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 6.4.2017 E-mail: tuomas.tenkanen@helsinki.fi Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models 6.4.2017 1 / 18
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 6.4.2017 2 / 18
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 6.4.2017 3 / 18
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. 1See e.g. Farrar & Shaposhnikov (1993). Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models 6.4.2017 4 / 18
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 6.4.2017 5 / 18
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. 2Kajantie et.al. (1996) Tuomas V.I. Tenkanen EW Baryogenesis and DR in BSM models 6.4.2017 6 / 18
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 6.4.2017 7 / 18
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 6.4.2017 8 / 18
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 ( i ω n τ ) , where ω n = 2 n π T contribute to 3d (tree-level) masses for 3d fields φ n � = 0 . ◮ Integrate out n � = 0 modes (scale separation) → effective 3d theory: � Z = D φ 0 D φ n exp ( − S ( φ 0 ) − S ( φ 0 , φ n )) (1) � = D φ 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 6.4.2017 9 / 18
Dimensional reduction ( # 2) ◮ There is scale separation in 3d masses: non-zero bosonic Matsubara modes and all fermionic modes have masses of order π T (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 6.4.2017 10 / 18
SM+real singlet µ h φ † φ + λ h ( φ † φ ) 2 V ( φ, σ ) = − 1 σ σ 2 + µ 1 σ + 1 3 µ 3 σ 3 + 1 2 µ 2 4 λ σ σ 4 + 1 2 µ m σφ † φ + 1 2 λ m σ 2 φ † φ + ◮ Scaling of µ m : ≃ µ 2 ∼ g 2 a m g b ≥ g 2 (2) µ 2 σ 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 6.4.2017 11 / 18
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!) 180 0 x = 0.050 0 0 x = 0.200 0 0 5 x = 0.300 0 160 . 1 1 0 . . 0 0 = = = x x x 140 T (GeV) x = 0.350 120 x = 0.250 0 0 0 2 . - = y y = 1.000 100 0 0 y = -1.000 0 . 0 0 = 0 y . 0 y = -3.000 - 4 = 0 y 0 . 0 - 5 = y 80 60 70 80 90 100 110 120 130 140 m H (GeV) 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 6.4.2017 12 / 18
Critical line in SM + superheavy singlet ◮ 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. 140 . 0 y = 0 . 2 5 0 137 . 5 135 . 0 132 . 5 y = 0 . 0 0 T (GeV) 0 130 . 0 127 . 5 x = 0.150 0 0 x = 0.100 5 0 y = -0.250 0 0 . . 0 0 125 . 0 = = x x 122 . 5 y = -0.500 120 . 0 160 180 200 220 240 260 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 6.4.2017 13 / 18
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. 350 300 250 µ m (GeV) 200 150 First order PT 100 µ 2 m ≥ µ 2 s x < 0 50 Action is complex 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 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 6.4.2017 14 / 18
Strong 1st order transitions and physical predictions ◮ Region in ( m s , λ m , µ m ) -space which have point x = 0 . 036 in critical line. 350 325 µ 2 m ≥ µ 2 σ 300 300 250 275 µ m (GeV) m S (GeV) 200 250 150 225 100 200 50 175 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 λ m For this value x = 0 . 036 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 6.4.2017 15 / 18
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 6.4.2017 16 / 18
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