!"#$%
Marco Cirelli(CNRS LPTHE Jussieu Paris)
NewDark
5 February 2016IPMU, Kashiwa, Japan
Minimal Dark Matter,reloaded
Based on: Cirelli, Fornengo, Strumia ‘Minimal Dark Matter’, NPB 2006 +…Cirelli, Sala, Taoso, JHEP 2014Cirelli, Hambye, Panci, Sala, Taoso, JCAP 2015
IntroductionIntroduction
IntroductionIntroductionDM exists
IntroductionDM exists
galactic rotation curvesweak lensing (e.g. in clusters)
‘precision cosmology’ (CMB, LSS)
IntroductionDM exists
galactic rotation curvesweak lensing (e.g. in clusters)
‘precision cosmology’ (CMB, LSS)
But: what is it?
weakly int., massive, neutral, stableMost likely a
relic particle.
weakly int., massive, neutral, stableMost likely a
has the correct relic abundance today!
Kolb
,Tur
ner,
The
Early
Univer
se, 1
995
ΩX ≈6 10−27cm3s−1
⟨σannv⟩
Boltzmann eq. in the Early Universe:
Weak cross section:
⟨σannv⟩ ≈α2
w
M2≈
α2w
21TeV
ΩX ∼ O(few 0.1)⇒
Most likely a
has the correct relic abundance today!
Kolb
,Tur
ner,
The
Early
Univer
se, 1
995
ΩX ≈6 10−27cm3s−1
⟨σannv⟩
Boltzmann eq. in the Early Universe:
Weak cross section:
⟨σannv⟩ ≈α2
w
M2≈
α2w
21TeV
ΩX ∼ O(few 0.1)⇒
weakly int., massive, neutral, stable(or we would
have seen it...)
Most likely a
has the correct relic abundance today!
Kolb
,Tur
ner,
The
Early
Univer
se, 1
995
ΩX ≈6 10−27cm3s−1
⟨σannv⟩
Boltzmann eq. in the Early Universe:
Weak cross section:
⟨σannv⟩ ≈α2
w
M2≈
α2w
21TeV
(or we would have seen it...)
at least on cosmological time scales, i.e.
ΩX ∼ O(few 0.1)⇒
weakly int., massive, neutral, stable
τ > tuniverse
Most likely a
weakly int., massive, neutral, stable
Popular candidates:
Theories beyond the SM have ambitious goals (hierarchy prob, EWSB, unification).As a byproduct, they can provide DM candidates at the EW scale.
...BUT:
SuperSymmetric LSP, Extra dimensional LKP...
Most likely a
weakly int., massive, neutral, stable
Popular candidates:
Theories beyond the SM have ambitious goals (hierarchy prob, EWSB, unification).As a byproduct, they can provide DM candidates at the EW scale.
...BUT: (i) these theories are by now very uncomfortably fine tuned (the LHC did not find New Physics, at least yet)
SuperSymmetric LSP, Extra dimensional LKP...
Most likely a
weakly int., massive, neutral, stable
Popular candidates:
...BUT:
(ii) these theories have many parameters, DM phenomenology is unclear (scatter plots)
Theories beyond the SM have ambitious goals (hierarchy prob, EWSB, unification).As a byproduct, they can provide DM candidates at the EW scale.
(i) these theories are by now very uncomfortably fine tuned (the LHC did not find New Physics, at least yet)
SuperSymmetric LSP, Extra dimensional LKP...
Most likely a
weakly int., massive, neutral, stable
Popular candidates:
...BUT:
(ii) these theories have many parameters, DM phenomenology is unclear (scatter plots)
(iii) DM stability is imposed by hand (R-parity, T-parity, KK parity)
Theories beyond the SM have ambitious goals (hierarchy prob, EWSB, unification).As a byproduct, they can provide DM candidates at the EW scale.
(i) these theories are by now very uncomfortably fine tuned (the LHC did not find New Physics, at least yet)
SuperSymmetric LSP, Extra dimensional LKP...
Minimalistic approach
Minimalistic approachOn top of the SM, add only one extra multiplet X
and systematically search for the ideal DM candidate...
=
⎛
⎜
⎝
X1
X2...
⎞
⎟
⎠
L = LSM + X̄ (iD/ + M)X if is a fermionX
if is a scalarXL = LSM + |DµX|2 − M2|X |2
Minimalistic approachOn top of the SM, add only one extra multiplet X
and systematically search for the ideal DM candidate...
=
⎛
⎜
⎝
X1
X2...
⎞
⎟
⎠
L = LSM + X̄ (iD/ + M)X if is a fermion
if is a scalar
X
X
gauge interactions the only parameter, and will be fixed by .ΩDM
(other terms in the scalar potential)
(one loop mass splitting)
L = LSM + |DµX|2 − M2|X |2
X
X
W±
, Z, γ
[g2, g1, Y ]
weakly int., massive, neutral, stableThe ideal DM candidate is
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
spin
3
The ideal DM candidate is
6( is similar to )4
α−1
2 (E′) = α−12 (M) −
b2(n)
2πln
E′
M
n ≤ 5
n ≤ 7
these are all possible choices:for fermionsfor scalars
to avoid explosion in the running coupling
X =
⎛
⎜
⎜
⎜
⎝
X1
X2...
Xn
⎞
⎟
⎟
⎟
⎠
(actually, including 2-loops, for real (complex) scalars) n 6 (n 4)
Di Luzio, Nardecchia et al., 1504.00359
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
spin
3
The ideal DM candidate is
1/2
3/2
0
1
1/2
0
1
2
0
Q = T3 + Y
e.g. for : T3 =⎛
⎝
+ 12
−
1
2
⎞
⎠n = 2 ⇒ |Y | =1
2
≡ 0
Each multiplet contains a neutral component with a proper assignment of the hypercharge, according to
e.g. for :n = 3 T3 =
⎛
⎝
+10−1
⎞
⎠⇒ |Y | = 0 or 1
etc.
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
spin
3
The ideal DM candidate is
1/2
3/2
0
1
1/2
0
1
2
0
Q = T3 + Y
e.g. for : T3 =⎛
⎝
+ 12
−
1
2
⎞
⎠n = 2 ⇒ |Y | =1
2
≡ 0
Each multiplet contains a neutral component with a proper assignment of the hypercharge, according to
e.g. for :n = 3 T3 =
⎛
⎝
+10−1
⎞
⎠⇒ |Y | = 0 or 1
etc.
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
0.43
1.2
2.0
2.6
1.4
1.8
2.4
2.4
2.5
2.5
5.0
8.5
The mass is determined by the relic abundance:
M (TeV)
for scalarX
for fermionX
M
(- include co-annihilations) (- computed for ) M ≫ MZ,W
X
X
X
Vµ
Vµ
X
X
Vµ
Vµ
µVµV
µ
X
X
Vµ
Vµ
(- include co-annihilations) (- computed for ) (- computed for ) Z,W(- computed for )
X
X h
hX
X f̄
f
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
3.5
3.5
ΩDM =6 10−27cm3s−1
⟨σannv⟩∼= 0.24
3.2
3.2
⟨σAv⟩ ≃g42 (3 − 4n
2 + n4) + 16 Y 4g4Y
+ 8g22g2Y
Y 2(n2 − 1)
64π M2 gX
⟨σAv⟩ ≃g42 (2n
4 + 17n2 − 19) + 4Y 2g4Y
(41 + 8Y 2) + 16g22g2Y
Y 2(n2 − 1)
128π M2 gX
4.2
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
h
h
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
2.7
2.5
25
1.0
Non-perturbative corrections (and other smaller corrections) induce modifications:
(more later)
⟨σannv⟩ ! R · ⟨σannv⟩ + ⟨σannv⟩p−wave
with R ∼ O(few) → O(102)
full
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9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) EW loops induce a mass splittinginside the n-uplet:
∆M
MQ − MQ′ =α2M4π
{
(Q2 − Q′2)s2W
f(MZM
)
+ (Q − Q′)(Q + Q′ − 2Y )
[
f(MWM
) − f(MZM
)
]}
with f(r) r→0−→ −2πr
The neutral component is the lightest
DM0
DM+
∆M
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
537
906
534
900
X X
W, Z, γ
tree level
2.7
2.5
25
1.0
9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) decay ch. List all allowed SM couplings:EL
EH
HH∗
LH
HH, LH
LH
HHH∗
(LHH∗)
HHH
(LHH)(HHH∗H∗)
e.g.
e.g.1/2 1/2−1
2 21
XEH
X
e
h
XLHH∗
1/2 −1/2 1/2 −1/2
2 2 2
dim=5 operator, induces
Λ ∼ MPlforτ ∼ Λ2TeV−3 ≪ tuniverse
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
(HH∗H∗H∗)
(H∗H∗H∗H∗)
537
906
534
900
4
2.7
2.5
25
1.0
(��H⇤H) dim=5, loop decayDi Luzio,
Nardecchia et al.,
1504.00359
9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) decay ch. List all allowed SM couplings:EL
EH
HH∗
LH
HH, LH
LH
HHH∗
(LHH∗)
HHH
(LHH)(HHH∗H∗)
e.g.
e.g.1/2 1/2−1
2 21
XEH
X
e
h
XLHH∗
1/2 −1/2 1/2 −1/2
2 2 2
dim=5 operator, induces
Λ ∼ MPlforτ ∼ Λ2TeV−3 ≪ tuniverse
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
(HH∗H∗H∗)
(H∗H∗H∗H∗)
No allowed decay! Automatically stable!
537
906
534
900
4
2.7
2.5
25
1.0
(��H⇤H)
9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) decay ch.EL
EH
HH∗
LH
HH, LH
LH
HHH∗
(LHH∗)
HHH
(LHH)(HHH∗H∗)
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
(HH∗H∗H∗)
(H∗H∗H∗H∗)
537
906
not excluded by direct searches!
and
534
900
2.7
2.5
25
1.0
(��H⇤H)
9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) decay ch.EL
EH
HH∗
LH
HH, LH
LH
HHH∗
(LHH∗)
HHH
(LHH)(HHH∗H∗)
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
(HH∗H∗H∗)
(H∗H∗H∗H∗)
537
906
not excluded by direct searches!
and
X
N
σ ≃ G2F M2NY
2
≫ present bounds
Candidates with interact as
Y ̸= 0
need Y = 0
e.g. LUX
X
N
Y
Z0
X
534
900
2.7
2.5
25
1.0
Goodman Goodman Witten Witten 19851985
(��H⇤H)
9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) decay ch.EL
EH
HH∗
LH
HH, LH
LH
HHH∗
(LHH∗)
HHH
(LHH)(HHH∗H∗)
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
(HH∗H∗H∗)
(H∗H∗H∗H∗)
537
906
not excluded by direct searches!
and
534
900
2.7
2.5
25
1.0
(��H⇤H)
9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) decay ch.EL
EH
HH∗
LH
HH, LH
LH
(LHH∗)
HHH
(LHH)(HHH∗H∗)
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
(HH∗H∗H∗)
(H∗H∗H∗H∗)
537
906
not excluded by direct searches!
and
HHH∗
4
1/2353
347 (LHH∗)S
F
HHH∗
4
3/2729
712
HHH
(LHH)FS
534
900
2.7
2.5
25
1.02 1/2
348
342
EL
EHF
S 1.0
1540
526
HH, LH
LH
S
F
1S
F
(HH∗H∗H∗)537
534
2S
F
(H∗H∗H∗H∗)906
900
(��H⇤H)
9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) decay ch.EL
EH
HH∗
LH
HH, LH
LH
(LHH∗)
HHH
(LHH)(HHH∗H∗)
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
(HH∗H∗H∗)
(H∗H∗H∗H∗)
537
906
not excluded by direct searches!
and
HHH∗
3
534
900
2.7
2.5
25
1.02 1/2
348
342
EL
EHF
S 1.0
0166
166
HH∗
LHF
S
2.7
2.5
166 (HHH∗H∗)S
1S
F
(HH∗H∗H∗)537
534
2S
F
(H∗H∗H∗H∗)906
900
1540
526
HH, LH
LH
S
F
4
1/2353
347 (LHH∗)S
F
HHH∗
4
3/2729
712
HHH
(LHH)FS
(��H⇤H)7 0 166S 25 (��H⇤H)
9.4
weakly int., massive, neutral, stableSU(2)L U(1)Y
2
4
5
7
1/2
3/2
0
1
spin
3
The ideal DM candidate is
1/2
0
1
2
0
M (TeV)
348
342
166
540
526
353
347
729
712
166
166
166
166
∆M(MeV) decay ch.EL
EH
HH∗
LH
HH, LH
LH
(LHH∗)
HHH
(LHH)(HHH∗H∗)
F
S
F
S
F
S
F
F
F
S
S
S
F
S
F
S
S
(HH∗H∗H∗)
(H∗H∗H∗H∗)
537
906
not excluded by direct searches!
and
HHH∗
3
We have a winner!
534
900 (oth
er te
rms
in th
e
scal
ar p
oten
tial
)
2.7
2.5
25
1.02 1/2
348
342
EL
EHF
S 1.0
0166
166
HH∗
LHF
S
2.7
2.5
1540
526
HH, LH
LH
S
F
4
1/2353
347 (LHH∗)S
F
HHH∗
4
3/2729
712
HHH
(LHH)FS
166 (HHH∗H∗)S
1S
F
(HH∗H∗H∗)537
534
2S
F
(H∗H∗H∗H∗)906
900
7 0 166S 25
9.4
e.g. mixing with an extra state splits the 2 components of ; if splitting is large enough, NC scattering is kinematically forbidden...
If you want to cure ill candidates...: introduce some mechanism to forbid coupling with anyway
Y ̸= 0
impose some symmetry to forbid decays (e.g. R-parity)...stability:
X
Z0
Y
Z0
impose some symmetry to forbid decays (e.g. R-parity)...
Y
Z0
X
NN
X′
...the case of SuSy higgsino...the case of SuSy higgsinomixing is with bino;
even for pure higgsino, some mixing is ‘inevitable’
due to higher dim operators
A fermionic quintuplet with ,provides a DM candidate with ,
which is fully successful: - neutral
- automatically stable and
not yet discovered by DM searches.
Recap:SU(2)L Y = 0
(Other candidates can be cured via non-minimalities.)
like proton stability in SM!
M = 9.4 TeV
Detection and Phenomenology
1. Collider searchesAt 9.4 TeV, no hope at the LHC.
relax the mass constraint consider next-to-minimal cases (e.g. the triplet = pure wino) explore reach of 100 TeV future collider
q'
q
W±
c±
c0
c0
g p±
q'g
W± c±
c0
c0
p±' tra
cker'
Mono-X VBF Disappearing tracksq
q
q'
q'
W±
W±
c±
c±
c0
c0
c0
p±
p±
di-jets + MET
1. Collider searchesAt 9.4 TeV, no hope at the LHC.
relax the mass constraint consider next-to-minimal cases (e.g. the triplet = pure wino) explore reach of 100 TeV future collider
For triplet MDM (a.k.a. wino DM)
Cire
lli, S
ala,
Taos
o 14
07.7
058
For 5plet MDM
Ostd
iek, 1
506.
0344
5
2. Direct DetectionNo tree level scattering. 1-loop and 2-loops:
Cirelli, Fornengo, Strumia hep-ph/0512090
Essig 0710.1668
Hisano, Ishiwata, Nagata1007.2601
Hisano, Ishiwata, Nagata, Takesano 1104.0228
Hill, Solon 1111.0016
Hisano, Ishiwata, Nagata1010.5985
Farina, Pappadopulo, Strumia 1303.7244
Hill, Solon 1309.4092
Hill, Solon 1401.3339
Hisano, Ishiwata, Nagata 1504.00915
�nSI = 2 · 10�46 cm2
2. Direct DetectionSensitivity Projections: Spin-Independent Interactions
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CDMS II Ge (2009) Xen
on100 (2012
)
CRESST
CoGeNT!(2012)
CDMS Si!(2013)
EDELWEISS (2011)
DAMA SIMPLE (20
12)
ZEPLIN-III (201
2)COUPP (201
2)
LUX (2013)
DAMIC (2012)
CDMSlite (2013)
DarkSide-50
(2014)
CRESST (2015)
Xenon1T
LZ
LUX 300day
SuperCDMS S
NOLAB
DEAP3600
XMASS
DarkSide-G2
SuperCDMS
EDELWEISS
CRESST
Cush
man
et a
l., 13
10.8
327
PS: SD cross section equally challenging Hisano, Ishiwata, Nagata 1010.5985
3. Indirect Detection
8 kpc
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Consistent conclusions in: Garcia-Cely et al. 1507.05536
Bonus trackSome interesting recent extensions:
- millicharged MDMDel Nobile, Nardecchia, Panci 1512.05353
assume Y = ! " 0, -> implies stability -> for suitable !, no DD
relic abundance constraints
- decaying MDM, if " < MPlanckDel Nobile, Nardecchia, Panci 1512.05353
-‘natural’ MDMFabbrichesi, Urbano 1510.03861
-> observable consequences in gamma rays
MDM induces (at 2-loops) mh corrections => small hierarchy prob -> supersymmetrize it!:
- fermion/boson cancellations restore naturalness - stability preserved by SuSy
Bonus trackSome interesting recent extensions:
-MDM and vacuum stabilityCai,Ramsey-Musolf et al., 1108.0969 Cai et al., 1508.04034
-asymmetric MDMBoucenna, Krauss, Nardi 1503.01119
-non-thermally produced MDMAoki, Toma, Vicente 1507.01591
ConclusionsThe DM problem requires physics beyond the SM.
Introducing the minimal amount of it, we find one fully successful DM candidate:
massive, neutral, automatically stable.
fermionic quintuplet with , mass = 9.4 TeV
- too heavy to be produced at LHC, - challenging in next gen direct detection exp’s, - tested by indirect detection (ữ ray) exp’s:
Its phenomenology is precisely computable:
SU(2)L Y = 0
(Other candidates have different properties.)
- excluded if cuspy - not probed if cored
ConclusionsThe DM problem requires physics beyond the SM.
Introducing the minimal amount of it, we find one fully successful DM candidate:
massive, neutral, automatically stable.
fermionic quintuplet with , mass = 9.4 TeV
SU(2)L Y = 0
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Simulations and observations do not resolve ≲ 2 kpc
The cosmic inventoryMost of the Universe is Dark
Ωlum ∼ 0.01
Ωb ≃ 0.040 ± 0.005
-mass to light ratio in typical systems
-BBN -CMB
Ωde ∼ 0.7 - CMB + SNIa - CMB - DM - acoustic peak in baryons
(
Ωx =ρx
ρc; CMB first peak ⇒ Ωtot = 1 (flat);
HST h = 0.71 ± 0.07)
ΩDM ∼ 0.24
- CMB + SNIa
particle physics cosmology
⋂
1) galaxy rotation curves
Beg
eman
et a
l., M
NR
AS
249
(199
1)
ΩM ! 0.1
vc(r) ∼ const ⇒ ρM (r) ∼1
r2
vc(r) =
√2GNM(r)
r
The Evidence for DM
[bac
k to
mai
n sl
ide]
1) galaxy rotation curves
2) clusters of galaxies- “rotation curves” - gravitation lensing - X-ray gas temperature
“bullet cluster” - NASA astro-ph/0608247
ΩM ! 0.1
ΩM ∼ 0.2 ÷ 0.4
[further developments]
The Evidence for DM
[bac
k to
mai
n sl
ide]
3) CMB+LSS(+SNIa:)
ΩM ≈ 0.26 ± 0.05
TT TE
EE LSS
M.Cirelli and A.Strumia, astro-ph/0607086
WMAP-3yr ACbarCBI
Text
BoomerangDASIVSA
SDSS, 2dFRGSLyA Forest Croft LyA Forest SDSS
ΩM ! 0.1
ΩM ∼ 0.2 ÷ 0.4
1) galaxy rotation curves
2) clusters of galaxies
The Evidence for DM
[bac
k to
mai
n sl
ide]
Comparison with SplitSuSy-like modelsA-H, Dimopoulos and/or Giudice, Romanino 2004
Pierce 2004; Arkani-Hamed, Dimopoulos, Kachru 2005 Mahbubani, Senatore 2005
MDMSplitSuSy-like- Higgsino (a fermion doublet)
- + something else (a singlet)
- stabilization by R-parity
- want unification also
- unification scale is low, need to embed in 5D to avoid proton decay
- arbitrary multiplet, scalar or fermion
- nothing else (with Y=0)
- automatically stable
- forget unification, it’s SM
- nothing
Common feature: the focus is on DM, not on SM hierarchy problem.
Mahbubani, Senatore 2005
Non-Minimal terms in the scalar caseλH(X
∗T
a
XX ) (H∗T
a
HH) + λ′
H |X |2|H|2 +
λX
2(X ∗T aXX )
2 +λ′X
2|X |4
Quadratic and quartic terms in and :X H
- do not induce decays (even number of , and )⟨X ⟩ = 0X- [3] and [4] do not give mass terms
[1] [2] [3] [4]
- after EWSB, [2] gives a common mass to all components; negligible for
√
λ′H
v ≈ O(! 100 GeV)
Xi
M = O(TeV)
- after EWSB, [1] gives mass splitting between components; assume so that
Xi
∆Mtree =λHv
2|∆T 3X|
4M= λH · 7.6 GeV
TeV
M
λH ! 0.01 ∆Mtree ≪ ∆M
(Anyway, scalar MDM is less interesting.) [back to Lagrangian]
- [1] (and [2]) gives annihilations assume so that these are subdominant |λ′H | ≪ g2Y , g22
X̄X → H̄H
[back to table]
( basis)
Neutralino “properties’’
Mχ =
⎛
⎜
⎜
⎝
M1 0 −mZcβsW mZsβsW0 M2 mZcβcW −mZsβcW
−mZcβsW mZcβcW 0 −µmZsβsW −mZsβcW −µ 0
⎞
⎟
⎟
⎠
neutralino mass matrix in MSSM B̃ − W̃ 3 − H̃01 − H̃02
superpotentialW = −µH1H2 + H1h
ij
eLLiERj + H1h
ij
dQLiDRj −H2h
ij
uQLiURj
soft SUSYB terms
Lsoft = −1
2
(
M1¯̃BB̃ + M2
¯̃W
a
W̃a + M3
¯̃G
a
G̃a
)
+ . . .
tanβ =⟨v1⟩
⟨v2⟩
3. Indirect DetectionPropagation for positrons:
[back]
�f
�t�K(E) ·⇤2f � �
�E(b(E)f) = Q
K(E) = K0(E/GeV)� b(E) = (E/GeV)2/�E�E = 1016 s
Model � K0 in kpc2/Myr L in kpcmin (M2) 0.55 0.00595 1med 0.70 0.0112 4max (M1) 0.46 0.0765 15
diffusion energy loss
Q =12
��
MDM
⇥2finj, finj =
⇤
k
�⇥v⇥kdNke+dE
�e+(E,�r�) = Bve+
4⇥⇤EE2
� MDM
EdE⇥ Q(E⇥) · I (�D(E,E⇥))
Solution:
⇥2D = 4K0⇤E�(E/GeV)��1 � (E⇥/GeV)��1
� � 1
⇥
3. Indirect DetectionPropagation for antiprotons:
diffusion convective wind
Solution:
⇥f
⇥t�K(T ) ·⇤2f + ⇥
⇥z(sign(z) f Vconv) = Q� 2h �(z) �annf
K(T ) = K0� (p/GeV)�spallations
Model � K0 in kpc2/Myr L in kpc Vconv in km/smin 0.85 0.0016 1 13.5med 0.70 0.0112 4 12max 0.46 0.0765 15 5
�p̄(T,�r�) = Bvp̄4�
�⇥�
MDM
⇥2R(T )
⇤
k
12�⇤v⇥k
dNkp̄dT
T kinetic energy
[back]
Indirect Detection
AMS-01 Caprice
BESSBESSCaprice
Solar wind Modulation of cosmic rays:
spectrum at Earth
d�p̄�dT�
=p2�p2
d�p̄dT
, T = T� + |Ze|�Fspectrum
far from Earth
Fisk potential �F � 500 MV
Indirect DetectionBoost Factor: local clumps in the DM halo enhance the density, boost the flux from annihilations. Typically:
Lava
lle e
t al.
2006
Lava
lle e
t al.
2007
positrons antiprotons
In principle, B is different for e+, anti-p and gammas, energy dependent, dependent on many astro assumptions, with an energy dependent variance, at high energy for e+, at low energy for anti-p.
B ⇥ 1� 20 (104)
[back]
Indirect DetectionBoost Factor: local clumps in the DM halo enhance the density, boost the flux from annihilations. Typically: B ⇥ 1� 20 (104)
Ber
tone
, Bra
nchi
ni, P
ieri
200
7
Kuh
len,
Die
man
d, M
adau
200
7
Milky Way
Milky Way
For illustration:
Results for anti-protons:3. Indirect Detection
Astro uncertainties:- propagation model - DM halo profile - boost factor B
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Ant
i-pr
oton
flux
in1êHG
eVm
2se
csrL
NFW halo
5
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Background?MEDMAX
MIN
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1 10 102 103 10410-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
T HGeVL
Ant
i-pr
oton
flux
in1êHG
eVm
2se
csrL
MED propagation
5
Boost = 15
Background?NFWMoore
IsoT
Results for anti-protons:3. Indirect Detection
Astro uncertainties:- propagation model - DM halo profile - boost factor B