dynamics of a two-step electroweak phase transition · sphaleron proc. must be quenched! via bubble...

Hiren [email protected]

May 2, 2014

Dynamics of a two-step Electroweak Phase Transition

ACFI Higgs Portal Workshop

Pavel Fileviez Pérez Michael J. Ramsey-Musolf Kai Wang

in Collaboration with

mailto:[email protected]

Hiren Patel 2

First order electroweak phase transition

B+L-violating EW Sphalerons convert baryons back to anti-leptons.

Sphaleron proc. must be quenched!

via bubble nucleation

baryons captured, and preserved.

Electroweak Baryogenesis and

Sakharov’s Criteria

e-�H Generation of particle/antiparticle asymmetry

C,CP B Generation of baryon

asymmetry

Thermal jumps

0 1

“EW Sphaleron”

Hiren Patel 3










asymmetry

Thermal jumps

0 1

“EW Sphaleron”

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.

?

Hiren Patel 3










asymmetry

Thermal jumps

0 1

“EW Sphaleron”





?

This talk (outline):set C, CP-violation aside

1. New Strategy to strengthen phase transition

Two-step phase transition

Connection to colliders

H.Patel, M.J. Ramsey-Musolf, PRD 88 (2013), 035013

P. Fileviez Pérez, H.Patel, M.J. Ramsey-Musolf, K. Wang. PRD 79 (2009), 055024

Hiren Patel 3










asymmetry

Thermal jumps

0 1

“EW Sphaleron”





?







Problem: This is gauge dependent

H.Patel, M.J. Ramsey-Musolf, JHEP 1107 (2011), 029

2. Gauge dependence

Hiren Patel

Previous Strategies

4

(to strengthen phase transition)

Tune parameters, or add new fields (DoF) to model to:

In general, very difficult.

Condition from requiring quenched sphalerons:

> related to model parameters

Make bigger.

Make smaller.

Central quantity of interest: Effective Potential

Hiren Patel

Previous Strategies

5

Extend model with extra scalar degrees of freedom.


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Previous Strategies

5


Effective potential a function of multiple order parameters.


Hiren Patel

Previous Strategies

5



In regions of parameter space, structure of free energy is such that there could be a multi-step phase transition.

step 2

step 1


Hiren Patel

Previous Strategies

5



In regions of parameter space, structure of free energy is such that there could be a multi-step phase transition.

step 2

step 1

If extra degrees of freedom are SM-gauge singlets, EW sphaleron not affected in essential way, !Condition on phase transition strength

?

Applied only on final step.


Hiren Patel 6

If extra scalar degrees of freedom carry gauge quantum numbers,

step 2

step 1

Sphalerons would couple to scalar field, phase transitions induced by these could influence them.

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.

(model-builder’s POV)

(but possibly measured at LHC)

Hiren Patel

SM — Formulation

7

Scalar Field Content:

Higgs doublet

2

SU(2) real triplet

3


Hiren Patel

SM — Formulation

7

Scalar Field Content:

Higgs doublet

2

SU(2) real triplet

3

Couplings:

Fermiophobic — incompatible hypercharge

(renormalizable)

Standard modelnew particle mass + self coupling Higgs portal interaction

Gauge-couplings: couples to W, Z and EM field

Scalar potential:

Four unmeasured parameters


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Phenomenological Constraints

8

In general, potential permits VEVs for both and .

Triplet VEV contributes to W mass (but not Z)

W mass Z mass

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8



W mass Z mass

SM relation: weak charged and neutral current rates upset

SM (L.O.) SM

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8



W mass Z mass

SM relation: weak charged and neutral current rates upset

SM (L.O.) SM

Experimentally, SM relation satisfied to high prec.

(95% conf.)

Translates to bound:

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9

Translates to bound:Experimentally, SM relation satisfied to high prec.

(95% conf.)

Easy and natural explanation of smallness:

depends linearly on (for small values):(1% EW scale)

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9


(95% conf.)



Technically natural, but make simplifying assumption:

Three unmeasured parameters

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Potential is now SO(3) symmetricand has


9


(95% conf.)



Technically natural, but make simplifying assumption:

Three unmeasured parameters

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Particle Spectrum

10

…(LHC)

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Particle Spectrum

10

…(LHC)

Three new scalar states

(LEP)

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Cirelli, Fornengo, Strumia arXiv:0706.4071 (hep-ph)

Particle Spectrum

10

…

(97%)( 3%)

(stable)

EW radiative corrections split degeneracy

(LHC)


(LEP)

Hiren Patel

Cirelli, Fornengo, Strumia arXiv:0706.4071 (hep-ph)

Particle Spectrum

10

…

Fix

(97%)( 3%)

(stable)

EW radiative corrections split degeneracy

(LHC)


(LEP)

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Zero-temperature Vacuum Structure

11

Electroweak vacuum

metastable vacuum

Region B

Electroweak vacuum

Region A

Pattern of phase transition influenced by zero-T vacuum structure

100 120 140 160 180 2000.0

0.5

1.0

1.5

2.0

A

B

EW vacuum metastable

model potential


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Zero-temperature Vacuum Structure

11

Electroweak vacuum

metastable vacuum

Region B

Electroweak vacuum

Region A

Finite temperature:

Baryon asymmetry generation in first step

Step

1 Step 2one step

Pattern of phase transition influenced by zero-T vacuum structure

100 120 140 160 180 2000.0

0.5

1.0

1.5

2.0

A

B

EW vacuum metastable

model potential


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’t Hooft—Polyakov Monopoles

12

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.

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12



Rubakov effect: scattering with Fermions violates B+L exactly like sphalerons.In addition to sphaleron processes, monopoles would also wipeout baryon asymmetryBut to what extent?

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12



Rubakov effect: scattering with Fermions violates B+L exactly like sphalerons.In addition to sphaleron processes, monopoles would also wipeout baryon asymmetryBut to what extent?

Depends on monopole concentration:

1. Kibble mechanism2. Thermal production (Dominant)

(monopole-antimonopole pair-production)

( )equil. monopole number density

Bigger Higher mass Lower concentration

Hiren Patel

100 120 140 160 180 2000.0

0.5

1.0

1.5

2.0

Baryon preservation

13

Step

1 Step 2 Step 1:

- Sphalerons rates suppressed - Monopole density suppressed

stronger Step 1 greater suppression

model potential

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100 120 140 160 180 2000.0

0.5

1.0

1.5

2.0

Baryon preservation

13

Step

1 Step 2 Step 1:



Qualitatively:

Smaller leads to stronger transition:

(gauge-dep) Step 10.44

0.50

0.56

0.62

0.68

0.74

model potential

Hiren Patel

100 120 140 160 180 2000.0

0.5

1.0

1.5

2.0

Baryon preservation

13

Step

1 Step 2 Step 1:



Qualitatively:

Smaller leads to stronger transition:

(gauge-dep) Step 10.44

0.50

0.56

0.62

0.68

0.74

model potential

1.2

4.0

Step 2:

- SM EW Klinkhamer-Manton Sphalerons rates suppressed

always sufficiently strong

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Modified Higgs Decay

14

Currently, most sensitive to

Higgs-portal coupling adds new contribution to amplitude

model potential

—20%

—30%

+10%

+20%

0%

1.0 0.5 0.0 0.5 1.0 1.5 2.0

80

100

120

140

160

180

200

—40%

—10%

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Modified Higgs Decay

15

Currently, most sensitive to

Higgs-portal coupling adds new contribution to amplitude

model potential

—20%

—30%

+10%

+20%

0%

1.0 0.5 0.0 0.5 1.0 1.5 2.0

80

100

120

140

160

180

200

—40%

—10% April 2014

) µSignal strength (0 1 2 3

ATLAS

-1Ldt = 4.6-4.8 fb∫ = 7 TeV s

-1Ldt = 20.7 fb∫ = 8 TeV s

= 125.5 GeVHm

0.28-

0.33+ = 1.55µ

γγ →H

0.15±

0.21±

0.23±

0.4-

0.5+ = 1.6µTtLow p 0.3±

0.6-

0.7+ = 1.7µTtHigh p 0.5±

0.6-

0.8+ = 1.9µmass (VBF)2 jet high

0.6±

1.1-

1.2+ = 1.3µVH categories 0.9±

0.35-

0.40+ = 1.43µ

4l→ ZZ* →H 0.14±

0.17±

0.33±

0.9-

1.6+ = 1.2µcategoriesVBF+VH-like

0.9- 1.6+

0.36-

0.43+ = 1.45µcategoriesOther 0.35±

0.28-

0.31+ = 0.99µ

νlν l→ WW* →H 0.12±0.21±

0.21±

0.32-

0.33+ = 0.82µ0+1 jet 0.22±

0.6-

0.7+ = 1.4µ2 jet VBF 0.5±

0.18-

0.21+ = 1.33µ

, ZZ*, WW*γγ→Comb. H

0.11±

0.15±

0.14±

Total uncertaintyµ on σ 1±

(stat)σ

(sys)σ

(theo)σ

1 20 3

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LHC Production:

16

1 charged track missing

Potential has Z2 symmetry: associated production of .

2 charged tracks missing

Distinctive LHC signature

model potential

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LHC Production:

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1 charged track missing

Potential has Z2 symmetry: associated production of .

2 charged tracks missing

Production cross section:

Distinctive LHC signature

model potential

Hiren Patel

as a CDM candidate

17

M. Cirelli, A. Strumia, M. Tamburini. Nucl. Phys. B787, 152 (2007)

0 0.5 1 1.5 2 2.5 3 3.50

0.05

0.1

0.15

0.2

observed abundance

no resum

Sommerfeld resum.

Rel

ic A

bund

ance

Annihilation channels: model potential

Hiren Patel

as a CDM candidate

17


0 0.5 1 1.5 2 2.5 3 3.50

0.05

0.1

0.15

0.2

observed abundance

no resum

Sommerfeld resum.

Rel

ic A

bund

ance

Annihilation channels:

Dark matter saturation at 2.7 TeV

model potential

Hiren Patel

as a CDM candidate

17


0 0.5 1 1.5 2 2.5 3 3.50

0.05

0.1

0.15

0.2

observed abundance

no resum

Sommerfeld resum.

Rel

ic A

bund

ance

Annihilation channels:

14 TeV LHC:production

Dark matter saturation at 2.7 TeV

model potential

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?







Problem: This is gauge dependent


Hiren Patel

(standard) Computation of

19

1. Track evolution of minima in as a function of temperature.

2. Numerically solve minimization and degeneracy condition equations:

1

2

decreasing temperature

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19



1

2


In a gauge theory, the effective potential is gauge dependent.

0 50 100 150 200

Standard Model

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19



1

2


In a gauge theory, the effective potential is gauge dependent.

0 50 100 150 200

Standard Model

Computed and depends on gauge parameter

Hiren Patel

Diagnosis & Resolution I

20

Determination of (or )Tc TN

h�iTc

& 1

Nielsen identity

gauge-independentTc

• valid order-by-order in loop-expansion !

• But, numerical solution to minimization condition

•

leads to inconsistent truncation in loop-expansion!

~Diagnosis~

1.

2.

Hiren Patel


20


h�iTc

& 1

Nielsen identity

gauge-independentTc



•


~Diagnosis~

1.

2.

Minimize by an inversion of series

V (�, T ) = V0 + ~V1 + ~2V2 + . . .

�min = �0 + ~�1 + ~2�2 + . . .

~Resolution~

Equation for ea. power of ; yields .

counts # of loops

Subs. into each side;

V (�min, T ) = V0(�0) + ~V1(�0, T )

“h-bar Expansion method”

Hiren Patel


21


h�iTc

& 1

Nielsen identity

gauge-independentTc



•


~Diagnosis~

1.

2.

Minimize by an inversion of series

V (�, T ) = V0 + ~V1 + ~2V2 + . . .

�min = �0 + ~�1 + ~2�2 + . . .

~Resolution~

Equation for ea. power of ; yields .

counts # of loops

Subs. into each side;

V (�min, T ) = V0(�0) + ~V1(�0, T )

T

VeffHfminL

phase 1phase2

phase 3

TC, 1TC, 2

Gauge-independent critical temperatures

Expression gives gauge independent minima of the effective potential.

consistent with Nielsen identity. (explicitly checked at 1-loop)

Hiren Patel

Diagnosis & Resolution II

22

h�iTc

& 1

Nielsen identity

gauge-independent

• h�i

• minimizing field is an inherently unphysical quantity. !

• Sets the sphaleron energy scale. !• Nielsen identity applies to

sphaleron energy.

~Diagnosis~

Determination of .h�i

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22

h�iTc

& 1

Nielsen identity

gauge-independent

• h�i



sphaleron energy.

~Diagnosis~

1. Compute sphaleron energy based on gauge-invariant effective action.

~Resolution~

2. Extract gauge-invariant scale from .


Hiren Patel


22

h�iTc

& 1

Nielsen identity

gauge-independent

• h�i



sphaleron energy.

~Diagnosis~

1. Compute sphaleron energy based on gauge-invariant effective action.

~Resolution~

2. Extract gauge-invariant scale from .

Gauge-invariant baryon number preservation criterion:

1.Use gauge invariant sphaleron scale !2. Determine Tc gauge-

invariantly

Bottom line


Hiren Patel

Back up

23

Hiren Patel



24

symmetric phase

bubble

B C,CP e-�H

e-�H

Bubble nucleation

bubblesymmetric phase

C,CP

B

(+2nd & 3rd gen.)

Thermal jumps

tunneling0 1

“EW Sphaleron”

Symmetric phase

�EW � (gT )4

bubble

Hiren Patel 25

“ —Expansion Method”

Calculation of the vacuum energy:

Key observation:“Brute force” minimization retains incomplete higher-order estimates. Must drop these incomplete estimates.


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Insert here

( counts # of loops)

1. ~

~

~


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Insert here


1. ~

~

~

Effective potential will be a series in .

2.~

eff ~ ~as will its derivative:

eff ~ ~


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Insert here


1. ~

~

~


2.~


eff ~ ~

Minimization condition:

eff min


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Insert here


1. ~

~

~


2.~


eff ~ ~


eff min

Solve by “inversion of series”:3.min ~ ~


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Insert here


1. ~

~

~


2.~


eff ~ ~


eff min


“tree-level VEV” quant. corr.


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Insert here


1. ~

~

~


2.~


eff ~ ~


eff min



Insert into minimization condition

eff min ~~ ~


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Insert here


1. ~

~

~


2.~


eff ~ ~


eff min




eff min ~~ ~

expand:

~


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establishes “tree-level VEV”

GENUINE one-loop correction


Insert here


1. ~

~

~


2.~


eff ~ ~


eff min




eff min ~~ ~

expand:

~

Each power of h-bar must satisfy equality.

...~


Hiren Patel 26


~

min ~ ~

“ —Expansion Method”Key observation:

“Brute force” minimization retains incomplete higher-order estimates. Must drop these incomplete estimates.


Hiren Patel 26


4. Insert into potential:eff min

~

min ~ ~




Hiren Patel 26


min ~ min ~ min


~

min ~ ~




Hiren Patel 26


min ~ min ~ min


~ ~~ ~ ~

~

min ~ ~




Hiren Patel 26


min ~ min ~ min


~ ~~ ~ ~

~

min ~ ~

expand once more~

~




Hiren Patel 26


min ~ min ~ min


~ ~~ ~ ~

~

min ~ ~

~

~

expand once more~

~




Hiren Patel 26


min ~ min ~ min


~ ~~ ~ ~

~

min ~ ~

~

~

Therefore, to order , the vacuum energy is obtained by evaluating the one-loop potential at the tree-level minimum .

~

expand once more~

~




dynamics of a two-step electroweak phase transition · sphaleron proc. must be quenched! via bubble...

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