SLIDE 1
Implications of a 125 GeV Composite Higgs
Alex Pomarol, UAB (Barcelona)
SLIDE 2 A 125 GeV Higgs-like state has been discovered
with no significant deviations from a SM Higgs!
) µ Signal strength (
Combined 4l →
(*)
ZZ → H γ γ → H ν l ν l →
(*)
WW → H τ τ → H bb → W,Z H
Ldt = 4.6 - 4.8 fb
∫
= 7 TeV: s
Ldt = 5.8 - 5.9 fb
∫
= 8 TeV: s
Ldt = 4.8 fb
∫
= 7 TeV: s
Ldt = 5.8 fb
∫
= 8 TeV: s
Ldt = 4.8 fb
∫
= 7 TeV: s
Ldt = 5.9 fb
∫
= 8 TeV: s
Ldt = 4.7 fb
∫
= 7 TeV: s
Ldt = 5.8 fb
∫
= 8 TeV: s
Ldt = 4.7 fb
∫
= 7 TeV: s
Ldt = 4.6-4.7 fb
∫
= 7 TeV: s
= 126.0 GeV
H
m
0.3 ± = 1.4 µ
ATLAS 2011 - 2012
SM
σ / σ Best fit
1 2 3 bb → H τ τ → H WW → H ZZ → H γ γ → H
CMS
= 8 TeV, L = 5.3 fb s
= 7 TeV, L = 5.1 fb s
= 125.5 GeV
H
m
SLIDE 3 Energy Strong Dynamics territory
SM only
MSSM NMSSM, ...
S u s y t e r r i t
y
TC PGB Higgs
Unknown Planckian Territory
U n n a t u r a l t e r r i t
y ( M u l t i v e r s e ? )
Higgs territory
Road Map of possible BSM scenarios
MP
TeV
100 GeV
1979-2012
SLIDE 4
How well this recently discovered 125 GeV Higgs fit in Composite Higgs Models ?
Purpose of my talk here:
SLIDE 5
Spectrum:
inspired by QCD where one observes that the (pseudo) scalar are the lightest states Mass protected by the global QCD symmetry!
Are Pseudo-Goldstone bosons (PGB)
π → π + α
π
π ρ
Composite PGB Higgs
GeV 100 MeV
SLIDE 6
We’d like the spectrum of the new strong sector to be:
Pseudo-Goldstone bosons (PGB)
h
100 GeV TeV
Can the light Higgs be a kind of a pion from a new strong sector?
ρ
SLIDE 7 Potential from some new strong dynamics at the TeV: H
4 Goldstones Higgs doublet
➠
e.g. SO(5) ➝ SO(4)
SLIDE 8 Potential from some new strong dynamics at the TeV: H
e.g. SO(5) ➝ SO(4)
4 Goldstones Higgs doublet
➠
H
SM-loop effects: EWSB minimum
SM-field couplings to the strong sector break the global SO(5)
SLIDE 9 Potential from some new strong dynamics at the TeV: H
e.g. SO(5) ➝ SO(4)
4 Goldstones Higgs doublet
➠
H
SM-loop effects EWSB minimum two symmetry- breaking scales: f ≳ 500 GeV v ≈ 246 GeV
SLIDE 10 = 0 it’s a Goldstone h h
contribution from the strong sector
h h h
SM fields
V (h) = g2
SMm2 ρ
16π2 h2 + · · · h
Difficult to get predictions due to the intractable strong dynamics!
+ ➥
Higgs Mass
SLIDE 11 AdS/CFT approach
Strongly-coupled systems in the Large Nc Large λ≡g²Nc Weakly-coupled Gravitational systems in higher-dimensions
Very useful to derive properties of composite states from studying weakly-coupled fields in warped extra-dimensional models
A possibility to move forward has been to use the...
SLIDE 12 in a AdS5 throat
hard/soft wall
Mass gap ~ TeV Holographic composite PGB Higgs model
Agashe,Contino,A.P . ds2 = L2 z2 ⇥ dx2 + dz2⇤
SLIDE 13 in a AdS5 throat
hard/soft wall
Mass gap ~ TeV SO(5) gauge theory Holographic composite PGB Higgs model
ds2 = L2 z2 ⇥ dx2 + dz2⇤
Agashe,Contino,A.P .
SLIDE 14 in a AdS5 throat
hard/soft wall
Mass gap ~ TeV SO(5) gauge theory Symmetry : SO(4) Holographic composite PGB Higgs model
Breaking of symmetry by boundary conditions
Agashe,Contino,A.P . ds2 = L2 z2 ⇥ dx2 + dz2⇤
SLIDE 15 Massless Spectrum
hard/soft wall
Higgs = 5th component
- f the SO(5)/SO(4) gauge bosons
(Gauge-Higgs unification, Hosotani Mechanism,...) ➥ Normalizable modes = Composite h
SLIDE 16
hard/soft wall
: SO(4)~SU(2)xSU(2) Gauge Bosons ➥ Non-normalizable modes = External states = Some of them dynamical (SU(2)) h
Aµ Aµ
Achieve, as in Randall-Sundrum models, by a brane at z~0
Massless Spectrum
SLIDE 17
What about fermions? (Main difficulty in composite models)
SLIDE 18 ξq = (Ψq L , Ψq R) = (2, 2)q
L =
q
L(−+)
qL(++)
R =
q
R(+−)
qR(−−)
L(−−)
, (1, 1)q
R(++)
ξu = (Ψu L , Ψu R) =
L(+−) , (2, 2)u R(−+)
(1, 1)u
L(−+) , (1, 1)u R(+−)
(
The fermionic sector: We have to choose the bulk symmetry representation of the fermions and b.c. giving
- nly the 4D massless spectrum of the SM
Up-quark sector:
s 52/3 of SO(5)×U(1)X.
IR-bound. mass:
×
q L(2, 2)u R +
Mu (1, 1)
q R(1, 1)u L + h.c.
SLIDE 19
hard/soft wall
ψ(z) ψ(z)
h 3rd family 1st & 2nd family (Top = Most Composite) (Elementary)
Simple geometric approach to fermion masses
SLIDE 20 4D CFT Interpretation
L = λ Ψ · OΨ + LCFT
SM fermions are linearly coupled to a CFT operator:
Ψ
Contino,AP
Dim[OΨ] = 3 2 + |MΨ + 1 2|
5D mass
MΨ ≥ 1/2 → γλ ≥ 0 MΨ < 1/2 → γλ < 0 Relevant coupling
Irrelevant coupling | |
SLIDE 21 115 125 135 145 155 165 175 185 0.5 1.0 1.5 2.0 2.5
mKK
[TeV]
mHiggs
[GeV]
12/3 21/6 27/6
Contino,DaRold, AP 07
mρ = 2.5 TeV , f = 500 GeV
SLIDE 22 115 125 135 145 155 165 175 185 0.5 1.0 1.5 2.0 2.5
mKK
[TeV]
mHiggs
[GeV]
12/3 21/6 27/6
For a 125 GeV Higgs, the fermionic resonances of the top are lighter ~ 600 GeV
Contino,DaRold, AP 07
mρ = 2.5 TeV , f = 500 GeV
SLIDE 23
Why this correlation?
m2
h ∼ Nc
π2 m2
t
f 2 m2
Q ∼ (125 GeV)2 ⇣
mQ 700 GeV ⌘2
But why the model can accommodate light resonances? Is it natural?
SLIDE 24 Why this correlation?
m2
h ∼ Nc
π2 m2
t
f 2 m2
Q ∼ (125 GeV)2 ⇣
mQ 700 GeV ⌘2
But why the model can accommodate light resonances?
Dim[OΨ] = 3 2 + |MΨ + 1 2|
AdS/CFT dictionary: becomes a free field ~ decouple from the CFT ➥ in this limit, new light states
MΨ = −1/2 → Dim[OΨ] = 3/2
Is it natural? Yes
5D mass: free parameter
SLIDE 25
Why this correlation?
m2
h ∼ Nc
π2 m2
t
f 2 m2
Q ∼ (125 GeV)2 ⇣
mQ 700 GeV ⌘2
But why the model can accommodate light resonances? Is it natural? Yes
The more we localize the top towards the IR boundary, the more composite it is
If fully composite, it must come in full reps of SO(5): ➥ there must be extra massless partners
SLIDE 26
Simpler derivation of the connection: Light Higgs - Light Resonance
SLIDE 27 Simpler derivation of the connection: Light Higgs - Light Resonance ✒ Deconstruction: Matsedonskyi,Panico,Wulzer; Redi,Tesi 12 ✒ “Weinberg Sum Rules”: Marzocca,Serone,Shu; AP, Riva 12
➥ As Das,Guralnik,Mathur,Low,Young 67
for the charged pion mass:
m2
π+ m2 π0 ' 3α
2π m2
ρ log 2 ' (37 MeV)2
quite successful!
γ π+ π+
SLIDE 28 Higgs potential Gauge contribution (limit g’=0):
V (h) = 9 2
(2π)4 log ΠW
Encode the strong-sector contribution to the gauge propagator in the h-background
h
Broken and Conserved current-current correlators of the strong sector
W W
ΠW ' p2 g2 + sin2 h/f 2 [hJˆ
aJˆ ai hJaJai]
SLIDE 29
Easy derivation using spurion techniques:
L = Lstrong + LSM + Jµ
strongWµ
promote them to an SO(5) rep: 10=6+4
Aµ ∈
The most general SO(5) invariant action as a function of after integrating out the strong sector:
Aµ
Leff = 1 2Pµν h Π0(p) Tr ⇥ AµAν⇤ + Π1(p) ΣAµAνΣT i + O(A3)
parametrizes the coset SO(5)/SO(4) (equivalent SO(4) vacuums)
Σ = Σ0eΠ/fπ , Σ0 = (0, 0, 0, 0, 1)
SLIDE 30 Leff = 1 2Pµν h Π0(p) Tr ⇥ AµAν⇤ + Π1(p) ΣAµAνΣT i + O(A3)
hΣi = (0, 0, 0, 0, 1)
hΣi = (0, 0, 0, sin h/f, cos h/f)
Aµ = W µ
ΠW = Π0 + Π1 4 sin2 h fπ h
Πˆ
a = hJˆ aJˆ ai = Π0 + 1
2Π1
Πa = hJaJai = Π0
}
Π0 ' p2 g2
ΠW ' p2 g2 + sin2 h/f 2 [hJˆ
aJˆ ai hJaJai]
SLIDE 31 Gauge contribution:
V (h) = 9 2
(2π)4 log ΠW
Higgs Mass from Weinberg Sum Rules ➥
= 1 2m2
hh2 + · · ·
m2
h ' 9g2
2f 2 Z d4p (2π)4 Π1(p) p2
Large N
}
=
X
n
}
Π1 = 2 [hJˆ
aJˆ ai hJaJai] = f 2 + 2p2 ∞
X
n
F 2
an
p2 + m2
an
2p2
∞
X
n
F 2
ρn
p2 + m2
ρn
Fan = h0|Jˆ
a|ani
Fρn = h0|Ja|ρni an ∈ 4
ρn ∈ 6
Euclidean momentum
SLIDE 32 Gauge contribution:
V (h) = 9 2
(2π)4 log ΠW
1) Demand convergence of the integral:
lim
p2→∞ Π1(p) = 0 ,
lim
p2→∞ p2Π1(p) = 0 , “Weinberg Sum Rules”
= 1 2m2
hh2 + · · ·
Procedure: Higgs Mass from Weinberg Sum Rules
Π1 = 2 [hJˆ
aJˆ ai hJaJai] = f 2 + 2p2 ∞
X
n
F 2
an
p2 + m2
an
2p2
∞
X
n
F 2
ρn
p2 + m2
ρn
m2
h ' 9g2
2f 2 Z d4p (2π)4 Π1(p) p2
➥
SLIDE 33 Gauge contribution:
V (h) = 9 2
(2π)4 log ΠW
1) Demand convergence of the integral:
lim
p2→∞ Π1(p) = 0 ,
lim
p2→∞ p2Π1(p) = 0 , “Weinberg Sum Rules”
= 1 2m2
hh2 + · · ·
Procedure: Higgs Mass from Weinberg Sum Rules
Π1 = 2 [hJˆ
aJˆ ai hJaJai] = f 2 + 2p2 ∞
X
n
F 2
an
p2 + m2
an
2p2
∞
X
n
F 2
ρn
p2 + m2
ρn
[hJˆ
aJˆ ai hJaJai] ⇠ hOi
pd−2 + · · ·
Just from the OPE at large p ➥ symmetry breaking operator
d = Dim[O]
➥ WSR = demand d>4 m2
h ' 9g2
2f 2 Z d4p (2π)4 Π1(p) p2
➥
SLIDE 34 Gauge contribution:
V (h) = 9 2
(2π)4 log ΠW
1) Demand convergence of the integral:
lim
p2→∞ Π1(p) = 0 ,
lim
p2→∞ p2Π1(p) = 0 , “Weinberg Sum Rules”
= 1 2m2
hh2 + · · ·
Procedure: Higgs Mass from Weinberg Sum Rules
Π1 = 2 [hJˆ
aJˆ ai hJaJai] = f 2 + 2p2 ∞
X
n
F 2
an
p2 + m2
an
2p2
∞
X
n
F 2
ρn
p2 + m2
ρn
qi2/p4
Just from the OPE at large p
e.g. in QCD:
m2
h ' 9g2
2f 2 Z d4p (2π)4 Π1(p) p2
➥
SLIDE 35 Gauge contribution:
V (h) = 9 2
(2π)4 log ΠW
1) Demand convergence of the integral:
lim
p2→∞ Π1(p) = 0 ,
lim
p2→∞ p2Π1(p) = 0 , “Weinberg Sum Rules”
= 1 2m2
hh2 + · · ·
Procedure: Higgs Mass from Weinberg Sum Rules
Π1 = 2 [hJˆ
aJˆ ai hJaJai] = f 2 + 2p2 ∞
X
n
F 2
an
p2 + m2
an
2p2
∞
X
n
F 2
ρn
p2 + m2
ρn
2) The Correlators are dominated by the lowest resonances (minimal number to satisfy WSR)
m2
h ' 9g2
2f 2 Z d4p (2π)4 Π1(p) p2
➥
SLIDE 36 Result:
Π1(p) = f 2m2
ρm2 a1
(p2 + m2
ρ)(p2 + m2 a1)
two resonances needed: ⍴ and a₁
m2
h '
9g2m2
ρm2 a1
64π2(m2
a1 m2 ρ) log
✓m2
a1
m2
ρ
◆
➥
Similar result as the electromagnetic contribution to the charged pion mass
SLIDE 37 Similarly, for the top contribution...
L = Lstrong + LSM + Jµ
strongWµ + Ostrong · ψSM
we must specify which rep of SO(5)
MCHM5 ≡ Rep[O] = 5
Top contribution to the Higgs potential:
Encode the strong sector contribution to the top propagator in the h-background
V (h) = −2Nc Z d4p (2π)4 log ⇥ −p2 ΠtLΠtR − |ΠtLtR|2⇤
h
tL,R tL,R
SLIDE 38
V (h) = −2Nc Z d4p (2π)4 log ⇥ −p2 ΠtLΠtR − |ΠtLtR|2⇤
= −m2h2 + λhh4 + · · ·
Triggers EWSB!
SLIDE 39 m2
h ' 8Ncv2
f 4 Z d4p (2π)4 |M t
1|2
p2 + 1 4
1
2 +
1
2
Higgs mass contribution:
SLIDE 40 m2
h ' 8Ncv2
f 4 Z d4p (2π)4 |M t
1|2
p2 + 1 4
1
2 +
1
2
ΠtL
1 (p) = ΠL Q1(p) ΠL Q4(p) ,
ΠtR
1 (p) = ΠR Q1(p) ΠR Q4(p) ,
M t
1(p) = MQ1(p) MQ4(p) .
ΠL
Q4(p) =
X
n
|F L
Q(n)
4 |2
p2 + m2
Q(n)
4
, ΠL
Q1(p) =
X
n
|F L
Q(n)
1 |2
p2 + m2
Q(n)
1
, and similarly for ΠR
Q4,1 with the replacement L ! R, while
MQ4(p) = X
n
F L
Q(n)
4 F R ∗
Q(n)
4 mQ(n) 4
p2 + m2
Q(n)
4
, MQ1(p) = X
n
F L
Q(n)
1 F R ∗
Q(n)
1 mQ(n) 1
p2 + m2
Q(n)
1
.
{
Higgs mass contribution:
5=4+1 of SO(4):
Large N:
Q1 ∈ 1 Q4 ∈ 4
h
tL tR
responsible
fermion-fermion correlators
SLIDE 41 Demanding again WSR:
le limp→∞ M t
1(p) = 0.
s, limp→∞ pnΠ
tL,R 1
(p) = 0 (n = 0, 2),
... being fulfilled with the minimal set of resonances, two in this case, Q1 and Q4:
⌘ ⌘ Π
tL,R 1
= |F L,R
Q4 |2
(m2
Q4 m2 Q1)
(p2 + m2
Q4)(p2 + m2 Q1) ,
M t
1(p)
= |F L
Q4F R ∗ Q4 |mQ4mQ1(mQ4 mQ1eiθ)
(p2 + m2
Q4)(p2 + m2 Q1)
✓ 1 + p2 mQ4mQ1 mQ1 mQ4eiθ mQ4 mQ1eiθ ◆
SLIDE 42 m2
h ' Nc
π2 " m2
t
f 2 m2
Q4m2 Q1
m2
Q1 m2 Q4
log m2
Q1
m2
Q4
! !#
For a 125 GeV Higgs:
AP ,Riva 12
WSR + Minimal set of resonances (Q1 and Q4) + proper EWSB
500 1000 1500 2000 500 1000 1500 2000 mQ1HGeVL mQ4 HGeVL
f=1000 GeV f=500 GeV
SLIDE 43 m2
h ' Nc
π2 " m2
t
f 2 m2
Q4m2 Q1
m2
Q1 m2 Q4
log m2
Q1
m2
Q4
! !#
For a 125 GeV Higgs:
AP ,Riva 12
WSR + Minimal set of resonances (Q1 and Q4) + proper EWSB
500 1000 1500 2000 500 1000 1500 2000 mQ1HGeVL mQ4 HGeVL
f=1000 GeV f=500 GeV
Fermionic resonances below 700 GeV
SLIDE 44 What about other representations?
L = Lstrong + LSM + Jµ
strongWµ + Ostrong · ψSM
MCHM10 ≡ Rep[O] = 10
10=4+6 under SO(4)
SLIDE 45 What about other representations?
L = Lstrong + LSM + Jµ
strongWµ + Ostrong · ψSM
MCHM10 ≡ Rep[O] = 10
MCHM5+1 MCHM5 M C H M10 500 1000 1500 2000 500 1000 1500 2000 mQ1HGeVL mQ4 HGeVL
f=500 GeV
AP ,Riva 12
Demanding WSR with minimal set
+ proper EWSB:
6
SLIDE 46 What about other representations?
L = Lstrong + LSM + Jµ
strongWµ + Ostrong · ψSM
MCHM10 ≡ Rep[O] = 10
MCHM5+1 MCHM5 M C H M10 500 1000 1500 2000 500 1000 1500 2000 mQ1HGeVL mQ4 HGeVL
f=500 GeV
AP ,Riva 12
Demanding WSR with minimal set
+ proper EWSB:
6
In most of the models always an upper bound on the resonance mass < TeV, but exceptions exist!
SLIDE 47
we must find at the LHC color vector-like fermions in the 4 or 1 rep. of SO(4): If the 125 GeV Higgs is composite... EM charges: 5/3,2/3,-1/3
SLIDE 48 ¯ q q g g ¯ T5/3 q ¯ q g W − W + b ¯ b ¯ t l+ ν l+ ν t T5/3 W − W +
If this fermion is light, it can be double produced:
Contino,Servant Mrazek, Wulzer Aguilar-Saavedra, Dissertori, Furlan,Moorgat,Nef
same-sign di-leptons
Color vector-like fermions with charge 5/3:
SLIDE 49 ¯ q q g g ¯ T5/3 q ¯ q g W − W + b ¯ b ¯ t l+ ν l+ ν t T5/3 W − W +
If this fermion is light, it can be double produced:
same-sign di-leptons
Color vector-like fermions with charge 5/3:
ATLAS-CONF-2012-130:
MT5/3 & 700 GeV
Contino,Servant Mrazek, Wulzer Aguilar-Saavedra, Dissertori, Furlan,Moorgat,Nef
SLIDE 50
Higgs couplings
SLIDE 51 Couplings dictated by symmetries (as in the QCD chiral Lagrangian)
Giudice,Grojean,AP ,Rattazzi 07
ghW W gSM
hW W
= s 1 − v2 f 2 ghff gSM
hff
= 1 − (1 + n) v2
f 2
q 1 − v2
f 2
n = 0, 1, 2, ...
small deviations on the h𝜹𝜹(gg)-coupling due to the Goldstone nature of the Higgs
Composite PGB Higgs couplings
AP ,Riva 12
= Decay-constant of the PGB Higgs
f
MCHM5,10
SLIDE 52 ¯
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
1 2 a c
Allowed area where constructive interference between top and W loops enhances the 𝜹𝜹 channel
from, e.g., Montull,Riva arXiv:1207.1716
1 2
ghff ghff
SM
0.2 0.6 1 1.4
ghWW ghWW
SM
SM
n=0 n=1 n=5
Fit slightly better than the SM!
SLIDE 53
G H PGB SO(5) SO(4) 4=(2,2) SO(6) SO(5) 5=(2,2)+(1,1) O(4)xO(2) 8=(2,2)+(2,2) SO(7) SO(6) 6=(2,2)+(1,1)+(1,1) G2 7=(1,3)+(2,2) ... ... ...
Other symmetry-breaking patterns G→H:
SLIDE 54 G H PGB SO(5) SO(4) 4=(2,2) SO(6) SO(5) 5=(2,2)+(1,1) O(4)xO(2) 8=(2,2)+(2,2) SO(7) SO(6) 6=(2,2)+(1,1)+(1,1) G2 7=(1,3)+(2,2) ... ... ...
One doublet + Singlet
Gripaios, AP , Riva, Serra
Other symmetry-breaking patterns G→H:
SB of minimal TC: Just by replacing SU(3)c by SU(2)c
Galloway, Evans, Luty, Tacchi 10
SLIDE 55 101 102 103 10-3 10-2 10-1 100 eVD
e 1
100 fb
101 102 103 10-3 10-2 10-1 100 mh @GeVD l
mh = 125 GeV, f = 1 TeV, case 2
XENON100 LHC, 5 fb-1 Wh < WDM DAMAêCoGeNT CRESST-II Wh > WDM
Wh > WDM
If SO(6)→SO(5) breaking pattern: Doublet h +Singlet η
Frigerio,AP ,Riva,Urbano 12
- If extra parity 𝜽 → -𝜽 (e.g. if O(6)): η can be Dark Matter !
- Mass of eta very model-dependent: depends on how the
SO(2) ⊂ SO(6) is explicitly broken
New player in the game:
101 102 10-3 10-2 10-1 100 mh @GeVD l
mh = 125 GeV, f = 500 GeV, case 2
XENON100 LHC, 5 fb-1 Wh < WDM Wh > WDM DAMAêCoGeNT CRESST-II
purple solid line: proper relic density
SLIDE 56 If lighter than h, possibility for an “invisible” decay width for h:
h → ηη → b¯ bb¯ b h → ηη
Main impact in Higgs physics: Not disfavored!
from, e.g., Montull,Riva arXiv:1207.1716
0.0 0.1 0.2 0.3 0.4 0.5 28 30 32 34 36 38 BRinv Χ2
ξ = 0
ξ = 0.25
ξ = 0.1
ξ = 0.5
.
ξ = v2/f 2
If not stable:
SLIDE 57 If h and eta mix, possible enhancement of the decay to 𝜹𝜹
H V V
𝜹 𝜹 𝞱 h
from anomalies
p 8 p 4 3 p 8
5 10 a GhggêGhgg
It can improve the fit!
from, e.g., Montull,Riva arXiv:1207.1716
= mixing angle
SLIDE 58 𝜃 𝜃
Possible ways to “see” eta (if DM) at the LHC:
- Searches with Monojets+Missing ET:
- In heavy resonances decays:
qq→ 𝜃 𝜃 +Gluons
SLIDE 59 Conclusions
- Composite Higgs as a PGB a natural possibility
(Higgs mass at the loop level)
Nature has chosen a light Higgs for EWSB:
- A 125 GeV composite Higgs implies either from
AdS/CFT, Weinberg Sum rules, deconstructed models:
Fermionic colored vector-like resonances (either QEM=5/3,2/3,-1/3) with masses can be ~ 700 GeV Hope to see them at the LHC !
- It gives clear predictions for the Higgs couplings
and their deviations from the SM
