vector-like fermions and the electroweak phase transition · h =125gev: a smooth crossover (1-order...
TRANSCRIPT
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 = 4.8 fb0 = 7 TeV: s-1Ldt = 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.
Thursday, July 11, 13
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)
Thursday, July 11, 13
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
Thursday, July 11, 13
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
Thursday, July 11, 13
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
Thursday, July 11, 13
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
Thursday, July 11, 13
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
Thursday, July 11, 13
( , 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
Thursday, July 11, 13
�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
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
�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
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
� = �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)
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
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
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
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
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
Eduardo Pontón
The Shape of the Eff. Pot.
14
⇠ 600 GeV � EW scale
• Effective Potential in EFT shows instability at
massless vector-like state
0 100 200 300 400 500 600 700Φ !GeV"
V#Φ$
T " 0
Φ2
Φ4
Φ6
Φ8
Total
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
Eduardo Pontón
The Shape of the Eff. Pot.
14
⇠ 600 GeV � EW scale
• Effective Potential in EFT shows instability at
massless vector-like state
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 :
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
Eduardo Pontón
The Shape of the Eff. Pot.
14
⇠ 600 GeV � EW scale
• Effective Potential in EFT shows instability at
massless vector-like state
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)
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
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
(Davoudiasl, Lewis & EP, 1211.3449)
Thursday, July 11, 13
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)
Thursday, July 11, 13
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
(Davoudiasl, Lewis & EP, 1211.3449)
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
Thursday, July 11, 13
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:
Thursday, July 11, 13
��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.
Thursday, July 11, 13
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!
Thursday, July 11, 13
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)
Thursday, July 11, 13