Dynamics of a two-step Electroweak Phase Transition

Transcription

1 Dynamics of a two-step Electroweak Phase Transition May 2, 2014 ACFI Higgs Portal Workshop in Collaboration with Pavel Fileviez Pérez Michael J. Ramsey-Musolf Kai Wang hiren.patel@mpi-hd.mpg.de

2 Electroweak Baryogenesis and Sakharov s Criteria C, CP First order electroweak e - Ĥ Generation of particle/ phase transition antiparticle asymmetry B Generation of baryon asymmetry via bubble nucleation baryons captured, and preserved. B+L-violating EW Sphalerons convert baryons back to anti-leptons. Thermal jumps EW Sphaleron Sphaleron proc. must be quenched! 0 1 2

3 First order electroweak e - Ĥ Generation of particle/ phase transition (energy) antiparticle asymmetry Sphaleron mass dependent on Higgs field value inside bubble via bubble nucleation At phase transition, need ratio to be large. baryons captured, and preserved. Electroweak Baryogenesis Kinetic theory: sphaleron rate related to its mass? and Sakharov s Criteria C, CP Baryon number preservation criterion on strength of phase transition. This talk (outline): set C, CP-violation aside B Generation of baryon asymmetry 1. New Strategy to strengthen phase transition Two-step phase transition H.Patel, M.J. Ramsey-Musolf, PRD 88 (2013), Connection to colliders P. Fileviez Pérez, H.Patel, M.J. Ramsey-Musolf, K. Wang. B+L-violating EW PRD Sphalerons 79 (2009), convert baryons back to anti-leptons. 2. Gauge dependence EW Problem: Sphaleron Thermal This is gauge dependent jumps Sphaleron proc. must H.Patel, M.J. Ramsey-Musolf, be quenched! JHEP 1107 (2011),

4 Previous Strategies (to strengthen phase transition) Central quantity of interest: Effective Potential Condition from requiring quenched sphalerons: > related to model parameters Tune parameters, or add new fields (DoF) to model to: Make Make bigger. smaller. In general, very difficult. 4

5 Previous Strategies Extend model with extra scalar degrees of freedom. Effective potential a function of multiple order parameters. In regions of parameter space, structure of free energy is such that there could be a multi-step phase transition. (to strengthen phase transition) If extra degrees of freedom are SM-gauge singlets, EW sphaleron not affected in essential way,! Condition on phase transition strength step 1 step 2? Applied only on final step. 5

6 If extra scalar degrees of freedom carry gauge quantum numbers, Sphalerons would couple to scalar field, phase transitions induced by these could influence them. (model-builder s POV) In this setup, it may be easier to generate a strong first order phase transition at step 1. underlying parameters controlling this step are largely unconstrained. step 2 (but possibly measured at LHC) step 1 6

7 Scalar Field Content: Higgs doublet 2 SM Formulation SU(2) real triplet 3 P. Fileviez Pérez, H.Patel, M.J. Ramsey-Musolf, K. Wang. PRD 79 (2009), Couplings: (renormalizable) Fermiophobic incompatible hypercharge Gauge-couplings: couples to W, Z and EM field Scalar potential: Standard model new particle mass + self coupling Higgs portal interaction Four unmeasured parameters 7

8 Phenomenological Constraints In general, potential permits VEVs for both and. Triplet VEV contributes to W mass (but not Z) W mass Z mass SM relation: weak charged and neutral current rates upset SM (L.O.) SM Experimentally, SM relation satisfied to high prec. Translates to bound: (95% conf.) 8

9 Phenomenological Constraints Experimentally, SM relation satisfied to high prec. Translates to bound: (95% conf.) Easy and natural explanation of smallness: depends linearly on (for small values): (1% EW scale) Technically natural, but make simplifying assumption: Potential is now SO(3) symmetric and has Three unmeasured parameters 9

10 Particle Spectrum Three new scalar states Fix (LEP) (LHC) (stable) (97%) ( 3%) EW radiative corrections split degeneracy Cirelli, Fornengo, Strumia arxiv: (hep-ph) 10

11 Zero-temperature Vacuum Structure Pattern of phase transition influenced by zero-t vacuum structure 2.0 Region B H.Patel, M.J. Ramsey-Musolf, PRD 88 (2013), Region A 1.5 A B EW vacuum metastable metastable vacuum Electroweak vacuum Electroweak vacuum model potential Step 1 Step 2 one step Finite temperature: Baryon asymmetry generation in first step 11

12 t Hooft Polyakov Monopoles Peculiar feature: Sigma phase resembles Glashow-Salam model of EW interactions (no weak-neutral currents) t Hooft and Polyakov showed stable magnetic monopole solution. => early universe populated by monopoles => subsequently wiped out after 2nd phase transition to EW phase. Rubakov effect: scattering with Fermions violates B+L exactly like sphalerons. In addition to sphaleron processes, monopoles would also wipeout baryon asymmetry But to what extent? Depends on monopole concentration: 1. Kibble mechanism 2. Thermal production (Dominant) (monopole-antimonopole pair-production) ( equil. monopole ) number density Bigger Higher mass Lower concentration 12

13 Baryon preservation Step 1 Step 2 model potential Step 1: - Sphalerons rates suppressed - Monopole density suppressed stronger Step 1 greater suppression Qualitatively: (gauge-dep) Step Smaller leads to stronger transition: Step 2: SM EW Klinkhamer-Manton Sphalerons rates suppressed always sufficiently strong 13

14 Modified Higgs Decay Currently, most sensitive to model potential Higgs-portal coupling to amplitude adds new contribution % +20% 0% 10% 20% 30% 40%

15 Modified Higgs Decay Currently, most sensitive to model potential Higgs-portal coupling to amplitude adds new contribution % +20% 0% % April % 30% 40% 15 ATLAS m H = GeV H γγ µ = ±0.23 ±0.21 ± Low p µ = 1.6 Tt -0.4 ± High p µ = 1.7 Tt -0.6 ± jet high mass (VBF) µ = ±0.6 VH categories µ = 1.3 ± 0.9 H ZZ* 4l µ = 1.43 ±0.33 ±0.17 σ(stat) Total uncertainty ± 1σ on µ σ(sys) σ(theo)

16 LHC Production: Potential has Z2 symmetry: associated production of. model potential Distinctive LHC signature 1 charged track missing 2 charged tracks missing Production cross section: 16

17 as a CDM candidate Annihilation channels: M. Cirelli, A. Strumia, M. Tamburini. Nucl. Phys. B787, 152 (2007) model potential Relic Abundance observed abundance no resum Sommerfeld resum. Dark matter saturation at 2.7 TeV 14 TeV LHC: production 17

18 Kinetic theory: sphaleron rate related to its mass (energy) Sphaleron mass dependent on Higgs field value inside bubble At phase transition, need ratio to be large.? Baryon number preservation criterion on strength of phase transition. This talk (outline): set C, CP-violation aside 1. New Strategy to strengthen phase transition Two-step phase transition H.Patel, M.J. Ramsey-Musolf, PRD 88 (2013), Connection to colliders P. Fileviez Pérez, H.Patel, M.J. Ramsey-Musolf, K. Wang. PRD 79 (2009), Problem: This is gauge dependent H.Patel, M.J. Ramsey-Musolf, JHEP 1107 (2011),

19 (standard) Computation of 1. Track evolution of minima in as a function of temperature. 2. Numerically solve minimization and degeneracy condition equations: In a gauge theory, the effective potential is gauge dependent. Standard Model 1 2 decreasing temperature Computed and depends on gauge parameter 19

20 Diagnosis & Resolution I Nielsen identity ~Diagnosis~ h i Determination & 1 of T c (or T N ) T c T c gaugeindependent ~Resolution~ h-bar Expansion method Minimize by an inversion of series counts # of loops valid order-by-order in loopexpansion! But, numerical solution to minimization condition leads to inconsistent truncation in loop-expansion! V (,T)=V 0 + ~V 1 + ~ 2 V min = 0 + ~ 1 + ~ Equation for ea. power of ; yields. Subs. into each side; V ( min,t)=v 0 ( 0 )+~V 1 ( 0,T) 20

21 Diagnosis & Resolution I Nielsen identity ~Diagnosis~ h i Determination & 1 of T c (or T N ) T c T c gaugeindependent Expression gives gauge independent minima of the effective potential. V eff Hf min L ~Resolution~ Minimize by an inversion of series T C, 2 phase 3 T C, 1 phase 2 counts # of loops phase 1 T valid order-by-order in loopexpansion! But, numerical solution to minimization condition leads to inconsistent truncation in loop-expansion! V (,T)=V 0 + ~V 1 + ~ 2 V min = 0 + Gauge-independent ~ 1 + ~ critical temperatures Equation for ea. power of ; yields. consistent with Nielsen identity. Subs. (explicitly into each checked side; at 1-loop) V ( min,t)=v 0 ( 0 )+~V 1 ( 0,T) 21

22 Diagnosis & Resolution II Bottom ~Diagnosis~ line Determination of h i. Gauge-invariant Nielsen hbaryon i gaugeindependent number preservation identity criterion: minimizing field is an inherently unphysical quantity.! Sets the sphaleron energy scale.! 1.Use gauge invariant sphaleron Nielsen identity applies to scale sphaleron energy.! 2. Determine Tc gaugeinvariantly h i T c & 1 ~Resolution~ 1. Compute sphaleron energy based on gauge-invariant effective action. 2. Extract gauge-invariant scale from. 22