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Dark Matterin a twisted bottle!
Giacomo CacciapagliaIPN Lyon (France)
University of the WitwatersrandJohannesburg, 12-11-2013
With: A.Arbey, A.Deandrea, B.Kubik, J.Llodra-Perez, L.Panizzi
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Why do we need BSM?
The Higgs boson has beendiscovered.
The Standard Modelis now complete!
Ian MacNicol / AFP - Getty Images
The discovery of the Higgs boson has brought the Naturalness problem toreality! New Physics at the TeV scale needed more than before!
There are other unresolved puzzles: what is Dark Matter made of?
2
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Dark Matter evidences:
The Universe contains 4.6% of
baryons, and 23.3% of unknownmatter.
The flat rotation curves of spiralgalaxies can be explained by thepresence 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:
3
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WIMP paradigm
A stable neutral particle:
Thermally produced in the early universe:
Left as a relic when the annihilations become ineffective!
A Forbidden bysymmetry!
A
A
A
A
A A
A
AA
A
A
A
A A
AA
CfAsurvey
Gravity!
Extra
dimensions?
4
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A closer look to Extra Dimensions
Action for a masslessscalar in D-dimensions
Expansion in 4-dim fieldson compact extra space:
D-dim fields correspond to tower of massive 4-dim fields
S =
dDx
D4j=5
jj
(x, xj) =
d4p
(2)4eipx
k
k(p)fk(xj)
5
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A closer look to Extra Dimensions
Action for a masslessscalar in D-dimensions
Expansion in 4-dim fieldson compact extra space:
D-dim fields correspond to tower of massive 4-dim fields
S =
dDx
D4j=5
jj
(x, xj) =
d4p
(2)4eipx
k
k(p)fk(xj)
0
2
x5
R5 0
2
x6
R6
1.0
0.5
0.0
0.5
.0 The extra space islike a vibrating membrane,
a drum!
6
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A closer look to Extra Dimensions
Action for a masslessscalar in D-dimensions
Expansion in 4-dim fieldson compact extra space:
D-dim fields correspond to tower of massive 4-dim fields
ks are like frequenciesof vibrating membrane!
S =
dDx
D4j=5
jj
(x, xj) =
d4p
(2)4eipx
k
k(p)fk(xj)0
2
x5
R5 0
2
x6
R6
1.0
0.5
0.0
0.5
.0 Transferringenergy can excite a
vibration.02
x5
R5 0
2
x6
R6
1.0
0.5
0.0
0.5
1.0
7
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A closer look to Extra Dimensions
Action for a masslessscalar in D-dimensions
Expansion in 4-dim fieldson compact extra space:
D-dim fields correspond to tower of massive 4-dim fields
ks are like frequenciesof vibrating membrane!
Massesand interactions determined by the wave functions !fk(xi)
S =
dDx
D4j=5
jj
(x, xj) =
d4p
(2)4eipx
k
k(p)fk(xj)
Increasing energy:more massive mode!
!02
x5
R5 0
2
x6
R6
1.0
0.5
0.0
0.5
.0
E = mc2
0
2
x5
R5 0
2
x6
R6
1.0
0.5
0.0
0.5
1.0
8
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A closer look to Extra Dimensions
Action for a masslessscalar in D-dimensions
Expansion in 4-dim fieldson compact extra space:
D-dim fields correspond to tower of massive 4-dim fields
ks are like frequenciesof vibrating membrane!
Massesand interactions determined by the wave functions !
Symmetriesof the compact space = global symmetries of 4-dim fields:transformation properties of the wave functions!
Can such symmetry stabilise the Dark Matter?
fk(xi)
S =
dDx
D4j=5
jj
(x, xj) =
d4p
(2)4eipx
k
k(p)fk(xj)
Symmetries= geometry ofthe membrane!
0
2
x5
R5 0
2
x6
R6
1.0
0.5
0.0
0.5
.0
0
2
x5
R5 0
2
x6
R6
1.0
0.5
0.0
0.5
.0
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Stability of the Dark Matter requiresa symmetry!
Symmetries of the compact space ARE parities for the Kaluza-Klein modes!
The physics is in the wave functions: for instance
Can it arise ``naturally from extra dimensions?
However, fixed points (in red)are NOT invariant!
x5 R x5
coskx5
R
(1)k cos
kx5
R
.
S1/Z2Orbifold
0 !R
!R/2
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Stability of the Dark Matter requiresa symmetry!
Symmetries of the compact space ARE parities for the Kaluza-Klein modes!
The physics is in the wave functions: for instance
Can it arise ``naturally from extra dimensions?
However, fixed points (in red)are NOT invariant!
x5 R x5
coskx5
R
(1)k cos
kx5
R
.
S1/Z2Orbifold
0 !R
!R/2
KK-parity is ad-hocsymmetry!
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Stability of the Dark Matter requiresa symmetry!
Symmetries of the compact space ARE parities for the Kaluza-Klein modes!
The physics is in the wave functions: for instance
Can it arise ``naturally from extra dimensions?
However, fixed points (in red)are NOT invariant!
x5 R x5
coskx5
R
(1)k cos
kx5
R
.
S1/Z2Orbifold
0 !R
!R/2
In Gauge-Higgs Unification models, or models of flavour,fermion localisation is essential!
Bulk fermion masses breakthe KK parity!
Already pointed out byBarbieri, Contino, Creminelli, Rattazzi, Scrucca
hep-th/02030390 R2 R
eL eR
Higgs
KK-parity is ad-hocsymmetry!
KK-parity absentin interesting models!
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Do orbifolds exist without fixed pointsand with chiral fermions?
There is none in 5D...
In 6D there are 17 orbifolds (characterised by the discretesymmetry groups of the flat plane)...
only ONE has chirality and no fixed points/lines! Unique candidate!
Requiring an exact parityand chirality is rather restrictive!
G.C., A.Deandrea, J.Llodra-Perez 0907.4993
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R5 2R5
R6
2R6
!
pgg=r, g|r = (g r) = 1
r :x5 x5x6 x6
g :x5 x5 + 5x6 x6 + R6
Translations defined as:
t5 = g
t6 = (gr)2
Two singular points:
(0,) (,0)
(0,0) (,)
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
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The flat real projective plane
pgg=r, g|r = (g r) = 1 G.C., B.Kubik 1209.6556
Fundamental domain invariant under:
Can be redefined as a translation,which commutes with orbifold symmetries:
R5 2R5
R6
2R6
!
Modes (k, l) : pKK= (1)k+l
r:
x5 x5 + R5
x6 x6 + R6
pKK = rr :
x5 x5 + R5x6 x6 + R6
This is an exact symmetry!
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The flat real projective plane
pgg=r, g|r = (g r) = 1 G.C., B.Kubik 1209.6556
Fundamental domain invariant under:
Can be redefined as a translation,which commutes with orbifold symmetries:
This symmetry is respected by bulk interactions!
Violated by localised interactions!
R5 2R5
R6
2R6m4 :
x5 x5 + R5
x6 x
6
m4 g r :
x5 x5x6 x6 + R6
Modes (k, l) : pKK= (1)l
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The flat real projective plane
pgg=r, g|r = (g r) = 1 G.C., B.Kubik 1209.6556
R
R
2R
2R
Case of symmetric radii:
md :
x5 x6
x6 x5
md g md = g r :
x5 x5 + R5x6 x6 + R6
Fundamental domain invariant under:
However, it is not a good symmetry, becauseit does NOT commute with the glide:
It does not respect orbifold projections:e.g., a (-+) field mapped into a (--) field!
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Spectrum of the SM- -+ + +
DM candidate here!18
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Spectrum of the SM- -+ + +
One-loop corrections are crucial to determine spectrum and decays!G.C., A.Deandrea, J.Llodra-Perez 1104.3800
G.C., B.Kubik 1209.655619
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Spectrum of the SM
!R6
!R5
LSM =1
4F2 + i
yf H
+ (DH)2 V(H)
Lloc =(y5)(y6)
m2locH
2 +
+1
2 1
4
F2 + . . .Higher orderoperators!
Bulk: KK number conserving!
Localised: KK number violating!
Counter-terms for1-loop
log divergences!
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6D loops from 4D
i = g2C2(G)
ab
164i2
2
2M2(+ 3)g ( 5)(q2g qq)
= g2C2(G)
ab
164
4i2
q2g qq
i = g2C2(G)
ab
164i2
2 [iM(+ 3)q)] = 0
iV = ig fa cC2(G)
164i
4 (3+ 7) O
= ig3fabcC2(G)
1644i2
O
= log R
=3
In red
gauge
(2k,2l) (0,0)
(k,l)
(2k,2l)
(0,0)
(0,0)
(k,l)
G.C., A.Deandrea, J.Llodra-Perez 1104.3800
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6D loops from 4D
i = g2C2(G)
ab
164i2
2
2M2(+ 3)g ( 5)(q2g qq)
= g2C2(G)
ab
164
4i2
q2g qq
i = g2C2(G)
ab
164i2
2 [iM(+ 3)q)] = 0
iV = ig fa cC2(G)
164i
4 (3+ 7) O
= ig3fabcC2(G)
1644i2
O
= log R
=3
In red
gauge
(2k,2l) (0,0)
(k,l)
(2k,2l)
(0,0)
(0,0)
(k,l)
In gauge the divergences match withthe gauge-invariant counterterms!
= 3
r10
422R2=
r1
422R2=
g C(G)
162 log R
G.C., A.Deandrea, J.Llodra-Perez 1104.3800
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The two radii R5and R6
The effective cut-off ", enteringlogarithmically in the loop corrections
The localised Higgs mass mloc
Spectrum of the SM
The model has 4 free parameters:
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asymmetric radii R5 > R6
only (1,0) and (2,0) modes relevant
Spectrum of the SM
We focus on two different limits:
Spectrum of the SM
symmetric radii R5 = R6
(1,0) and (0,1) exactly degenerate (up to higher order ops)
only states (2,0) + (0,2) relevant: mass splitting nearly doubled,couplings to SM pair
tier (2,0) - (0,2) decouples (up to higher order operators)
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WMAP bounds!
5
There are several equally relevant
contributions:
Annihilation Co-annihilation(small mass splitting)
Resonant annihilation(s-channel level 2 states!)
Level 2 annihilation(level 2 decaying into SM pair!)
A.Arbey, G.C., A.Deandrea, B.Kubik 1210.0384
G.Belanger, M.Kakizaki, A.Phukov 1012.2577
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WMAP bounds: tier (2) effect
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
300200
100200 300 400 500 600 700 800 900
0.0
0.1
0.2
0.3
0.4
m_KKGeV
h2
WMAP
Only SM
300
200mloc = 100
Annihilation into level-2 increased cross-sections higher mKK
mloc controls H(2,0)resonance!
H(2,0)opens resonant funnel!
Numerical results from MICROMEGAS
R5> R6
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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
300200
100
Numerical results from MICROMEGAS
R5> R6
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WMAP bounds: R5> R6vs. R5= R6
In the symmetric case, we have typically smaller mKK
The reason is that two tiers contribute to the relic abundance!
Numerical results from MICROMEGAS
R5> R6
200 300 400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
m_KKGeV
h2
200 300 400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
m_KKGeV
h2
R5= R6
WMAP WMAP
Asymmetric Symmetric
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WMAP bounds: cut-off dependence
In the annihilation case, larger mass splitting suppressed cross sections
(t-channel exchange of massive states)
For co-annihilation, larger mass splitting implies the other statescontribute less, thus less degrees of freedom available!
Numerical results from MICROMEGAS
R5> R6
200 300 400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
m_KKGeV
h2
200 300 400 500 600 700 800 9000.0
0.1
0.2
0.3
0.4
m_KKGeV
h2
Annihilationonly
Co-annihilations"R
!mKK decreases
!mKK increases
WMAP WMAP
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Direct detection bounds
Relevant processes:crucial the loop correctionsto level-1 masses!
The Spin-Independent cross section is enhanced by the smallsplittings!
1000500200 2000300 150070010
46
1045
1044
10
43
1042
1041
1040
m
KKGeV
WIMPnucleonc
rosssectioncm
2
XENON 2012
!R = 2
!R = 5
!R = 10
Bound sensitive tocut-off "
via log-div. loops!
Independent onradii config.
Numerical results from MICROMEGAS
30
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Direct detection bounds
Relevant processes:crucial the loop correctionsto level-1 masses!
The Spin-Independent cross section is enhanced by the smallsplittings!
2 4 6 8 10200
400
600
800
1000
R
mKK
GeV
Excluded!Xenon2012
2 4 6 8 10200
400
600
800
1000
R
mKK
GeV
Excluded!
Xenon2012
R5> R6 R5= R6
Numerical results from MICROMEGAS
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LHC signatures without MET:tiers (2,0) and (0,2)
Cleanest channels are di-lepton (Z) and single lepton + MET (W):
Z(2,0), A(2,0)-> l l
W(2,0)-> l #
l+
l-loop
Z(2,0)q(2,0)
q(2,0)
BR: 0.2% !!
G.C., B.Kubik 1209.6556
32
ATLAS 20fb
CMS 20fb
Z' l l
8 TeV
300 400 500 600 700 800
0.1
1
10
100
0.1
1
10
100
mKK
fb
We assume here same efficiencies
as the Z model in the analysis.
The di-electron channel may beable to see two peaks!
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MET signatures from (1,0) and (0,1):
lighter, but relying on ISR!
G.C., A.Deandrea, J.Ellis, L.Panizzi, J.Marrouche 1302.4750
t
t
A(1,0)q(1,0)
q(1,0)
_
MET
33
Bound between600 and 700 GeV!
The second tierhas a strong impact!
LHC signatures with MET:
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Other LHC bounds
4-top final state: search in same-sign dileptons
G.C., R.Chierici, A.Deandrea, L.Panizzi, S.Perries, S.Tosi1107.4616
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!
34 [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,-1
Ldt = 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
R6R5
mKK
GeV Z (8 TeV)
MET (7 TeV)
4 tops (8 TeV)
XENON ("R=10)
XENON ("R=4)
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The phenomenology depends crucially on thegeometry: spherical RPP
Conclusions and outlook
KK modes labelled byangular momentum (l,m)
m2(l,n)=
l(l + 1)
R2
No fixed points:tiny finite loop corrections
Angular momentum isconserved on the orbifold!
Each KK tier containsa stable DM candidate!
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0.5
1.50.5
1.5
A
B
2 1 0 1 2
1.0
0.5
0.0
0.5
1.0
1.5
2.0
k
kgg
LHC: the Higgs discovery!
The KK resonances of W and top contribute to H$gg and H $%%loops!
G.C., A.Deandrea, J.Llodra-Perez 0901.0927G.C., A.Deandrea, G.Drieu La Rochelle, J.B.Flament 1210.8120
CMS data
(HCP12)
H $%%
H $ZZ
mKK = 600 GeV
kgg, k%%!1/mKK2
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