α ( κα ) 2 ( g ) 1/3 3.8 (f/fcol ) α (f/f col ) 3.8, For a very strong phase transition, the energy deposited into the fluid saturates to ( ) 2 α = v. T Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 7/10

39 Gravitational wave sources Sound waves created in the plasma Peak frequency is [10] The energy density is Ωh 2 sw(f) = ( β H MHD turbulence in the plasma Peak frequency is [12] The energy density is Ωh 2 turb (f) = ( β H f sw = β 1 T ( g ) 1/6 Hz. H v b ) 1 ( ) κα 2 ( g ) ( ) 1/3 f 3 ( ) 7 7/2 vb 1 + α 100 f sw (f/f sw) 2. f turb = β 1 T ( g ) 1/6 Hz. H v b ) 1 ( ) ɛκα 3/2 ( g ) 1/3 (f/f turb ) 3 (1 + f/f turb ) 11/3 vb 1 + α 100 [1 + 8πfa 0 /(a H )] where a (H ) = scale (Hubble) factor at T = T and ɛ 0.05 = efficiency factor. Ankit Beniwal Signals from a scalar singlet electroweak baryogenesis 8/10

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