156 K. Kong, J.-C. Park / Nuclear Physics B 888 (2014) 154–168
as model-independent as possible.
1
We choose annihilations of dark matter into
¯
and b
¯
b final
states as our reference, and present results in a (m
DM
, σv) plane. Other scenarios such as demo-
cratic annihilations into all kinematically accessible SM fermions and annihilations proportional
to m
2
f
are also discussed in Section 4. In most cases such as
¯
and b
¯
b final states, recast-process
is straightforward and results are easy to convert. For complicated final states in Section 4, we
rescale the limits by considering the corresponding annihilation fraction and characteristics of
each final state. In the case of LEP and LHC bounds, we recompute σv ourselv
es with limits
on the cutoff scale Λ obtained from a literature. We begin our discussion in Section 2 by review-
ing the Fermi-LAT GeV gamma-ray excess. We, then, consider various constraints in Section 3.
Section 4 is reserved for discussion.
2. Fermi-LAT GeV gamma-ray excess
A gamma-ray excess at GeV energies around the GC has been identified in the Fermi-LAT
data by several groups [16–23]. In Ref. [24], authors reexamined the gamma-ray emission with
high resolution gamma-ray maps which was obtained by applying cuts to the Fermi-LAT event
parameter CTBCORE and suppressing the tails of the point spread function. In the analysis, the
y
confirmed a significant GeV gamma-ray excess with a spectrum and morphology in close agree-
ment with the expectations from DM annihilation, which was very well fitted by 30–40 GeV DM
particles annihilating to b
¯
b with an annihilation cross section of σv =(1.4–2.0) ×10
−26
cm
3
/s
for a generalized Navarro–Frenk–White (NFW) halo profile with an inner slope of γ =1.26 and
a local DM density of ρ
= 0.3 GeV/cm
3
. With further investigation, it was found that the an-
gular distribution of the excess is approximately spherically symmetric and centered around the
dynamical center of the galactic plane. In addition, they observed that the signals are extended to
more than 10
◦
from the GC, and thus the possibility that millisecond pulsars are responsible for
the excess is disfavored.
In Refs. [21,24], it wa
s also shown that a DM mass of ∼10 GeV is required when DM anni-
hilates into lepton pairs but the fit to the data favors the case of a DM mass of 30–40 GeV with a
pure b
¯
b final state. Authors of Ref. [25] pointed out that a contribution of the dif
fuse photon emis-
sions originating from primary and secondary electrons produced in DM annihilations is quite
significant especially for leptonic final states (
¯
), which was however neglected in the literature,
while such contributions are sub-dominant for the b
¯
b channel. Considering the inverse Comp-
ton scattering and Bremsstrahlung contrib
utions from electrons, they found that annihilations of
∼10 GeV DM particles into the purely leptonic final state provide a little better fit than the pure
b
¯
b final state. In addition, it was shown that 10 GeV DM democratically annihilating into pure
¯
final states provides the best χ
2
fit for an annihilation cross section of σv =0.86 ×10
−26
cm
3
/s
for a generalized NFW halo profile with γ = 1.2 and ρ
= 0.36 GeV/cm
3
and 30 GeV DM
annihilating into pure b
¯
b states does for σv = 2.03 ×10
−26
cm
3
/s. Note that “democratic an-
nihilation into pure
¯
states” implies equal annihilation cross sections into each of e
+
e
−
, μ
+
μ
−
,
and τ
+
τ
−
channels.
We use the best-fit v
alues from Ref. [25] as reference points in our study: σv
¯
= 0.86 ×
10
−26
cm
3
/s with m
DM
= 10 GeV and σv
b
¯
b
= 2.03 ×10
−26
cm
3
/s with m
DM
= 30 GeV. As
1
In this work, we use a term “model independent” in the sense that we provide constraints on the DM annihilation
cross sections σv as a function of DM mass m
DM
for each final state without considering details of annihilation mech-
anism.
However in the case of collider limits, effective operators are used since we need to assume a certain production
mechanism for analysis, and thus collider limits have model-dependence.
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