vector-like fermions and the electroweak phase transition · h =125gev: a smooth crossover (1-order...

Vector-like Fermions and theElectroweak Phase Transition

Eduardo PontónInstituto de Física Teórica -UNESP

& ICTP-SAIFR

Beyond the SM after the first LHC run, GGI

July 11, 2013

(Work with H. Davoudiasl & I. Lewis, 1211.3449)

Thursday, July 11, 13

Eduardo Pontón

A SM-like Higgs

2

)µSignal strength ( -1 0 +1

Combined

4lA (*) ZZAH

aa AH

ili lA (*) WWAH

oo AH

bbAW,Z H

-1Ldt = 4.6 - 4.8 fb0 = 7 TeV: s-1Ldt = 13 - 20.7 fb0 = 8 TeV: s

-1Ldt = 4.6 fb0 = 7 TeV: s-1Ldt = 20.7 fb0 = 8 TeV: s



-1Ldt = 4.6 fb0 = 7 TeV: s-1Ldt = 13 fb0 = 8 TeV: s

-1Ldt = 4.7 fb0 = 7 TeV: s-1Ldt = 13 fb0 = 8 TeV: s

= 125.5 GeVHm

0.20± = 1.30 µ

ATLAS Preliminary

SMσ/σBest fit 0 0.5 1 1.5 2 2.5

0.28± = 0.92 µ ZZ→H

0.20± = 0.68 µ WW→H

0.27± = 0.77 µ γγ →H

0.41± = 1.10 µ ττ →H

0.62± = 1.15 µ bb→H

0.14± = 0.80 µ Combined

-1 19.6 fb≤ = 8 TeV, L s -1 5.1 fb≤ = 7 TeV, L s

CMS Preliminary = 0.65

SMp

= 125.7 GeVH m

Overall good agreement with SM expectations... but still room for interesting deviations.


Eduardo Pontón

The Nature of the EWPhT

3

Precise measurement of Higgs properties can illuminate nature of EW phase transition

T > Tc

T = Tc

T < Tc1

st-order

0 50 100 150 200

Φ !GeV"

V!Φ,T"

0 50 100 150 200

Φ !GeV"

V!Φ,T"

2

nd-order

T > Tc

T = Tc

T < Tc

But deviations (due to new physics) might have potentially important implications

- Baryon Asymmetry of the Universe

- Gravitational wave signals

mH = 125 GeV mH � 80 GeV1st -order PT only for( )In the SM, with : a smooth crossover(Rummukainen et. al., hep-lat/9805013)


8 > > > > > > < > > > > > > :

� ⇠ ET/�

V (�, T ) ⇠ m(T )2�2 + ET�3 + �(T )�4

�c

Tc⇠ E

�⇠ Ev2

m2h

�c/Tc ⌧ 1

0 50 100 150 200

Φ !GeV"

V!Φ,T"

Eduardo Pontón

The EWPhT in the SM

4

(

when positive:min. at origin ``far away min.”:

Small E:

(need non-perturbative methods toestablish nature of phase transition)

�Finite temperature: thermal masses + new cubic term in :

Barrier? Not in the SM

Should be > 1, for EW baryogenesis


Eduardo Pontón 5

BSM and the EWPhT

New physics required if the EWPhT plays a role in generation of the BAU

``Lore”: to strengthen the EWPhT, requires new bosonic degrees of freedom to either

• change the Higgs potential at tree-level (e.g. adding singlets)

• enhance the E-term at loop level

Both cases can be thought as relying on effective cubic terms

Typically, new fermions not thought to be particularly useful for this purpose...

... they do not induce a cubic term

Cohen, Morrissey & Pierce, 1203.2924

Huan, Shu & Zhang, 1210.0906

Chung, Long & Wang, 1209.1819

In light of Higgs discovery:

Fok, Kribs, Martin & Tsai, 1208.2784

Carena, Nardini, Quirós & Wagner, 1207.6330

Laine, Nardini & Rummikainen, 1211.7344


Eduardo Pontón

Can Fermions Help?

6

Carena, Megevand, Quirós & Wagner, hep-ph/041035

However, I know of one previous example where fermions can help the EWPhT:

100 200 300 400 500mu

5

10

15

20

25

30

g

h = 1.5

h = 2.5h = 2

h = 3

(from hep-ph/041035)

• Use the fact that when their mass depends on the Higgs vev, it is different in the broken and unbroken phases.

�c/Tc

• Decoupling from thermal bath in broken phase leads to reheating, delaying the phase transition:

increase in


Eduardo Pontón

Higgs Di-photon Rate

7

Loop-level processes prime suspects for deviations from SM

(pre-Moriond 2013)

(post-Moriond 2013)

RATLAS�� = 1.80+0.42

�0.36 RCMS�� = 1.56± 0.43

1.69+0.65�0.59 (7 TeV)

0.55+0.29�0.27 (8 TeV)

RATLAS�� = 1.65+0.34

�0.30 RCMS�� = 0.78+0.28

�0.26

(1.55+0.33�0.28

Signal strength-2 0 2 4 6 8 10

ATLAS Preliminary

= 8 TeVsData 2012, -1Ldt = 20.7 fb0

aa AH

= 126.8 GeVHm

2012 datacombined

One-lepton

significancemissTE

Low-masstwo-jet

Tight high-masstwo-jet

Loose high-masstwo-jet

Conv. transition

Conv. restTt

high p

Conv. restTt

low p

Conv. centralTt

high p

Conv. centralTt

low p

Unconv. restTt

high p

Unconv. restTt

low p

Unconv. centralTt

high p

Unconv. centralTt

low p

SMσ/σBest Fit -10 -5 0 5 10

Untagged 0

Untagged 1

Untagged 2

Untagged 3

Di-jet

Untagged 0

Untagged 1

Untagged 2

Untagged 3

Di-jet tight

Di-jet loose

Muon

Electron

MET

Event ClassCombined

= 125.0 GeVHm = 0.78+0.28-0.26SMσ/σ

(MVA)-1 = 8 TeV, L = 19.6 fbs (MVA)-1 = 7 TeV, L = 5.1 fbs

CMS preliminary

8TeV

7TeV


Eduardo Pontón

Vector-like Systems

8

R�� '��1�

F1/2(⌧1)Q21

FSM

@ lnm1(v)

@ ln v

��2

Higgs diphoton rate, normalized to SM

M =

m

1p2yv

1p2ycv m�

!

0.0 0.5 1.0 1.5 2.0 2.5 3.00

200

400

600

800

y ! yc

mi!GeV

" mΨ ! 500 GeVmΧ ! 200 GeV

m m� =1

2yycv

2

Recent interest in vector-like systems: appeal to ``level repulsion”:

Dawson and Furlan, 1205.4733Bonne and Moreau, 1206.3360

An, Liu and Wang, 1207.2473Joglekar, Schwaller and Wagner, 1207.4235 & 1303.2969

Almeida, Bertuzzo, Machado and Funchal, 1207.5254Kearney, Pierce and Weiner, 1207.7062Voloshin, 1208.4303

Carena, Low & Wagner, 1207.1093

Carena, Gori, Shah & Wagner, 1112.3336

Arkani-Hamed, Blum, D’Agnolo & Fan, 1207.4482

...Enhancement Suppression

But there is a different mechanism, that can be consistent with a diphoton enhancement,and more intimately connected to fermionic nature of new physics

(Davoudiasl, Lewis & EP, 1211.3449)

CMQW mechanism: if BSM states electromagnetically chargedHiggs diphoton ratesuppressed


( , c) ⇠ (1, 2)±1/2 (�,�c) ⇠ (1, 1)⌥1

�Lm = �m c +m��

c + yH �+ ycH† c�c + h.c.

m � m�

Eduardo Pontón

A Simple Model

9

Minimal extension (for illustration):

Mass and Yukawa terms:

(``vector-like leptons”)

EFT analysis with integrated out: may be more general than simple model

Interesting region for EWPhT when fermion masses hierarchical. Assume


�L = 2GmH†H��c

Gm =y2

2(m �m�)> 0

LYuk = ye↵h��c + h.c.

ye↵ = �2Gmv < 0

m1 = m� �Gmv2

Eduardo Pontón

EFT Analysis

10

!mψ

〈H〉

yc

〈H〉

yc

!mψ

〈H〉

y

〈H〉

y

ψc

ψc

χc

ψ

ψc

χ

ψ

ψW 3

µ W 3ν

〈H〉〈H〉

ψχ χ

1

m � v,m� “�”“ ”For , integrate out and obtain EFT for (SM + ):

where

Light vector-like fermion mass is

(``level repulsion”

Interactions of light state with physical Higgs (after EWSB):

ye↵ ⇠ O(1)

m1 ⇠ 100� 200 GeV

Interesting diphoton enhanc. when

and



�VE↵ =

= � 4

64⇡2m1(�)

4

ln

m1(�)2

µ2� 3

2

�+ counterterms

(in MS scheme)

“VTree” = �1

2µ2�2 +

1

4��4+

1

6��6 +

1

8��8

Eduardo Pontón

T = 0 Potential in EFT

11

!mψ

〈H〉

yc

〈H〉

yc

!mψ

〈H〉

y

〈H〉

y

ψc

ψc

χc

ψ

ψc

χ

ψ

ψW 3

µ W 3ν

〈H〉〈H〉

ψχ χ

+ + + · · ·

1

1-loop effective potential (T = 0)

�8�6Noting that and terms are divergent:

However, within the UV model, they are determined...

� �and

arbitrary within EFT



� = �th + �RG � = �th + �RG

Eduardo Pontón

Matching and Running

12

However, within the UV model, they are determined...

�th = �Z�y8

48⇡2

7m3 + 27m�m2

� 4m3�

(m �m�)7⇠ � 7y8

48⇡2

1

m4

�th =Z�y6

16⇡2

m (m2 + 7m�m � 2m2

�)

(m �m�)5⇠ y6

16⇡2

1

m2

with threshold contributions

Z� , Z� = 1(at lowest order(

�RG ⇡ �3G3mm�

2⇡2ln

m2

µ2

!

�RG ⇡ G4m

2⇡2ln

m2

µ2

!

and running contributions

• Determined by EFT only

• This is the only difference with naive CW potential in UV model (actually, just the sign)



16⇡2 d�

dt= �

�6�� 9g22 � 3g21 + 12y2t

��6y4t +

3

8

h2g22 +

�g22 + g21

�2i�48G2mm2

�

Eduardo Pontón

Quartic Instabilities?

13

fermionic terms induce ``instability”

from new light fermion

m RG running of Higgs quartic (below ):

Quartic coupling from effective potential at low and high temperatures:

60 80 100 120 140 160 180 200

!0.01

0.00

0.01

0.02

0.03

0.04

T !GeV"

Λ#T$High!T Expansion

T as proxy for RG running

0 100 200 300 400 500 600 700

0.00

0.05

0.10

0.15

Φ !GeV"

Λ#Φ$

T # 0

� as proxy for RG running

massless vector-like state



0 100 200 300 400 500 600 700Φ !GeV"

V#Φ$

T " 0

Eduardo Pontón

The Shape of the Eff. Pot.

14

⇠ 600 GeV � EW scale

• Effective Potential in EFT shows instability at



Eduardo Pontón


14




0 100 200 300 400 500 600 700Φ !GeV"

V#Φ$

T " 0

Φ2

Φ4

Φ6

Φ8

Total



Eduardo Pontón


14




0 100 200 300 400 500 600 700Φ !GeV"

V#Φ$

T " 0

Φ2

Φ4

Φ6

Φ8

Total

0 50 100 150 200 250 300Φ !GeV"

V#Φ$

T " 0

Φ2

Φ4

Φ6

Φ8

Total

8 > > > > > > < > > > > > > :� ⇠ EW m2 < 0, � > 0• At T = 0 and :



Eduardo Pontón


14




0 100 200 300 400 500 600 700Φ !GeV"

V#Φ$

T " 0

Φ2

Φ4

Φ6

Φ8

Total

0 50 100 150 200 250 300Φ !GeV"

V#Φ$

T " 0

Φ2

Φ4

Φ6

Φ8

Total

8 > > > > > > < > > > > > > :� ⇠ EW m2 < 0, � > 0• At T = 0 and :

0 50 100 150Φ !GeV"

V#Φ,T$

Φ2

Φ3 Φ4

Φ6

Φ8

Total

At T " Tc " 154.16 GeV

m2 > 0, � < 0• At T ~ EW :

stabilization by higher-dim operators

(Realization of idea in hep-ph/0407019)



Eduardo Pontón

Back to the Instability

15

� m m� ⇠ v• EFT with integrated out: match correlators and run from to

captures ``small � “ behavior, but not large

(finite radius of convergence of Taylor expansion of effective potential)

• Coleman-Weinberg potential in full UV model suggests instability delayed to

⇠ m multi-TeV scale ( )

• Thus, in non-renormalizable theories one should be careful in interpreting the familiar quartic instability

0 500 1000 1500 2000 2500 3000 3500

f @GeVD

V@fD-V@f=

0D0 100 200 300 400 500 600 700

EFTColeman-Weinbergin UV th.

T = 0



V (�, T ) ⇠ 1

2µ2�2 +

1

4��4 +

1

6��6

µ2 > 0, � < 0, � > 0 � ⇠q

��/�

�2 ⇠ 6�µ2 ⌧ 1

�c ⇠pµ/�1/4 �c/Tc

� < 0

Eduardo Pontón

The Mechanism

16

Keep it simple by dropping non-crucial terms, e.g. cubic:

8 > > > > > > < > > > > > > :

``far away min.”:When

Degenerate with min. at origin when (determines critical temp.)

Also estimate

may get sizeable !

Similar to proposal by Grojean, Servant & Wells. Here, from fermions and finite Temp.(hep-ph/0407019)


m = 4 TeV m� = 300 GeV y = yc = 4

�(µ = m�)

�c/Tc

�ye↵ = 2Gmv

Eduardo Pontón

EFT Agnostic Analysis

17

Star is a benchmark in UV model with:

Green regions: effect of 10% (1%) higher-loopcorrections at the matching scale

• Strength of the phase transition ( ) in

(coupling of light fermion to Higgs)

versus

(dim-6 stabilizing operator)

Observations:

y, yc ⇠ few• Need sizeable underlying

• Sensitivity to UV completion through stabilizing higher-dim. operators

• Consistent with important Higgs diphoton rate enhancement


0.5

1.

1.5

2.

0.6 0.7 0.8 0.9 1.0 1.1 1.20.0

0.5

1.0

1.5

2.0

1ê g Im = mcM @TeVD

2Gmv

1.2

Rgg = 1.5

2

3

¯

mc = 300 GeV, mH = 125 GeV

�c/Tc = 1


m � m�, v

�T ⇠ 1

16⇡s2W c2W

y2y2cv4

M2Zm

2

�S ⇠ 2y2v2

9⇡m2

[6 ln(m /m�)� 7]

Eduardo Pontón

EW Precision Tests

18

!mψ

〈H〉

yc

〈H〉

yc

!mψ

〈H〉

y

〈H〉

y

ψc

ψc

χc

ψ

ψc

χ

ψ

ψW 3

µ W 3ν

1

In the heavy doublet limit: , leading contribution to T from

(may be sizeable...)

The S-parameter is less constraining in the same limit:


��Lm = mnnnc + yH† n+ ycH

c�c + h.c.

(n, nc)

y = y yc = yc

⇠(c) ⌘✓

n(c)

��(c)

◆

SU(2)L ⇥ SU(2)R

� ⌘✓

H0⇤ H+

�H� H0

◆�LYuk = y �⇠ + yc

c�⇠c + h.c(0, 2) (2, 2)

mn = �m�

Eduardo Pontón

A Custodial Extension

19

Two important shortcomings so far:

m • In spite of large , sizeable T parameter suggests imposing custodial symmetry

• Lightest charged state must decay (so far stable)

Both can be addressed by adding a vector-like ``RH neutrino”,

When and, , can rewrite as invariant:

with

In this limit T = 0. Need to ensure neutral lightest state, which breaks custodial softly.


At T = Tc

Charged Neutral

m±2 = 4.06 TeV m0

2 = 4.06 TeV

m±1 = 240 GeV m0

1 = 191 GeV

At T = 0

Charged Neutral

m±2 = 4.11 TeV m0

2 = 4.11 TeV

m±1 = 189 GeV m0

1 = 140 GeV

�c = 179.3 GeV

Tc = 158.4 GeV

�c/Tc = 1.13

�T ⇠ 10�4

�S ⇡ 0.04

�U ⇠ 10�6

R�� ⇡ 1.5

m = 4 TeV m� = 300 GeV mn = �250 GeV y = 4 y = 4 yc = 3.5 yc = 3.5

Eduardo Pontón

A Detailed Example

20

Input parameters:

Vector-like spectrum:

Phase transition: EWPT and diphoton enhancement:

TcBubbles nucleate slightly below

(

Consistent at 95% CLwith current PDG ellipse

Look forward to furtherdevelopments!


V 000(v) = 3m2H/v + 8�v3

gg ! HHn

y ⇠ 3� 4

Conclusions & Outlook

• We illustrated in a simple model the potentially far-reaching consequences of deviations from the SM Higgs properties in answering long-standing questions:

• Within the model:

• Main ingredients:

- The nature of the EWPhT itself

- The relevance of EW scale physics in the generation of the BAU (details to be worked out)

- Triple Higgs coupling:

expect 40-60% suppression in

O(1)correction

measurement of stabilizing effect

(m�, Gmv)- Measurement of lightest charged fermion mass + diphoton rate:

- a parametrically lighter fermion state

- Underlying Yukawa interactions with

- a fermion state in the few TeV scale8><

>:Rather familiar from (warped)extra-dimensional constructions!

(a crucial ingredient in underlying mechanism)


vector-like fermions and the electroweak phase transition · h =125gev: a smooth crossover (1-order...

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