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Light DM,
An interesting
candidate?
Celine Boehm, 2004
• Heavy Dark Matter
TeV
string candidates
neutralinos
GeV
(proton mass)
• Light Dark Matter
MeV
``new’’ particles?
(10-6 eV
axions particles)
non thermal
Weakly Interacting Massive Particles
Silk (1968), Gunn et al (1978), Davis et al (1980), Peebles (1982) etc..
• No electromagnetic interactions: Weakly Interacting
• Not neutrino-like: Massive
Weakly Interacting Massive Particles (WIMPs)
• But in fact more complicated..damping.ppt
Damping constraints in a plane!
One can define ``WDM’’
particles as being at the
edge of the damping limit.
Means also ``Collisional WDM’’!
A very important criterion: Relic density
dn
 3H n dm  σ v (n dm 2  n dm,e 2 )
dt
the annihilation rate freezes-out when:
H n dm = σ v n dm 2
 dm
at tfo
 dm

 ndm mdm
c
 ndm (t fo )a fo 3mdm

H
a fo 3mdm
v
with H  a fo -2
m dm
Ω dm 
factors
Tfo
σv
The relic density criterion therefore requires:
 v  7 10
-27
-1
 Ωh 
3
cm
/s


 0.1 
2
Independent of
the DM mass!
Too much DM
The annihilation
Cross section is
too small
One value only
does the job!
Not enough
First calculations to be done: Lee-Weinberg (1977)
Massive neutrinos, Fermi interactions:
mdm 2
 v 
4
mw
• Depends mainly on mdm,
• if mdm too small, dm> 1 !
Lee-Weinberg limit:
mdm > O(GeV)
dm
f
dm
f
Light Dark Matter (mdm < GeV)
Forbidden by Lee-Weinberg because the cross section is too small!
But they considered massive neutrinos and with a cross section proportional to mdm!
Extension to more general DM candidates!
Examples: fermions
e-
dm
L
F
dm
(Dirac dm =  field)
 (Cl F f  r  Cr F f r  l )  h.c.
l
e+
2
2
m
7
v


2
2 2
dm
dm
 v  (cl +cr )
1+


4
mF 
3 
How to evade Lee-Weinberg?
dm
f+
F
dm
• By just obtaining a cross section
independent of mdm!
• Which DM particles then?
f-
– Fermions: always proportional to mdm
– Scalars: yes, some configurations OK!
L
  (cl f Fr  Cr f r Fl )  h.c.
l
2
2
mf 2
C
C
2
l
r
 v  (1
v
)
dm
mdm 2
mF2
Almost independent of mdm !
Possible to evade Lee-Weinberg when scalars!!
But DM can annihilate into the galactic center…
•
•
•
•
C.B., T. Ensslin, J. Silk
Gamma rays Expected between MeV and GeV depending on mdm
But already lot of observations in this range (notably OSSE!).
No indications for non standard physics so predictions have to be compatible.
Predictions depend on the DM halo profile
G M(r)
 M(r) =  4 2  (r) dr
r
vc 2
1
dM(r)
 (r) =
=
2
4 r
dr
4 G r 2
vc 2 
NFW profile
Isothermal profile
Binney Evans profile

σv
  m
-2

 th  105  observed  -26 3 1   dm 
 10 cm s   MeV 
Light DM ruled out then?
• No if the cross section ~ a + b v2 (with a << b)
• Why a cross section in v2 saves the scenario?
DM velocity in galaxy < 10-3 c
DM velocity in primordial U ~ c
• So v2
reduced the flux by a factor 10-6..
Is that possible in particle physics?
Summary mid-stage
Light DM OK but needs for a
v2 annihilation cross section!
•
Fermionic DM cannot do that!
2
2
m
7
v


 v  (cl2 +cr 2 ) 2 dm4  1+ dm 
mF 
3 
•
Scalar DM?
– if exchange fermions:
2
2
mf 2
C
C
2
l
r
 v  (1
v
)
dm
mdm 2
mF2
– If exchange gauge bosons?
Particle Physics models
• Possible if a new gauge boson (U):
dm
f+
U
dm
CU
fU
 v  vdm 2 CU 2
f-
 mdm 2 
2
2
(f
+
f

Ul
Ur )
4 
 mU 
Dependence in mdm!
But OK if light U and small couplings!
(U of a few MeV, < GeV)
Light DM finally possible because:
• small couplings as required by muon and electron g-2!
1
E2
• Could not be seen in past colliders:
e e  dm dm 
 
 v  vdm CU
2
2
 mdm 2 
2
2
(f
+
f

Ul
Ur )
4 
 mU 
1) cross section smaller than e  e      at high energy because
fU is much smaller than electroweak couplings!
2) cross section maximal at low energy (a few MeV).
Could be promising but dominated by
e e   
INTEGRAL/SPI: observation of a 511 keV line emission
A first evidence of Dark Matter annihilations?
dm dm -> e+ ee+ e- -> phot phot (phot)
1) e- and e+ at rest,
2) Photons with Ee,
3) Existence of e+ !
Prospectives (dwarfs galaxies)
In the sensitivity of Integral satellite
If a signal is detected: confirmation of LDM
If not, the LDM scenario is possibly ruled out
Sagittarius Dwarf Elliptical Galaxy
Heavy Dark Matter
• Light DM could involves a theory that also predicts a
heavy and stable particle
• 2 symmetries (R and M-parities): N=2 supersymmetry??
• The relic density will be ensured by the Light DM so no
restriction on the cross section
Conclusion
• Light Dark Matter (<GeV) is possible!
• Need for v2 cross section:
– possible with light scalars exchanging a light
gauge boson
– but other solutions may work….
• LDM explain the detection of a 511 keV line
in the centre of the galaxy very well.
• Possibility of having heavier stable
particles…
Collisionless WDM
M_WDM > keV