EW Baryogenesis and Dimensional Reduction in SM extensions

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1 EW Baryogenesis and Dimensional Reduction in SM extensions Tuomas V.I. Tenkanen In collaboration with: T. Brauner, A. Tranberg, A. Vuorinen and D. J. Weir (SM+real singlet) J. O. Anderssen, T. Gorda, L. Niemi, A. Vuorinen and D. J. Weir (2HDM) L. Niemi, H. H. Patel, M. Ramsey-Musolf and D. J. Weir (SM+real triplet) University of Helsinki and Helsinki Institute of Physics Making the Electroweak Phase Transition (Theoretically) Strong, Umass, Amherst MA Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

2 Contents EW phase transition and baryogenesis. Scalar sector extensions of SM: singlet, doublet, triplet... 3d effective theory and dimensional reduction. Results in SM+real (superheavy) singlet Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

3 EW Baryogenesis Baryogenesis - mechanism to explain observed baryon-antibaryon asymmetry. General criteria for imbalance (Sakharov conditions) and candidate Electroweak (EW) baryogenesis: Baryon number violating interactions (sphaleron transitions). C and CP violations (no counterbalance) (EW interactions). Deviation from thermal equilibrium (1st order phase transition, bubble nucleation). Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

4 Ingredients for EW baryogenesis 1 Electroweak interactions cause C and CP violations. B conserved at tree level, but violated by sphalerons (unstable nonperturbative field configurations with topological charge). effective interaction for all left-handed fermions, which violates baryon and lepton number. At T = 0 vanishing rate, but rapid at high T. EW phase transition should be 1st order, and also strong: when Higgs vev is large, sphaleron transitions are "turned off" in the broken phase. 1 See e.g. Farrar & Shaposhnikov (1993). Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

5 EW phase transition and baryogenesis Morrisey et al. If 1st order transition: bubble nucleation. CP violation: different scattering properties for baryons and antibaryons antibaryons accumulate to unbroken side sphalerons turn antibaryon excess to baryons. Expanding bubble devours baryon excess a net creation of baryons (sphalerons suppressed at broken side). Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

6 EW baryogenesis fails in the SM However, with observed m H = 125 GeV, EW phase transition in the SM is not of first order, but a smooth crossover instead. 2 J. M. Cline Also: CP violation in the SM is too weak at relevant temperatures. 2 Kajantie et.al. (1996) Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

7 EW baryogenesis in BSM models BSM models with modified scalar sector could offer viable setup for EW baryogenesis: Strong 1st order phase transitition? Sufficient amount of CP-violation? SM+real singlet (non-z 2 ): "Toy model", no extra CP-violation, no stable dark matter. Two-Higgs-doublet model (2HDM): More CP-violation, but also more strict collider constraints. SM+real triplet: 2-step phase transition, gives more freedom to avoid constraints and also rich features due to more complicated symmetry breaking pattern. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

8 Non-perturbative analysis For EW baryogenesis, the most relevant features of phase transition are: character (1st, 2nd order or crossover), T c, sphaleron transition rate and bubble nucleation rate. Non-perturbative lattice simulations are the most robust way to compute these quantities. Lattice simulations are most conveniently performed in effective 3d theory, which is obtained from the full 4d theory by using the method of dimensional reduction. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

9 Dimensional reduction At high T, system looks like 3d for long distance physics (with length scales x >> 1/T ): Decomposition of fields: φ(x, τ) = n= φ n(x)exp(iω n τ), where ω n = 2nπT contribute to 3d (tree-level) masses for 3d fields φ n 0. Integrate out n 0 modes (scale separation) effective 3d theory: Z = Dφ 0 Dφ n exp( S(φ 0 ) S(φ 0, φ n )) (1) = Dφ 0 exp( S(φ 0 ) S eff (φ 0 )) In practise: match static correlators; requires loop corrections to many n-point correlators in 4d theory. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

10 Dimensional reduction (#2) There is scale separation in 3d masses: non-zero bosonic Matsubara modes and all fermionic modes have masses of order πt (superheavy), but masses of zero-modes are proportional to perturbative coupling (heavy or light fields). Strategy: construct effective 3d theory of zero-modes only, by integrating out all fermionic modes and non-zero bosonic modes. Up to certain accuracy, 3d theory gives then same results as the full theory. In practise one matches static correlators in both theories; requires a calculation of loop corrections of many n-point correlators in 4d theory (superheavy or heavy internal lines). Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

11 SM+real singlet V (φ, σ) = µ h φ φ + λ h (φ φ) µ2 σσ 2 + µ 1 σ µ 3σ λ σσ µ mσφ φ λ mσ 2 φ φ Scaling of µ m : µ2 m µ 2 σ g2a g b g2 (2) If b = 2 and a = 2 vertex with µ m produces mostly higher than g 4 order effects. Yet if b = 0 and a = 1 then, σ is "superheavy" and will be integrated out completely. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

12 Critical line in pure SM Dimensionless 3-d lattice parameters x, y are given in terms of physical quantities of full 4-d theory (DR: matching relations; note that also for superheavy singlet effective 3-d theory is same as in the SM!) x = x = x = x = x = x = T (GeV) y = y = y = y = mh (GeV) x = y = y = x = y = Actual lattice simulation is needed to analyse strength of phase transition. Critical line with 1st order transition: y 0 and 0 < x < 0.1. Usual conclusion: cross-over with physical Higgs mass 125 GeV. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

13 Critical line in SM + superheavy singlet x = x = Example of 1st order region, with fixed m s = 300 GeV and λ m = 0.7, λ σ = 0.25, µ 3 = 0. Countours in x, y are not very sensitive to the singlet self-couplings y = T (GeV) y = y = x = x = y = µ m (GeV) Caution: in shaded region µ 2 m > µ 2 σ, and our scaling assumption for portal coupling µ m is not respected. Furthermore also close to this region one cannot trust our approximation completely. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

14 Slice of parameter space with m s = 300 GeV In 1st order region (red) there exist critical line with y 0 and 0 < x < 0.1 with some 100 < T < 200 GeV µm (GeV) First order PT µ 2 m µ 2 s 50 x < 0 Action is complex λ m In blue region and near it our approximation is unreliable, and in black region potential of 3-d theory becomes unbounded. Furthermore gray region is excluded as 4-d parameters become complex. Obvious improvement to our approximation is to treat singlet as heavy or light field, and keep it in 3-d effective theory. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

15 Strong 1st order transitions and physical predictions I Region in (ms, λm, µm )-space which have point x = in critical line µ2m µ2σ 300 µm (GeV) ms (GeV) λm For this value x = we can use existing simulation results and calculate physical predictions for critical and nucleation temperature, latent heat of transition, bubble nucleation and sphaleron rates. One can also obtain prediction for gravitational wave signal (work in progress!). Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

16 Summary for SM + superheavy singlet We are (soon) able to demonstrate how to obtain physical predictions for SM extension, by using method of finite T dimensional reduction. Coming soon: actual predictions for quantities of interest, comparison to purely perturbative analysis and collider constraints. Further work (already underway): Perform DR to full g 4 -accuracy: mass parameter at 2-loop and relations to physical parameters at 1-loop level. Similar analysis for heavy or light singlet. When singlet remains in effective 3-d theory, actual new simulations are needed. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

17 2HDM and SM+real triplet models Performing DR is underway: In 2HDM at 3-d theory other doublet tends to be heavy (in contrast of being light) near transition in many regions in parameter space. Consequently other heavy doublet can be integrated out (together with adjoint scalar with heavy Debye mass) leaving yet again same effective 3-d theory as in the case of SM. In other regions of parameter space, new simulations are needed. In SM + real triplet new scalar fields remain in effective 3-d theory, and new lattice simulations are required. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18

18 Summary EW baryogenesis might explain baryon asymmetry, if some BSM physics can cause enough C and CP violations and strong 1st order phase transition. Lattice simulations can be used to study EW phase transition in BSM models. Effective 3-d theory is derived by using finite T dimensional reduction. Coming soon: results for SM + superheavy singlet model. Coming later in the future: similar analysis in SM + real singlet with singlet being dynamical field in the 3-d theory. Furthermore: Similar analysis in 2HDM and SM + real triplet. Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models / 18