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Naturalness, the Twin Higgs
&
its Composite Incarnation
Riccardo Rattazzi, EPFL
Thursday, August 20, 2015
In QM whatever is possible is also compulsory
O =�
i
Oi
selection rules
If
dim = ∆ dim = ∆
Oi = ci λn1i1 . . .λnki
k
O|exp � max|Oi| it seems we are missing something
Un-Naturalness = failure of dimensional analysis and selection rulesThursday, August 20, 2015
ΛUV
ΛIR
∼ scale invariant dynamics
∼ fixed point of RGL
Mass Hierarchies
Naturalness of ΛIR � ΛUV stability of fixed point
3 optionsThursday, August 20, 2015
1. Marginality
ΛUV
ΛIR
the fixed point theory does not possess scalar operators with dimension strictly less than 4
Lmass = cΛ�UV O4−�
�IR = c�
UV ΛIR = c1/� ΛUV
algebraica"y small and is enough to produce hierarchyc �
Ex: Yang-Mills, TechniColor, Randall-Sundrum model Rattazzi, Zaffaroni 01Strassler 03
Thursday, August 20, 2015
2. Symmetry
ΛUV
ΛIR
Lmass = �Λ2UV O2
small parameter protected by symmetry
ΛIR =√�ΛUV
• ϵ must be hierarchica"y small• how does this smallness originate?
Ex: QCD, Supersymmetry
Thursday, August 20, 2015
ΛIR
ΛUV
3. Sequestering
Thursday, August 20, 2015
ΛIR
ΛUV
3. Sequestering
Thursday, August 20, 2015
SFT2
SFT1O(�)
ΛIR
ΛUV
3. Sequestering
Thursday, August 20, 2015
SFT2
SFT1O(�)
ΛIR
ΛUV
3. Sequestering
DilationsD1 ×D2 → D1+2
by small coupling �
ΛIR ∼ �ΛUV technically natural
Thursday, August 20, 2015
SFT2
SFT1O(�)
ΛIR
ΛUV
3. Sequestering
DilationsD1 ×D2 → D1+2
by small coupling �
ΛIR ∼ �ΛUV technically natural
a-gravity
• SFT2 = ‘UV completion of gravity’
• not clearly compatible with basic principles
• but imagine there was a gorgeous candidate for SFT1?
Ex.
� = ΛUV /MP
Salvio, Strumia 2012
....well there isn’t: Giudice, Isidori, Salvio, Strumia 2014
Thursday, August 20, 2015
The Standard Model
ΛUV
ΛIR ∼ mW
LSM ∼ Lfree
≣ fixed point
H†H ≣ relevant and unprotected
Naturalness demands not too large ΛUV
How large ΛUV can we tolerate compatibly with Naturalness?
What can we broadly say about the physics at ΛUV ?
Thursday, August 20, 2015
a seemingly un-natural hierarchy offers a remarkable bonus
• Accidenta"y possesses all the symmetries we observe in Nature: B, L, Flavor,...
• Not the case in any natural completion of the SM, where we have to resort to extra ad hoc assumptions
LSM = L(d≤4) +1
ΛUV
L(5) +1
Λ2UV
L(6) + . . .
But notice:
ΛUV � mW
Thursday, August 20, 2015
ΛUV
ΛIR ∼ mW
How large ΛUV can we tolerate compatibly with Naturalness?
What can we broadly say about the physics at ΛUV ?
Thursday, August 20, 2015
Λg < 1.1
�1
�TeVΛt < 0.45
�1
�TeV Λg� < 3.7
�1
�TeV
δm2h =
3y2t4π2
Λ2t − 9g2
32π2Λ2g − 3g�2
32π2Λ2g� + . . .
Thursday, August 20, 2015
Λg < 1.1
�1
�TeVΛt < 0.45
�1
�TeV Λg� < 3.7
�1
�TeV
δm2h =
3y2t4π2
Λ2t − 9g2
32π2Λ2g − 3g�2
32π2Λ2g� + . . .
For moderate O(10%) tuning new states must exist in LHC range
• superso# models
• so# models
composite Higgs, low scale susy breaking,...
high scale susy breaking, eg. SUGRA
Λ2t =
4π2
3y2t× m2
h
�
Λ2t =
4π2
3y2t× 1
log ΛUVΛt
× m2h
�∼ m2
h
�
Thursday, August 20, 2015
Naturalness sets the mass scale but not the quantum numbers
• Charged-Naturalness No Loose Theorem: LHC should definitely find colored partners for moderate tuning
• Alternatives to Charged-Naturalness should be analysed seriously
• Twin Higgs: concrete scenario for Neutral-NaturalnessPractically the only one we have at the moment...
Classic solutions to the hierarchy problem all satisfy Charged-Naturalness:states at Λt, Λg , ... have same gauge charge as corresponding SM states
Chacko, Goh, Harnik 2005
Thursday, August 20, 2015
SMSU(3)× SU(2)× U(1)
Ψ, H
�SM�SU(3)× �SU(2)× �U(1)
�Ψ, �H
Z2
H = (H, �H) ≡ 8 SO(8)of custodial
is crucial, but enhanced accidental symmetry is not always robust. Ex.: original SU(4) model cannot be exported to composite case Z2
4 SU(4)( of )
Barbieri, Greco, RR, Wulzer 2015
SO(8)dynamics H
• strongish
• accidentally invariant up to
• h = pseudoNG of O(y4t ), O(g4)
SO(8)/SO(7)
Thursday, August 20, 2015
V (H) = −m2H(|H|
2 + | �H|2) + λ∗(|H|
2 + | �H|2)2
+λh
2
�|H|4 + | �H|4
�+ . . .
Thursday, August 20, 2015
V (H) = −m2H(|H|
2 + | �H|2) + λ∗(|H|
2 + | �H|2)2
+λh
2
�|H|4 + | �H|4
�+ . . .
SO(8)
Thursday, August 20, 2015
V (H) = −m2H(|H|
2 + | �H|2) + λ∗(|H|
2 + | �H|2)2
+λh
2
�|H|4 + | �H|4
�+ . . .
SO(8)
δm2H
>∼3y2t4π2
Λ2∗
t �t+
Thursday, August 20, 2015
V (H) = −m2H(|H|
2 + | �H|2) + λ∗(|H|
2 + | �H|2)2
+λh
2
�|H|4 + | �H|4
�+ . . .
SO(8)
δm2H
>∼3y2t4π2
Λ2∗
t �t+
∼ 3y4t32π2
logΛ∗/mt
Thursday, August 20, 2015
vacuum dynamics
V (H) = −m2H(|H|
2 + | �H|2) + λ∗(|H|
2 + | �H|2)2 +
λh
2
�|H|4 + | �H|4
�+ . . .
� �H�2 =m
2H
2λ∗≡ f
2SO(8) → SO(7)
7 NG-bosons = 6 eaten + (SM Higgs)λh = 0
λh �= 0
Λ∗ <∼ 5TeV ×�
1
�×
�λ∗
16π2hyperso# model
δm2h = λh(δf
2) =λh
λ∗× 3y2t
4π2× Λ2
∗
Thursday, August 20, 2015
but notice the conditions to have the maximal boost of Λ∗mh
H m2H ∼ 3y2t
4π2Λ2∗• scalar has strong quartic but a small mass
• it seems one needs both compositeness and and low scale supersymmetry breaking to realize the hypersoft scenario
• more realistically one has m2H ∼ Λ2
∗
δm2h =
λh
λ∗× Λ2
∗ ∼ 3y2t16π2
× y2tg2∗
× logΛ∗mt
× Λ2∗
Λ∗ <∼ 0.45× g∗yt
�
1
log×
�1
�TeV
g2∗ ≡ λ∗
true in both compositeness and high scale susy breaking models
Thursday, August 20, 2015
Broad structure of the spectrum
Λ∗colored/charged partners
SO(8) → SO(7) f =Λ∗g∗
= g∗f
m�t = ytf twin tops = SM neutrals
mt = ytv top
mh ∼�
3y2t8π2
log(Λ∗/mt) ytvmh
fine tuning ≡ � ∼ v2
f2
Thursday, August 20, 2015
Under all circumstances the boost factor in the relation betweenthe charged/colored partners and the Higgs mass is controlledby a ratio of couplings: the Twin Higgs mechanism works at its
best in the presence of a new strong dynamics
For sufficiently strong coupling it is conceivable to have a moderately tuned scenario where the colored and charged partners are out of the
reach of direct LHC searches
The preference for strong coupling limits the appeal of the Twin Higgs in supersymmetry as gauge unification gets murky
see eg. Craig, Howe ’14
Thursday, August 20, 2015
ΛUV
Λ∗
SM �SMH-sector~CFT
SO(8)× SU(3)×�SU(3)× U(1)X
The composite Twin Higgs scenario
gauge gauge
proto-Yukawa proto-Yukawa
Barbieri, Greco, RR,Wulzer ‘15Low, Tesi, Wang ‘15
Geller, Telem ’14
Thursday, August 20, 2015
ΛUV
Λ∗
SM �SMH-sector~CFT
SO(8)× SU(3)×�SU(3)× U(1)X
The composite Twin Higgs scenario
gauge gauge
proto-Yukawa proto-Yukawa
SO(8) → SO(7)
f ≡ Λ∗/g∗
SO(8) ⊃�
SO(4) 0
0 �SO(4)
�
2 = int × extint =
�0 4
4 0
�∈ SO(8)
Barbieri, Greco, RR,Wulzer ‘15Low, Tesi, Wang ‘15
Geller, Telem ’14
Thursday, August 20, 2015
• Physics robustly determined by symmetries and selection rules
• Explicit construction in 4D is in the realm of dreams
• But can be concretely realized via warped compactifications
• Weak scale simplified models through deconstruction (eg. 2 site model)
• In order to obtain a realistic vacuum dynamics, Z2 must be broken explicitly by a small amount
Geller, Telem ’14
Thursday, August 20, 2015
top yLQ̄LOR + yRt̄ROL + �yL �̄QL�OR + �yR�̄tR �OL
QL tR yt ∼yLyRg∗
yL = �yL yR = �yR yt = �ytZ2
SU(3) to protectneed g3 � �g3 yL,R = �yL,R across RG scales
elementary twin sector replicates matter content of SM: 3 families
SU(2) g2 � �g2 to protect O(g2) corrections to mh2
and push vector partners above LHC reach
Thursday, August 20, 2015
U(1)Y no real need to gauge �U(1)YΛg� = 3.7
�1
�TeV
we assume is not gauged �U(1)Y
advantages• get rid of massless twin photon• introduce a small and partly controllable source of twin
parity breaking y2L − �y2Ly2L
=g2Y16π2
logΛUV
Λ∗
Thursday, August 20, 2015
Scalar potential & vacuum dynamics
SO(8)/SO(7) 6 + 1 NG-bosons
eaten Higgs
Σ(h) ≡ U(h)Σ(0) =
000h000�
f2 − h2
h ≡ fs�
f2 − h2 ≡ fc
V (h) Symmetries and selection rules
Thursday, August 20, 2015
W �W one invariantO(g2)
+
∝ s2 + c2 = const
W �WO(g4)
Ag2 s2 Ag2 c2
∝ g4(s4 + c4) �= const
Notice: at O(g2) in SU(4)/SU(3) there instead exist two invariants !!
As2 +Bs4 Ac2 +Bc4 �= const
Thursday, August 20, 2015
O(g2Y )B �B ∼ 3Λ2
∗f2
128π2g2Y s2
Thursday, August 20, 2015
most convenient choice of quantum numbersyR, �yR respect SO(8)
yL, �yL break SO(8)
y2L − �y2Ly2L
= small
3Λ2∗f
2
32π2A
�y2L − �y2L
�s2
� 3f4
32π2B y4L
�s4 + c4
�
UV
IR � 3f4
64π2y4t
�s4 log
Λ2∗
y2t f2s2
+ c4 logΛ2∗
y2t f2c2
�.
yL = ytg∗yR
> yt
Thursday, August 20, 2015
putting all relevant effects together
V (h)
f4= αs2 + β
�s4 log
a
s2+ c4 log
a
c2
�
β =3y4t64π2
log a = logΛ2∗
y2t f2+
y4Ly4t
B
α =g2Y g
2∗
64π2C
α
β= −1 + 2 log a+O(ξ)v2
f2= ξ ≡ �s2� � 1
mh
vlog a � 6 + log
�ξ
Λ∗ = 7TeV ξ = 0.1 B = 0Ex.:
must push C to the edge
Thursday, August 20, 2015
UV issues
Precision Physics
Thursday, August 20, 2015
Precision Physics
Flavor: effect of resonances scales likey#
Λ2∗∝ 1
Λ2∗
weak proto Yukawa
(SM fermions approx elementary)
• clear benefit from twin mechanism• still need flavor symmetries to control FCNC and CP violation
Higgs: effect of resonances scales like(Higgs is composite)
g2∗Λ2∗
∝ 1
f2
• corrections to Higgs coupling are unaffected• this percolates to EWPT
Thursday, August 20, 2015
∆�3 = O(1)× m2W
Λ2∗
+g2
96π2
v2
f2ln(Λ∗/mh)
∆�1 =A
16π2
y4L v2
Λ2∗
− 3g2 tan θ2W32π2
v2
f2ln(Λ∗/mh)
68�, 95�, 99� CL
0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
Ε3
Ε10.2
1
0.1
v2
f2
�1
�3
Thursday, August 20, 2015
∆�3 = O(1)× m2W
Λ2∗
+g2
96π2
v2
f2ln(Λ∗/mh)
∆�1 =A
16π2
y4L v2
Λ2∗
− 3g2 tan θ2W32π2
v2
f2ln(Λ∗/mh)
68�, 95�, 99� CL
0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
Ε3
Ε10.2
1
0.1
v2
f2
�1
�3
Thursday, August 20, 2015
∆�3 = O(1)× m2W
Λ2∗
+g2
96π2
v2
f2ln(Λ∗/mh)
∆�1 =A
16π2
y4L v2
Λ2∗
− 3g2 tan θ2W32π2
v2
f2ln(Λ∗/mh)
68�, 95�, 99� CL
0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
Ε3
Ε10.2
1
0.1
v2
f2
�1
�3
Thursday, August 20, 2015
∆�3 = O(1)× m2W
Λ2∗
+g2
96π2
v2
f2ln(Λ∗/mh)
∆�1 =A
16π2
y4L v2
Λ2∗
− 3g2 tan θ2W32π2
v2
f2ln(Λ∗/mh)
68�, 95�, 99� CL
0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
Ε3
Ε10.2
1
0.1
v2
f2in principle can compensate
by pumping yL
yL = ytg∗yR
�1
�3
Thursday, August 20, 2015
∆�3 = O(1)× m2W
Λ2∗
+g2
96π2
v2
f2ln(Λ∗/mh)
∆�1 =A
16π2
y4L v2
Λ2∗
− 3g2 tan θ2W32π2
v2
f2ln(Λ∗/mh)
68�, 95�, 99� CL
0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
Ε3
Ε10.2
1
0.1
v2
f2in principle can compensate
by pumping yL
yL = ytg∗yR
�1
�3
But must study correlation with and higgs quartic Zbb̄
∆���yL
= Cm2
h
Λ2∗= 10−3 C
�4TeV
Λ∗
�2
Ex.:
Thursday, August 20, 2015
IR issues
Cosmology and Phenomenology
Craig, Katz, Strassler, Sundrum ’15Craig, Katz ’15Farina ’15Garcia Garcia, Lasenby, March-Russell ’15
Thursday, August 20, 2015
effective relativistic species at nucleosynthesis and recombination ν̃i γ̃ ∆Neff
Planck 2015 Neff = 3.15± 0.23
breaking from and do not generate sufficient asymmetry 2 v2 � f2 gY
Two broad options
• introduce and give the twin neutrinos a mass Ex.: seems a good range
• raise all other twin states just above the temperature TD where the SM and the twin SM decouple
ν̃iRmν̃ � 1− 20GeV
Barbieri, Hall, Gregoire ’05Craig, Katz, Strassler, Sundrum ’15
Thursday, August 20, 2015
�SM SM
TD
SM �SMh very roughly
TD ∼ GeV × (0.1/ξ)1/3
∆Neff < 0.5
can be pushed up by raising twin quark masses�ΛQCD
m�u,�d,�s,�c,�b ≡ M�q�ΛQCD
ΛQCD∼ 4.5
�0.1
ξ
� 233
�M�q
90GeV
� 1033
ΛQCD < TD < �ΛQCD
Thursday, August 20, 2015
Tentatively, a consistent picture arises in the parameter where the glueballs are the lighest massive states in the Twin sector
and thus dominate final state dynamics at collider
is low enough not to affect Higgs potential M�q = 90GeV
but safely above thresholdh → �q�̄q
Thursday, August 20, 2015
production in Higgs decay
q̃ Γ(h → �g�g)Γ(h → gg)
=
�6�α3
α3
v2
f2
�2
Br(h → �g�g) = 0.03×�
ξ
0.1
�2
Glueballs tend to decay to SM ouside detector
glueball decays via Higgs mixing0++
cτG = 3m
�8GeV
mG
�7 �0.1
ξ
�2
fragmentation and decay
Craig, Katz, Strassler, Sundrum ’15
Thursday, August 20, 2015
• Naturalness: Symmetries & Selection Rules
• Natural Hierarchy (business as usual): new states around the weak scale
• Unnatural Hierarchy: history and a landscape enter particle physics•cosmological constant: first blatant case of fine tuning•global symmetries : tuned SM structurally superior to its natural extensions•the neatest incarnations of naturalness have since long missed their appointment
• Well motivated model building remains our only way to give shape to the unknown and guide experimental searches
Summary
Thursday, August 20, 2015
• Twin Higgs concretely illustrates how the signature of naturalness at the LHC may not be the production of colored and weakly interacting states, but rather exotic higgs decays channels (possibly with displaced vertices)
• The mass of colored states is boosted up by the strength of a new dynamics
• The idea seems a bit too clever and cosmology forces us to open a Pandora box of options. But their exploration is necessary to picture the phenomenology.
Thursday, August 20, 2015
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