its Composite Incarnation - Chalmers fysik... · its Composite Incarnation Riccardo Rattazzi, EPFL...

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−�

Λ�IR = cΛ�

UV ΛIR = c1/� ΛUV

algebraica"y small and is enough to produce hierarchyc �

Ex: Yang-Mills, TechniColor, Randall-Sundrum model Rattazzi, Zaffaroni 01Strassler 03


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


ΛIR

ΛUV

3. Sequestering


SFT2

SFT1O(�)

ΛIR

ΛUV

3. Sequestering


SFT2

SFT1O(�)

ΛIR

ΛUV

3. Sequestering

DilationsD1 ×D2 → D1+2

by small coupling �

ΛIR ∼ �ΛUV technically natural


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


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 ?


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


ΛUV

ΛIR ∼ mW

How large ΛUV can we tolerate compatibly with Naturalness?

What can we broadly say about the physics at ΛUV ?


Λg < 1.1

�1

�TeVΛt < 0.45

�1

�TeV Λg� < 3.7

�1

�TeV

δm2h =

3y2t4π2

Λ2t − 9g2

32π2Λ2g − 3g�2

32π2Λ2g� + . . .


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

�


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


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)


V (H) = −m2H(|H|

2 + | �H|2) + λ∗(|H|

2 + | �H|2)2

+λh

2

�|H|4 + | �H|4

�+ . . .


V (H) = −m2H(|H|

2 + | �H|2) + λ∗(|H|

2 + | �H|2)2

+λh

2

�|H|4 + | �H|4

�+ . . .

SO(8)


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+


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


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

∗


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


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


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


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


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


• 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


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


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∗


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


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


O(g2Y )B �B ∼ 3Λ2

∗f2

128π2g2Y s2


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


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


UV issues

Precision Physics


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


∆�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


∆�3 = O(1)× m2W

Λ2∗

+g2

96π2

v2

f2ln(Λ∗/mh)

∆�1 =A

16π2

y4L v2

Λ2∗


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


∆�3 = O(1)× m2W

Λ2∗

+g2

96π2

v2

f2ln(Λ∗/mh)

∆�1 =A

16π2

y4L v2

Λ2∗


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.:


IR issues

Cosmology and Phenomenology

Craig, Katz, Strassler, Sundrum ’15Craig, Katz ’15Farina ’15Garcia Garcia, Lasenby, March-Russell ’15


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


�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


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


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


• 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


• 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.


its Composite Incarnation - Chalmers fysik... · its Composite Incarnation Riccardo Rattazzi, EPFL...

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