Low mass dark matter
Christopher
McCabe
Effective Theories and Dark Matter, Mainz – 19th March 2015
1.  General considerations
2.  A peculiar neutralino model Results from:
Boehm, Dolan, CM,
Increasing Neff with particles in thermal equilibrium with neutrinos - arXiv:1207.0497
A lower bound on the mass of cold dark matter from Planck - arXiv:1303.6270
Christopher McCabe
GRAPPA - University of Amsterdam
1. General considerations:
How low is low mass? Christopher McCabe
GRAPPA - University of Amsterdam
Low-mass dark matter candidates WIMP
GeV
MeV
Sterile neutrino
Gravitino
Axion
keV
eV
Christopher McCabe
GRAPPA - University of Amsterdam
Low-mass dark matter candidates WIMP
GeV
MeV
Sterile neutrino
Gravitino
Axion
keV
eV
How light can we make WIMPs?
Christopher McCabe
GRAPPA - University of Amsterdam
What is a WIMP? - 
- 
- 
Weak scale mass…
Weak scale cross-section: ~0.1-10 pb
Abundance from thermal freeze-out mechanism:
Christopher McCabe
GRAPPA - University of Amsterdam
WIMP mass? • 
SM fermion get mass from the Higgs vev...
…yet most are below a GeV
• 
Lee-Weinberg argument
-  On dimensional grounds:
- 
If
mweak = 100 GeV, for h vi ⇡ 1 pb
) mDM
• 
• 
m2DM
h vi = 4
mweak
1 GeV
Light WIMPs are sub-GeV
Light WIMPs require a light mediator
Christopher McCabe
GRAPPA - University of Amsterdam
The thermal bath • 
• 
‘Freeze-out’ from what? Need a thermal bath of particles
Kept in equilibrium with annihilations
f
f
• 
f
could be SM states or BSM states
SM
e
+
e
BSM
p
⌫
n
⌫¯
?
?
?
Christopher McCabe
?
?
GRAPPA - University of Amsterdam
Two cases • 
I’ll consider when WIMP in equilibrium with SM particles
SM
e
+
e
• 
• 
p
⌫
n
⌫¯
Case 1: In equilibrium with neutrinos
Case 2: In equilibrium with electrons/photons
Christopher McCabe
GRAPPA - University of Amsterdam
Reminder: The usual Timeline 10 MeV
• 
1 MeV
0.1 MeV
1 eV
1 meV
Plasma of particles in a thermal bath:
T
e
+
e
⌫¯
⌫
p
n
Christopher McCabe
GRAPPA - University of Amsterdam
Timeline: Neutrino decoupling 10 MeV
Events:
• 
• 
1 MeV
⌫
0.1 MeV
1 eV
1 meV
decoupling
=n v⇠H
Species remain in thermal equilibrium until
Neutrinos decouple at ~2.3 MeV
T⌫ = T
⌫
⌫¯
T
e+
e
n
Christopher McCabe
p
GRAPPA - University of Amsterdam
Timeline: Big Bang Nucleosynthesis BBN
10 MeV
Events:
1 MeV
⌫
0.1 MeV
1 eV
decoupling
T
T
D
+
p
H+
e
He++
7 +++
Li
++
4
+
n
e
1 meV
3
He
+
e
Christopher McCabe
e
GRAPPA - University of Amsterdam
Timeline: Photon reheating BBN
10 MeV
Events:
• 
• 
1 MeV
⌫
decoupling
me/3 MeV
0.1 MeV
1 eV
1 meV
reheating
When electrons and positrons become non-relativistic, they
transfer their entropy to photons
Photon thermal bath heated
relative to neutrino bath:
T⌫
=
T
Christopher McCabe
✓
4
11
◆1/3
GRAPPA - University of Amsterdam
Timeline: CMB formation BBN
10 MeV
Events:
1 MeV
⌫
decoupling
me/3 MeV
0.1 MeV
reheating
1 eV
1 meV
decoupling
H+ + e ! H +
• 
Electrons recombine with protons:
• 
Photons decouple from matter: cosmic microwave
background is formed
Christopher McCabe
GRAPPA - University of Amsterdam
Timeline: Today BBN
10 MeV
Events:
• 
1 MeV
⌫
decoupling
me/3 MeV
0.1 MeV
1 eV
reheating
decoupling
1 meV
today
Today we have (at least) two thermal relics:
1.  CMB with T = 2.725 K (measured)
2.  Cosmic neutrino background
with T⌫ = 1.945 K (not measured)
Christopher McCabe
GRAPPA - University of Amsterdam
New timeline: With light dark matter 10 MeV
• 
1 MeV
0.1 MeV
1 eV
Plasma of particles in a thermal bath, including
in equilibrium with the neutrinos
1 meV
, which is
T
e
e+
⌫¯
⌫
p
n
Christopher McCabe
GRAPPA - University of Amsterdam
New timeline: Neutrino decoupling 10 MeV
Events:
• 
1 MeV
⌫,
0.1 MeV
1 eV
1 meV
decoupling
Neutrinos and
decouple at ~2.3 MeV
T⌫ = T
⌫
⌫¯
T
e+
e
n
Christopher McCabe
p
GRAPPA - University of Amsterdam
New timeline: Neutrino heating BBN
10 MeV
Events:
• 
• 
1 MeV
⌫,
m /3 MeV
decoupling
⌫
reheating
me/3 MeV 0.1 MeV
1 eV
1 meV
reheating
transfers entropy to
neutrinos heating them
Neutrinos hotter at end of BBN:
T⌫
=
T
✓
4
11
◆1/3 
3 + F (m /2.3 MeV)
3 + F (m /T )
1/3
Christopher McCabe
GRAPPA - University of Amsterdam
New timeline: Today BBN
10 MeV
Events:
• 
1 MeV
⌫,
decoupling
m /3 MeV
⌫
reheating
me/3 MeV 0.1 MeV
reheating
1 eV
⌫ decoupling
decoupling
1 meV
today
Today we have (at least) two thermal relics:
1.  CMB with T = 2.725 K (measured)
2.  Cosmic neutrino background now warmer:

1/3
F (m /2.3 MeV)
T⌫ = 1.945 K · 1 +
(not measured) 3
Christopher McCabe
GRAPPA - University of Amsterdam
Changes to BBN? Kolb, Turner, Phys.Rev. D34 (1986)
Raffelt, Serpico, Phys.Rev. D70 (2004)
Steigman, Nollett, arXiv:1312.5725
• 
A new light particle can contribute to the energy
density (if it is still relativistic during BBN)
• 
A different neutrino-photon temperature ratio changes:
1.  Neutrino energy density higher
2.  Change to the weak interaction rates for proton <->
neutron conversion (⌫e + n $ p + e )
Christopher McCabe
GRAPPA - University of Amsterdam
Changes to abundances • 
We implemented the changes into PArthENoPE BBN code
arXiv:0705.0290
PDG values
Yp = 0.2465 ± 0.0097
D/H = (2.53 ± 0.04) ⇥ 10
Christopher McCabe
GRAPPA - University of Amsterdam
5
In equilibrium with EM particles • 
We implemented the changes into PArthENoPE BBN code
arXiv:0705.0290
PDG values
Yp = 0.2465 ± 0.0097
D/H = (2.53 ± 0.04) ⇥ 10
Christopher McCabe
GRAPPA - University of Amsterdam
5
CMB: Neff changes • 
Higher neutrino temperature increases Neff
" ,✓ ◆ #4
1/3
T⌫
4
Ne↵ = 3.046
T
11
Planck TT,TE,EE
+lowP+BAO (2015)
Ne↵ = 3.04 ± 0.18
Christopher McCabe
GRAPPA - University of Amsterdam
Mini-conclusion • 
Assumptions:
-  Light WIMPs are sub-GeV
-  If in equilibrium with SM particles…
• 
Then…MeV mass particles can show up through BBN
and CMB through effects on the neutrino-photon
temperature relation
Christopher McCabe
GRAPPA - University of Amsterdam
2. A peculiar neutralino model
Christopher McCabe
GRAPPA - University of Amsterdam
How light can we make the neutralino? • 
The answer might be surprising:
it can be as light as we like - even massless
• 
Certain conditions are required…
•  Bino-like
•  Selectrions and squarks are reasonably heavy
•  (some tuning of the parameters)
Christopher McCabe
Explored in a series of papers
by Dreiner and others
GRAPPA - University of Amsterdam
How light can we make neutralino dark matter? In the MSSM, difficult to go below ~10 GeV:
7
10
10
Freeze-out Temperature [MeV]
Profumo
arXiv:0806.2150
6
5
10
V)
e
/k
4
10
2
3
Ωstdh
• 
10
2
h
Ω
2
.5
16
~
(m χ
std
10
1
10
0
1
10
tanβ = 50
tanβ = 5
Optimistic Limit
Optimistic Limit
tanβ = 50
tanβ = 5
10
-1
10
0
-2
10
2
10
-6
10
-5
10
-4
10
-3
-2
10
10
mχ [GeV]
-1
10
0
10
1
10
10 -2
10
-1
10
0
10
1
10
2
10
2
Ωstdh
FIG. 3: (Left): the thermal relic abundance of the lightest neutralino, as a function of its mass, in a
Observed value
scenario where the energy density of the universe is radiation dominated at arbitrarily large temper
plot, filled black dots refer to the conservative models with tan β = 50, while empty red diamonds to
Christopher
McCabe GRAPPA
- University
of Amsterdam
curve indicates “optimistic” models with
a light supersymmetric
spectrum.
(Right):
The correlation bet
abundance and the freeze-out temperature (defined in Eq. (9), in a standard cosmological scenario) for
Solution is clear: need another light superpartner • 
Introduce sterile rhd sneutrino that mix with lhd sneutrino
Vsoft
• 
m2⌫˜L |˜
⌫Li |2 + m2ñ |ñi |2 + Aij hu · L̃i ñj + h.c.
Light mass eigenstates are mostly rhd
⌫˜1 =
sin ✓1 ⌫˜L↵
+ cos ✓1 ñ
↵?
2Ai v sin
⇠ 0.1 .
with tan 2✓i = 2
2
m⌫˜L mñ
Christopher McCabe
GRAPPA - University of Amsterdam
Solution is clear: need another light superpartner • 
Neutralino remains in equilibrium with neutrinos:
• 
Freeze-out happens as usual with a weak scale cross-section:
✓
◆4 ✓
◆2 ✓
◆4
0
m
35 MeV
sin ✓
˜1
h vi ⇡ 7 pb
0.1
5 MeV
m⌫˜1
Christopher McCabe
GRAPPA - University of Amsterdam
How can we test this? • 
• 
• 
No collider constraints
Not visible in Z, h or meson decays
No direct detection (from electron scattering):
✓
◆4
195 GeV
46
2
⇡
3
⇥
10
cm
e
mẽ
• 
No usual indirect detection signal:
dominant annihilation is to low energy neutrinos
Is this WIMP invisible? Christopher McCabe
GRAPPA - University of Amsterdam
Consequence: Neff is larger • 
Recall: Higher neutrino temperature increases Neff
" ,✓ ◆ #4
1/3
T⌫
4
Ne↵ = 3.046
T
11
• 
We now have a way to probe a light neutralino
Christopher McCabe
GRAPPA - University of Amsterdam
Conclusions • 
WIMPs can be light
…need a light mediator
• 
Usual detection strategies may fail
…direct/indirect/collider
• 
Can still have observable consequences
…BBN and CMB are sensitive probes of new physics
Christopher McCabe
GRAPPA - University of Amsterdam