Dark Matterfrom extra dimensionsand strong dynamics

Giacomo CacciapagliaIPN Lyon (France)

KIAS Workshop2014/10/29

Dark Matter evidences:

The Universe contains 4.6% of baryons, and 23.3% of unknown matter.

The flat rotation curves of spiral galaxies can be explained by the presence of extra non-luminous matter.

WMAP science team

Observations both in Astrophysicsand Cosmology suggest

the presence of “Dark” Matter,not explained in the Standard Model!

Cosmic Microwave Background:

Astrophysical measurements:

2

Can the Higgs be a compositestate of a confining dynamics?

G → HGlobal symmetries:

Gauge symmetries:

U UGSM → U(1)em Georgi, Kaplan

1984

1 The Higgs as a (pseudo-)GB of a broken global symmetry:

h ∈ G/H

2 The Higgs as a heavy spin-0 resonance:

h singlet of HDilaton/Radion

Higgs

Can the Higgs be a compositestate of a confining dynamics?

G → HGlobal symmetries:

Gauge symmetries:

U UGSM → U(1)em Georgi, Kaplan

1984

1 The Higgs as a (pseudo-)GB of a broken global symmetry:

h ∈ G/H

2 The Higgs as a heavy spin-0 resonance:

h singlet of HDilaton/Radion

Higgs

Pions in QCD

σ meson in QCD

1 What underlying dynamics is up to the job?Principle: a simple model

Consider a confining gauge group G,

with N fermions in the rep R of G.ψf

If R is real or pseudo-real, the condensate will be:

�ψiψj�

symmetric ⇒ SU(N) → SO(N)

anti-symmetric ⇒ SU(N) → Sp(N)

(The fermions are chiral, and the global flavour symmetry is SU(N))

If R is complex, the condensate will be:(The fermions are not chiral, and the global flavour symmetry is SU(N) x SU(N))

�ψ̄iψj� ⇒ SU(N)× SU(N) → SU(N)

1

Minimal case 1 bi-doublet + 1 singlet

Non-custodial This is like QCD

Minimal 2HDM 2 bi-doublets + 6 singlets

Contains EW triplets

What underlying dynamics is up to the job?

Batra, Csako 0710.0333Ryttov, Sannino 0809.0713

Galloway, Evans, Luty, Tacchi 1001.1361Barnard, Gherghetta, Ray 1311.6562

G.C., Sannino 1402.0233

Ferretti 1404.7137

G.C., Lespinasse, work in progress

Bellazzini, Csaki, Serra, 1401.2457

The minimal case:

Sp(4) has rank = 2, and it contains an SU(2)xSU(2) subgroup

SU(4)→ Sp(4) ∼ SO(5)

The condensate transforms as:

�ψiψj� = 6SU(4) → 5Sp(4) ⊕ 1Sp(4)

5Sp(4) → (2, 2)⊕ (1, 1) of SU(2)xSU(2): Higgs doublet + singlet

Goldstone bosons

Massivescalar

like the σ mesonin QCD

Question 1: does this breaking patternreally take place?

1Sp(4) → (1, 1)

Katz, Nelson, Walker hep-ph/0504252Gripaios, Pomarol, Riva, Serra, 0902.1483Galloway, Evans, Luty, Tacchi 1001.1361

SU(2)L × U(1)Y → U(1)em

SU(4)→ Sp(4) ∼ SO(5)U U

θ θ=0No EWSB

θ=π/2Technicolour

A pseudo-Goldstone (composite) Higgsexists in between!

2 light scalars, no HiggsHiggs must be a TC excitation

4 massless Goldstone Bosons

Cacciapaglia, Sannino1402.0233

Question 2: how is EW symmetry broken?(This is an issue of alignment!)

Do we have a dynamicalmodel for this?

SU(4)→ Sp(4) ∼ SO(5)

< QiQj > condensate forms and breaks(proven on the lattice)

Lewis, Pica, Sannino 1109.3513+ Hietanen 1404.2794

with 4 Weyl doublets QiG = SU(2)

�Q1

Q2

�= (2, 1) ,

�Q3

Q4

�= (1, 2)

The EW symmetry can be embedded in SU(4)by assigning the following properties:SU(2)L × SU(2)R

Batra, Csako 0710.0333Ryttov, Sannino 0809.0713

Introducing a potential for θ

V (θ) = y�t2Ct cos2 θ − 4Cm cos θ + const.

|cos θ|min =2Cm

y�t2Ct

if y�t2Ct > 2|Cm|

y�t2Ct ∼ 2CmNote: to obtain θ∼0, we need to tune 0 Π�4 Π�2 3Π�4 Π

0.0

0.2

0.4

0.6

0.8

1.0

Cm = 0

2Cm > y�t2Ct

m2η =

y�t2Ct

4f2

m2h =

y�t2Ct

4f2 sin2 θ = m2

η sin2 θ =Ctm2

t

4

mh = 125 GeV for Ct ∼ 2

∼ v2

The Higgs mass fine-tuning

Both Order f!

δm2h

��top

=Cty�

t2f2

8(2 sin2 θ − 1)

δm2h

��m

=2Cmf2

8cos θ

The Higgs mass fine-tuning

✗✗δm2h

��m

=2Cmf2

8cos θ =

Cty�t2f2

8(1− sin2 θ)

✗ ✗δm2h

��top

=Cty�

t2f2

8(2 sin2 θ − 1) Sum is Order

v = f sin θ

The tuning that keeps θ smallprotects the Higgs mass:

mh → 0 for θ → 0

Predictions from the Lattice:

Lewis, Pica, Sannino 1109.3513+ Hietanen 1404.2794

{

{

Predictions from the Lattice:

Spectrum:

Higgs mH = 125 GeV

scalar singlet mη =mH

sin θ

vector resonancesρ and a mρ =

2.5± 0.5sin θ

TeV

ma =3.3± 0.7

sin θTeV } Lattice

results!

Not a prediction!

15/19

For sin θ = 0.2 (typical value):

Higgs mH = 125 GeV

scalar singlet

vector resonancesρ and a } Lattice

results!

Not a prediction!

ma = 16.5± 3.5 TeV

mρ = 12.5± 2.5 TeV

mη = 625 GeV

Predictions from the Lattice:

No light top partnersare needed to cancel

the top loop!

15/19

A slide on the θ = π/2 vacuum:

- +

h + i η charged under a global unbroken U(1)Candidate for asymmetric Dark Matter

m2DM = Ct

y�t2f2

4= Ct

m2t

4

Generic θ:

η has no linear couplings:Candidate for Dark Matter?

Frigerio, Pomarol, Riva, Urbano 1204.2808

NO!

Once a dynamical theory is defined, η can decay via the “chiral” anomaly:

LWZW =dR

48π2

cos θ

2√

2fη

�g2WµνW̃µν − g�2BµνB̃µν

�+ . . .

η → W W, ZZ, Zγ

dimension of Q under confining group

Q

Q

Q

η

V

V

Minimal case NO DARK MATTER

Minimal 2HDM 4 neutral singlets

Contains EW triplets

Back to the table:

8/19

Extra dimensions:

Chiral fermions

An exact parity from the compactification

★

★

☀

☀

πR5 2πR5

πR6

2πR6

☒

pgg = �r, g|r2 = (g2r)2 = 1�

r :�

x5 ∼ −x5

x6 ∼ −x6g :

�x5 ∼ x5 + πR5

x6 ∼ −x6 + πR6

Translations defined as:

t5 = g2

t6 = (gr)2

Two singular points:

(0, π) ∼ (π, 0)

(0, 0) ∼ (π, π)

KK parity is an exact symmetryof the space!

Spectrum and interactionsdetermined by

these symmetries!

The “flat” real projective plane

G.C., A.Deandrea, J.Llodra-Perez 0907.4993

The “flat” real projective plane

pgg = �r, g|r2 = (g2r)2 = 1� G.C., B.Kubik 1209.6556

Fundamental domain invariant under:

Can be redefined as a translation, which commutes with orbifold symmetries:

★

★

☀

☀

πR5 2πR5

πR6

2πR6

☒

Modes (k, l) : pKK = (−1)k+l

r� :�

x5 → −x5 + πR5

x6 → −x6 + πR6

pKK = r� ∗ r :�

x5 → x5 + πR5

x6 → x6 + πR6

This is an exact symmetry!

Spectrum of the SM

π R6

★

★

☀

☀

π R5

LSM =− 14F

2 + iψ̄∂ψ

− yf ψ̄ψ H

+ (DH)2 − V (H)

Lloc =δ(y5)δ(y6)�−m

2locH

2 +

+1Λ2

�−1

4F

2 + . . .

��

Higher orderoperators!

Bulk: KK number conserving!

Localised: KK number violating!

Counter-terms for1-loop

log divergences!

WMAP bounds: H(2) resonance

WMAP preferred range:700 < mKK < 1000

Annihilation into level-2 ⇒ increased cross-sections ⇒ higher mKK

mloc controls H(2,0) resonance!

H(2,0) opens resonant funnel up to 1200!

200 400 600 800 1000 1200 1400200

250

300

350

400

450

500

m_KK !GeV"

mloc

Disfavoured byT parameter!

H(2,0) resonance

200 300 400 500 600 700 800 9000.0

0.1

0.2

0.3

0.4

m_KK �GeV��h2

WMAP

Includes level 2

300200100

Numerical results from MICROMEGAS

R5 > R6

Other LHC bounds4-top final state: search in same-sign dileptons

G.C., R.Chierici, A.Deandrea, L.Panizzi, S.Perries, S.Tosi 1107.4616

t

tH.O.

A(1,1)q(1,1)

q(1,1)

_

Tier (1,1) cannot decay at loop level into SM,nor into a pair of (1,0) + (0,1)!

Chain decay into lightest state A(1,1)

A(1,1) can decay into t tbar!

HUGE production cross sections: all KK statescontribute to it!

[TeV]KKm0.6 0.7 0.8 0.9 1 1.1 1.2

BR

[pb]

×

-310

-210

-110

1

Expected limit at 95% CL

1 ±Expected limit

2 ±Expected limit

Theory approx. LO

Observed limit at 95% CL

ATLAS Preliminary

= 8 TeVs, -1Ldt = 14.3 fb

Dedicated ATLAS searchin same-sign dilepton final states.

1.0 1.2 1.4 1.6 1.8 2.0

600

650

700

750

800

850

900

R6�R5

mKK�GeV

� Z’ (8 TeV)

MET (7 TeV)

4 tops (8 TeV)

XENON (ΛR=10)

XENON (ΛR=4)

Conclusions

A composite Higgs is still compatible with the LHC data (depending on the model...)

Dark matter can arise as an additional pNGB

In extra dimensions, only very few orbifolds have a residual exact parity, thus a DM candidate

Testable at the LHC and Direct Detection