dark matter from extra dimensions and strong dynamics -...
TRANSCRIPT
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:
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
★
★
☀
☀
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)