ew baryogenesis beyond the high t expansion

EW Baryogenesis beyond the High T Expansion

Ran Huo

IPMU

September 25, 2013

Ran Huo (IPMU) EW Baryogenesis beyond the High T Expansion September 25, 2013 1 / 41

Outline

Review of the SM and MSSM EW Baryogenesis.

Entropy release mechanism as new source of EW Baryogenesis.

A model designed for diphoton enhancement.

The vector-like supersymmetric model.


EW Baryogenesis

Genesis = Creation of cosmic matter antimatter asymmetry.

EW Baryogenesis = Asymmetry creation is associated with electroweak symmetrybreaking, or the turning on of the Higgs VEV.


How Sakharov's three conditions are ful�lled

Baryon number violating process: Nonperturbative anomalous sphaleron.

@�j�B � @�j

�L = ng

�g 2

2(4�)2W��

~W �� g 02

2(4�)2B�� ~B

��

�

Such interaction will create/annihilate 3ng quarks and ng leptons.

CP violation: Too small in the CKM matrix of the SM, but new physics may havelarge enough sources. Not Our Focus.

Deviation from thermal equilibrium: Latent heat in �rst order phase transition.


EW Symmetry Breaking: SU(2)L � U(1)Y ! U(1)EM

The SM tree level Higgs potential is

V0 = �1

4m

2h�

2 +1

4��4:

SUH2LL ´ U H1LY

U H1LEM U H1LEM

-400 -200 200 400Φ

VHΦL

The minimum is chosen � = v = mhp2�

= 246:2 GeV.

Masses are given to W� and Z 0 gauge boson, only photon associated withelectromagnetism remains massless.


Hmm... A Negative Mass Square Term

We don't know how it comes within the SM.

In extended model like the MSSM, it can be interpreted as an RGE running e�ectfrom high scales.

At uni�cation scale, it is positive and no EW symmetry breaking.

This is an example that symmetry should be restored at high scales.

Within the SM could the symmetry be restored at higher scales? ...Need tocompensate the negative mass square.

Sure!

QFT at �nite temperature always provides positive mass square corrections.


Field at Finite Temperature

In thermal quantum �led theory

Time: t ! �i� = � iT, Energy E = p0 ! 2n�iT .

Thermal propagator: � i

(2n�T )2 + ~p2 +m2.

Thermal loop: iT1X

n=�1

Zd3p

(2�)3=

i

�

1Xn=�1

Zd3p

(2�)3.


Thermal Mass Correction

Example: Higgs loop, contribution at �nite T

�m2 = ��(T ) = �i

Zd4p

(2�)4i�

i

p2

! TXn

Zd3p

(2�)3i�

�i

(2n�T )2 + ~p2= �T

Zd3p

(2�)3�

2�Tpcoth

�p

2�T

=1

2�

Zp dp

2�2

�1 +

2e�pT

1� e� p

T

�=

1

2�

Zp dp

2�2

�1 + 2

1Xn=1

e� np

T

�

!

�

2�2

1Xn=1

Zp dp e

� npT =

�

2�2

1Xn=1

T 2

n2=

�

2�2

�2T 2

6=

�T 2

12:

Mass corrected

�

1

4m

2h�

2 + cT2�2 +

1

4��4 + � � �

At high enough temperature

No Electroweak Symmetry Breaking.


Thermal Potential Correction

Resuming Higgs two point function, for each complex degree of freedom (+ for boson, �for fermion)

V1l Finite T = �T

2

Xn

Zd3p

(2�)3ln�(2n�T )

2+~p

2+ m

2+ �T

�= � � �

= �Z

d3p

(2�)3

�p~p2 + m2

2+ T ln

�1� e

�

q~p2+m2+�T

T

��

= � 1

64�2

�m2�2

lnm2

�2� 3

2

�� 12

!= V1(T=0)

+ �Z

d3p

(2�)3T ln

�1� e

�

q~p2+m2+�T

T

�= V1T

�mT

�

V1T

�mT

��

Zd3p

(2�)3T ln

�1� e

�

q~p2+m2

T

�� T 4

2�2JB=F

�mT

�

Quir�os, hep-ph/9901312.


The SM as an Example

With mh = 125 GeV,

What happens near T ' 170 GeV

Higgs VEV tunnels through the barrier from the � = 0 to nonzero values during thelast several frames.

During which every SM particle turns on mass (Not the masses measured today).


Cosmic Nucleation

In the real universe at the phase transition

1st order phase transition is described by bubble nucleation process.

Bubble with � 6= 0 expands into the � = 0 region near the speed of light.

Latent heat on the bubble wall makes departure from thermal equilibrium.

Nucleation temperature Tn: For a bubble to expand into the whole universe

SE

Tn' 140:

Critical temperature Tc : when a � 6= 0 local minimum satis�es V (�) = V (0).

Usually phase transition is right after passing the critical temperature,then Tn ' Tc .


Successful EW Baryogenesis

= To preserve the matter/antimatter asymmetry from being washed out.

= To freeze sphaleron process quickly after phase transition, by Boltzmannsuppression

� / �

�g 2

4�T

��3

mW (T )7e�EsT ;

Es � 8�mW (�)

g 2B(

�

g 2); B(

�

g 2) ' 1:96;

Es

Tc= 37:8

h�(Tc)iTc

:

= Phase transition strength

h�(Tc)iTc

& 1; The Goal.

M.E. Shaposhnikov, Nucl. Phys. B 287 (1987) 757.


Traditional EW Baryogenesis

= The high T expansion, namely the m(�)T

! 0 limit, in which

V1T =T 4

2�2JB=F

�mT

�=

T 4

2�2

8><>:��

4

45+�2

12

m2

T 2��6

�m2

T 2

� 32+O

�m4

T 4

�Boson

�7�4

360+�2

24

m2

T 2+O

�m4

T 4

�Fermion

:

= \The �2; �3; �4 system".

V (�;T ) = D(T 2 � T20 )�

2 � ET�3 +1

4��4:

At Tc and �c we have

Degenerated V (�c ;Tc) = D(T 2c � T

20 )�

2c � ETc�

3c +

1

4��4c = 0;

Minimum@

@�V (�;Tc)

��=�c

= 2D(T 2c � T

20 )�c � 3ETc�

2c + ��3c = 0:

Canceling the �2 term, we get�cTc

=2E

�:


EW Baryogenesis in the SM and MSSM

= A counting game of �3 term contribution.

�4 coe�cient � also receives small correction but not signi�cant.

In the SM only W� and Z 0 contribute (ignoring Higgs)

E =1

12�

�4�12g�3

+ 2�12

pg 2 + g 02

�3�= 6:4� 10�3 � � = 0:13

Note that only transverse DOF contributes.

In light stop scenario of the MSSM extra contribution comes from light unmixedright hand stop (m~t1

' 1p2yt�u)

E =1

12�

�4�12g�3

+ 2�12

pg 2 + g 02

�3+ 6� 1p

2yt sin�

�3�= 0:054 ' 1

2�

But it will raise problems such as in gluon fusion.


Outline






Large Unexplored Region on JB=F

The Boltzmann suppression is not that signi�cant as one just imagine

V1T

�mT

�= �

Zd3p

(2�)3T ln

�1� e

�p

~p2+m2

T

�� T 4

2�2JB=F

�mT

�Ran Huo (IPMU) EW Baryogenesis beyond the High T Expansion September 25, 2013 16 / 41

Some Argument for Going beyond the High T Expansion

Traditional EW baryogenesis always induces too light a new particle which mayalready be excluded.

New physics may introduce mass terms which are not related to Higgs VEV:

SUSY soft breaking masses, other vector-like masses, etc.

Currently the bounds are a few hundred GeVs.

Naive estimation: �c . 246:2 GeV, order one Yukawa, then the Yukawa mass iscomparable to the soft/vector-like mass.

With Tc � 200 GeV, the m(�)=T may have order one change, which inducesigni�cant change on JB=F even from start point of a few (not from zero of thetraditional case).


First E�ort: Fermions Contribute as Good as Bosons

Carena, Megevand, Quir�os and Wagner, Nucl. Phys. B 716 (2005) 319.

The special case of the neutralino/chargino mass matrices with M1 = M2 = ��,tan� = 1, arbitrary SU(2) gauge coupling h and U(1) gauge coupling h0 = 0.

Chargino/Neutralino mass square eigenstates m2(�) = M2 + h2�2, a total of 12DOF.


Entropy Release, or just Jump on JB=F

They call this e�ect as entropy release, since the m(�)=T ! 0 limit is just the

relativistic limit, in which the leading terms V1T = ��2

90T 4 or � 7

8�2

90T 4 are nothing

but the relativistic energy density for each bosonic and fermionic DOF. So they arerelated to entropy. We are to set free this entropy by turning on Higgs VEV anddeparting from the relativistic limit.

However, I think it is nothing but merely (and more intuitively) an upward jump onthe JB=F curve, associated with the Higgs VEV turning on.

We can go deep into the region where m(�)=T is a few.

We can consider multiple jumps, only the net contribution counts.


Some Common Features 1: Mass Matrix

The new particle mass (square) matrix usually have diagonal soft/vector-like massterms and o�-diagonal Yukawa mass terms.

Eigenvalues are solutions to a quadratic equation, usually with plus and minussquare roots

m�(�) =pM2 + a�2 � b�; or m2

�(�) = M2 + a�2 �

pb�4 + c�2; or � � �

The physical constraint is that sum of two dd�m�(�)

��=0

vanishes, or the � = 0 is

always a solution to the minimization dd�JB=F (

m(�)T

) =J0B=F

Tdd�m(�) condition.

If a term in mass is making m(�) overall heavier when the Higgs VEV is turned on,it contributes to EW baryogenesis.

If a term in mass is making m(�) split when the Higgs VEV is turned on, it does not(or even oppositely) contribute to EW baryogenesis.


Some Common Features 2: To Protect 125 and 246

Zero temperature one loop potential V1(T=0) are renormalized in a way that the SM

Higgs mass and Higgs VEV are not shifted (d2V1(T=0)

d�2= 0j�=v and

dV1(T=0)

d�= 0j�=v ).

If the mass square is m2(�) = a+ b�2, then the usual renormalized one looppotential is �ne

V1;i(T=0) = � gi

64�2

��m

2i (�)

�2�lnm2

i (�)

m2i (v)

� 3

2

�+ 2m2

i (�)m2i (v)

�:

In extended models the solution are

V1;i(T=0) = � gi

64�2

��m

2i (�)

�2lnm2

i (�) + ��2 + ��4�

� =1

2

�� 3!!0

v+ !02 + !!00

�ln! � 3

2

!!0

v+

3

2!02 +

1

2!!00

�

� =1

4v 2

��!!0v� !02 � !!00

�ln! +

1

2

!!0

v� 3

2!02 � 1

2!!00

�

where ! = m2i (v) and !

0 = dd�m2

i (�)��=v

, and so on.

In the 2HDM of MSSM I �nd the simple extension is not adequate to �x everycounter term.


Some Common Features 3: Supersymmetry for Quartic Coupling

Usually we need large Yukawa for a signi�cant jump on JPB=F .

However, it will induce large radiative corrections to the quartic coupling.For extra fermions it may render quartic coupling negative at high scales.For extra scalars it may develop other vacuum with lower zero point energy than ourEWSB one.

To avoid large corrections the trick for model building is to introduce nearlyunbroken supersymmetry.

Interestingly both bosonic and fermionic DOF contribute additively to phasetransition, but they cancel with each other on the quartic coupling RGE.


Outline






h! Excess: Alive or Die?

ATLAS 2012.7 result: � = 1:9� 0:5,

ATLAS 2013.3 result: � = 1:65� 0:2,

CMS 2012.7 result: � = 1:56� 0:43,

CMS 2013.3 result: � = 0:78+0:28�0:26

��MVA

(1:11+0:32�0:30)

��Cut Based

.

Practice is even worsethan I can expect lasttime.


The Fermionic Diphoton Excess Setup

Arkani-Hamed, Fan et al, arXiv:1207.4482

Charged fermion mass mixing matrix

MF� =

m

1p2y�

1p2y� m�

!

Mirror Leptonic: L;R � (1; 2)� 12and �L;R � (1; 1)�1,

L � �y cL��R � y�cL�

c R �m cL R �m��

cL�R + h:c::

Neutral fermion is 0.

Wino-Higgsino like: � (1; 2)� 12and � � (1; 3)0,

L � �p2y c

1�"��p2y�c"� 1�

p2y c

2��p2y�c� �m ( 1" 2+ 2" 1)�m��:

Induced neutral fermionic mixing

MF0 =

0@ 0 �m 1

2y�

�m 0 � 12y�

12y� � 1

2y� m�

1A :


The Supersymmetric Extension

Naive supersymmetry: same coupling, same degree of freedom, di�erent \soft"mass. No mixing in the bosonic component, the simplest boson mass square

M2S = m

2s +

1

2y2�2:

The model is just the SM plus a SUSY sector.

Step function beta coe�cient

1p2y �(0)

��(0)

+1p2y��(0)

� �(0)

= � 1p2y sin 2�F

�(0)1 �F

�(0)1 + interaction with F

�(0)2 :

By combinatorics, the 4 F�1 leg diagram, or the quartic RGE running from MF�1

to

MF�2, is suppressed by sin4 2�(')

Scalar \soft" mass can be solved with how much the quartic coupling runs

�� = � n�

64�2y4

0BB@ sin4 2�

2ln

M2S

M2

F�1

+2� sin4 2�

2ln

M2S

M2

F�2

1CCA� n0

64�2y4

0B@ sin4 2�

2ln

M2S

M2F02

+2� sin4 2�

2ln

M2S

M2F03

1CA :

RH, arXiv:1305.1973


Leptonic Model Benchmark 1

With �MF = 0:25 and �� = �0:5�SM

100100

150150

200200

250250

0.5

1

1.5

2

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

Yukawa

Cot

2Θ

0.0245

0.025

0.0255

0.0258

0.050.05 0.10.1 0.150.15 0.20.2

1.3

1.35

1.4

1.45

1.5

1.55

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

Yukawa

Cot

2ΘBlack: phase transition strength h�(Tc )i

Tc;

Red: Lightest fermion mass;

Grey Shaded: Excluded by Tc < 0;

Blue: Diphoton signal strength � ;

Green: Peskin - Takeuchi T parameter;

Purple: Peskin - Takeuchi S parameter.


Leptonic Model Benchmark 2

With �MF = 0:15 and �� = �0:5�SM

150150

200200

250250

300300

350350

400400

0.5

1

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

Yukawa

Cot

2Θ

0.0205

0.021

0.02150.050.05 0.10.1 0.150.15

1.2

1.25

1.3

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

Yukawa

Cot


Tc;




Green: Peskin - Takeuchi T parameter;



Wino - Higgsino Model Benchmark 1

With �MF = 0:25 and �� = �0:5�SM

100100

150150

200200

250250

0.5

1

1.5

2

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

Yukawa

Cot

2Θ

0.023

0.024

0.025

0.026

0.026

1.3

1.35

1.4

1.45

1.5

1.55

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

Yukawa

Cot


Tc;






Wino - Higgsino Model Benchmark 2

With �MF = 0:15 and �� = �0:5�SM

150150

200200

250250

300300

350350

400400

0.5

1

1.5

2

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

Yukawa

Cot

2Θ0.015

0.016

0.017

1.151.2

1.25

1.3

1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

2.0

Yukawa

Cot


Tc;






Discussion

Typical values: ms = 391 GeV, m = m� = 566 GeV, MS = 524 GeV, MF1 = 218GeV, MF2 = 915 GeV.

Wino-Higgsino is equivalent to tan� = 1, with custodial symmetry new physics haveno T parameter contribution.

Bosonic DOF: Mass just get overall heavier when the Higgs VEV is turned on.Useful for phase transition, bad for diphoton excess.

Fermionic DOF: Mass just get split when the Higgs VEV is turned on.Useful for diphoton excess, bad for phase transition.


Outline






Motivation

Two new generations of the SM fermions with vector-like masses mixing.

With supersymmetry (so that their sparticles):The gauge coupling RGE are modi�ed in a way that they can still get uni�ed at aroundthe GUT scale.The new contribution to quartic coupling can raise the SM Higgs mass.The vector-like Yukawa couplings are bounded by infrared �xed point, of order one.

However, for EW Baryogenesis we are doing dirty.


The Model

New vector-like super�elds

Q(3; 2; 13); U(3; 1; 4

3); D(3; 1;� 2

3); L(1; 2;�1); E(1; 1;�2);

Q(�3; 2;� 13); U(�3; 1;� 4

3); D(�3; 1; 2

3); L(1; 2; 1); E(1; 1; 2):

New superpotential

W = WMSSM +MQQQ +MUUU +MDDD +MLLL+MEEE

+kuHuQU + kdHuQD + k`HuLE � huHdQU � hdHdQD � h`HdLE :

Supersymmetry breaking term

�Lsoft = m2Q j ~Qj2 +m

2�Q j ~�Qj2 +m

2U j~Uj2 +m

2�U j~�Uj2 +m

2D j~Dj2 +m

2�D j~�Dj2

+m2Lj~Lj2 +m

2�Lj~�Lj2 +m

2E j~E j2 +m

2�E j~�E j2 + (BQMQ

~Q ~�Q + BUMU~U ~�U

+BDMD~D ~�D + BLML

~L~�L+ BEME~E ~�E + AkukuHu

~Q ~�U + Akd kdHu~�Q ~D

�AhuhuHd~�Q ~U � Ahd hdHd

~Q ~�D � Ah`h`Hd~L~�E + c.c.)


The Mass Matrices

The fermion mass matrices in a basis where the left vectors are FL;FR rather than�FL; �FR are

MU =

MQ

1p2ku�u

1p2hu�d MU

!MD =

MQ

1p2hd�d

1p2kd�u MD

!ML =

ML

1p2h`�d

1p2k`�u ME

!

The mass eigenstates are get from matrix

M2F =

� MFMyF 0

0 MyFMF

�

The scalar mass matrices are

M2S =M2

F+

0BB@

m2FL+�FL 0 B�FLM

�FL

k�f (A�kf� �� cot�)

0 m2FR

+�FR h�f (A�hf� �� tan�) B�FRM

�FR

BFLMFL hf (Ahf � � tan�) m2�FL+��FL

0

kf (Akf � � cot�) BFRMFR 0 m2�FR

+��FR

1CCA


The Mass Matrices

We set all supersymmetric vector like masses equal to MV , all supersymmetry breakingmasses equal to m and M2

S = M2V +m2, all up type Yukawa equal to k. Ignore all down

type Yukawa h and all Akf � � cot�, Ahf � � tan�, B and � terms. Then the masseigenstates are

m2f1;2(�u; �d) = M

2V +

1

4k2�2u � 1

4

qk4�4u + 8M2

V k2�2u;

m2~f1;2

(�u; �d) = M2S +

1

4k2�2u � 1

4

qk4�4u + 8M2

V k2�2u;

m2~f3;4

(�u; �d) = M2S +

1

4k2�2u +

1

4

qk4�4u + 8M2

V k2�2u:

Both becoming overall heavier and split e�ects.


Vector-Like Model Benchmark 1

With MS=MV = 1:5.

0.75

1

1.5

2

2.5

50

100

150

200

250

300350

400

100 200 300 400

1

2

3

4

MV

k

Black: phase transition strength h�(Tc )iTc

;

Blue: Lightest fermion mass;

Pink band: SM Higgs mass 124� 127 GeV.



With MS=MV = 1:1. The new light fermion is at the light charged lepton mass bound.

0.75

1

1.5

2

2.5

50

100

150

200

250

300350

400

100 200 300 400

1

2

3

4

MV

k


;





With MS=MV = 1:019. The vector like Yukawa is at the perturbativity bound.

0.75

1

1

1.5

2

2.5

50

100

150

200

250

300350

400

100 200 300 400

1

2

3

4

MV

k


;




Other Comments to the Model

We are not respecting the infrared �xed point Yukawa couplings k ' 1:0 andh ' 1:2.

Gluon fusion and Higgs diphoton rate are not changed, with h = 0 and MS ' MV .

EW precision measurement observables are always problems. We get order 30Peskin-Takeuchi T parameter.

One can break the degeneracy of the vector-like quarks and leptons, but due to lostof control of large corrections it's not that easy to �nd solutions in which even theEWSB happens at zero T .

The model is excluded.

Xue Chang and RH, submitted to PRD


Summary and Outlook

EW Baryogenesis with soft/vector-like masses beyond high T expansion areinteresting scenarios.

Probably the last hope of EW Baryogenesis.

Next we can �t the JB=F curve and do a semi-analytical analysis, with arbitrary kindsmass.


ew baryogenesis beyond the high t expansion

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