Phenomenology of light neutralinos in view of recent results at the CERN Large Hadron Collider

Abstract

We review the status of the phenomenology of light neutralinos in an
effective Minimal Supersymmetric extension of the Standard Model (MSSM) at the
electroweak scale, in light of new results obtained at the CERN Large Hadron
Collider. First we consider the impact of the new data obtained by the CMS
Collaboration on the search for the Higgs boson decay into a tau pair, and by
the CMS and LHCb Collaborations on the branching ratio for the decay $B_s
\rightarrow {\mu}^{+} + {\mu}^{-}$. Then we examine the possible implications
of the excess of events found by the ATLAS and CMS Collaborations in a search
for a SM--like Higgs boson around a mass of 126 GeV, with a most likely mass
region (95% CL) restricted to 115.5--131 GeV (global statistical significance
about 2.3 $\sigma$). From the first set of data we update the lower bound of
the neutralino mass to be about 18 GeV. From the second set of measurements we
derive that the excess around $m^{SM}_H$ = 126 GeV, which however needs a
confirmation by further runs at the LHC, would imply a neutralino in the mass
range 18 GeV $\lsim m_{\chi} \lsim$ 38 GeV, with neutralino--nucleon elastic
cross sections fitting well the results of the dark matter direct search
experiments DAMA/LIBRA and CRESST.

Full text

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arXiv:1112.5666v1 [hep-ph] 23 Dec 2011
Phenomenology of light neutralinos in view of recent results
at the CERN Large Hadron Collider∗
A. Bottino,1N. Fornengo,1and S. Scopel2
1Dipartimento di Fisica Teorica, Universit` a di Torino
Istituto Nazionale di Fisica Nucleare, Sezione di Torino
via P. Giuria 1, I–10125 Torino, Italy
2Department of Physics, Sogang University
Seoul, Korea, 121-742
(Dated: December 30, 2011)
We review the status of the phenomenology of light neutralinos in an effective Minimal Super-
symmetric extension of the Standard Model (MSSM) at the electroweak scale, in light of new results
obtained at the CERN Large Hadron Collider. First we consider the impact of the new data ob-
tained by the CMS Collaboration on the search for the Higgs boson decay into a tau pair, and by
the CMS and LHCb Collaborations on the branching ratio for the decay Bs → µ++ µ−. Then we
examine the possible implications of the excess of events found by the ATLAS and CMS Collabo-
rations in a search for a SM–like Higgs boson around a mass of 126 GeV, with a most likely mass
region (95% CL) restricted to 115.5–131 GeV (global statistical significance about 2.3 σ). From
the first set of data we update the lower bound of the neutralino mass to be about 18 GeV. From
the second set of measurements we derive that the excess around mSM
needs a confirmation by further runs at the LHC, would imply a neutralino in the mass range 18
GeV <
∼mχ<
∼38 GeV, with neutralino–nucleon elastic cross sections fitting well the results of the
dark matter direct search experiments DAMA/LIBRA and CRESST.
H
= 126 GeV, which however
I.INTRODUCTION
The phenomenology of light neutralinos has been thor-
oughly discussed in Refs. [1–3] within an effective Min-
imal Supersymmetric extension of the Standard Model
(MSSM) at the electroweak (EW) scale, where the usual
hypothesis of gaugino–mass universality at the scale of
Grand Unification (GUT) of the SUGRA models is re-
moved (this model containing neutralinos of mass mχ<
50 GeV was dubbed Light Neutralino Model (LNM) [3]);
this denomination will also be maintained here).
∼
In Refs. [1–3] it was shown that, in case of R–parity
conservation, a light neutralino within the LNM, when
it happens to be the Lightest Supersymmetric Particle
(LSP), constitutes an extremely interesting candidate
for the dark matter in the Universe, with direct detec-
tion rates accessible to experiments of present generation.
More specifically, the following results were obtained: a)
a lower bound on mχwas derived from the cosmological
upper limit on the cold dark matter density; b) it was
shown that the population of light neutralinos fits quite
well the DAMA/LIBRA annual modulation results [4, 5]
over a wide range of mχ; c) this same population can ex-
plain also results of other direct searches for dark matter
(DM) particles which show positive results (CoGeNT [6],
∗Preprint number: DFTT 34/2011
CRESST [7]) or possible hints (two–event CDMS [8]) in
some restricted intervals of mχ[3, 9, 10].
It is obvious that the features of the light neutralino
population, and its relevant properties (a-c), drastically
depend on the intervening constraints which follow from
new experimental results. Of particular impact over the
details of the phenomenological aspects of the LNM are
the new data obtained at the CERN Large Hadron Col-
lider (LHC) which, in force of its spectacular perfor-
mance, is providing a profusion of new information. In
this respect the most relevant results of LHC concern: i)
the lower bounds on the squark and gluino masses, ii)
the correlated bounds on tanβ (ratio of the two Higgs
v.e.v.’s) and mA(mass of the CP–odd neutral Higgs bo-
son) derived from the searches for neutral Higgs bosons
into a tau–lepton pair, iii) a new strict upper bound on
the branching ratio for the decay Bs→ µ++µ−, iv) the
indication of a possible signal (at a statistical significance
of 2.3 σ) for a SM–like Higgs boson with a mass of about
126 GeV [11, 12].
The impact of item (i) on the LNM was already con-
sidered in Ref.[13].In the present paper we derive
the consequences that the new bounds from searches for
neutral Higgs bosons into a tau–lepton pair and from
BR(Bs→ µ++ µ−) (item (ii) and (iii) above) have on
the phenomenology of the light neutralinos and discuss
the implications that a Higgs boson at about 126 GeV
(item iv) could have, in case this preliminary experimen-
tal indication is confirmed in next LHC runs.

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II.FEATURES OF THE LIGHT NEUTRALINO
MODEL
The LNM is an effective MSSM scheme at the elec-
troweak scale, with the following independent parame-
ters: M1, M2, M3, µ, tanβ, mA, m˜ q12, m˜ t, m˜l12,L, m˜l12,R,
m˜ τL, m˜ τRand A. We stress that the parameters are de-
fined at the EW scale. Notations are as follows: M1, M2
and M3are the U(1), SU(2) and SU(3) gaugino masses
(these parameters are taken here to be positive), µ is the
Higgs mixing mass parameter, tanβ the ratio of the two
Higgs v.e.v.’s, mAthe mass of the CP–odd neutral Higgs
boson, m˜ q12is a squark soft–mass common to the squarks
of the first two families, m˜ tis the squark soft–mass for the
third family, m˜l12,Land m˜l12,Rare the slepton soft–mass
common to the L,R components of the sleptons of the
first two families, m˜ τLand m˜ τRare the slepton soft–mass
of the L,R components of the slepton of the third family,
A is a common dimensionless trilinear parameter for the
third family, A˜b= A˜ t≡ Am˜ tand A˜ τ≡ A(m˜ τL+m˜ τR)/2
(the trilinear parameters for the other families being set
equal to zero). In our model, no gaugino mass unification
at a Grand Unified scale is assumed, and therefore M1
can be sizeably lighter than M2. Notice that the present
version of the LNM represents an extension of the model
discussed in our previous papers [1–3], where a common
squark and the slepton soft mass was employed for the 3
families.
The linear superposition of bino˜B, wino˜ W(3)and of
the two Higgsino states˜H◦
tralino state of lowest mass mχis written here as:
1,˜H◦
2which defines the neu-
χ ≡ a1˜B + a2˜ W(3)+ a3˜H◦
1+ a4˜H◦
2. (1)
A. The cosmological bound
Since no gaugino–mass unification at a GUT scale is
assumed in our LNM (at variance with one of the major
assumptions in mSUGRA), in this model the neutralino
mass is not bounded by the lower limit mχ>
is commonly derived in mSUGRA schemes from the LEP
lower bound on the chargino mass (of about 100 GeV).
However, in the case of R–parity conservation the neu-
tralino, when occurs to be the LSP, has a lower limit on
its mass mχwhich can be derived from the cosmological
upper bound on the cold dark matter (CDM) relic abun-
dance ΩCDMh2. Actually, by employing this procedure,
in Ref. [1] a value of 6–7 GeV for the lower limit of mχ
∼50 GeV that
was obtained, and this value was subsequently updated
to the value of about 8 GeV in Refs. [3, 10] as derived
from the experimental data available at that time. Now,
with the advent of fresh data from LHC, the lower bound
on mχhas to be redetermined; this will be done in Sect.
IIIA).
To set the general framework, let us recall that the
neutralino relic abundance is given by:
Ωχh2=
xf
g⋆(xf)1/2
9.9 · 10−28cm3s−1
?
?σannv?
,(2)
where
tegral from the present temperature up to the freeze–
out temperature Tfof the thermally averaged product of
the annihilation cross–section times the relative velocity
of a pair of neutralinos, xf is defined as xf ≡ mχ/Tf
and g⋆(xf) denotes the relativistic degrees of freedom of
the thermodynamic bath at xf. For
the standard expansion in S and P waves:
˜ a +˜b/(2xf). Notice that in the LNM no coannihilation
effects are present in the calculation of the relic abun-
dance, due to the large mass splitting between the mass
of the neutralino (mχ< 50 GeV) and those of sfermions
and charginos.
?
?σannv? ≡ xf?σannv?int, ?σannv?int being the in-
?
?σannv? we will use
?σannv? ≃
?
The annihilation processes which contribute to
at the lowest order are: i) exchange of a Higgs boson
in the s–channel, ii) exchange of a sfermion in the t–
channel, iii) exchange of the Z–boson in the s–channel.
In the physical region which we are going to investigate,
which entails light values for the masses of supersymmet-
ric Higgs bosons mh,mA,mH(for the lighter CP–even h,
the CP–odd A and the heavier CP–even H, respectively)
and a light mass for the stau ˜ τ, the contribution of the
Z–exchange is largely subdominant compared to the first
two which can be of the same order, with a dominance
of the A–exchange contribution for mχ<
a possible dominance of the ˜ τ–exchange afterward (see
numerical results in Fig. 3).
?
?σannv?
∼28 GeV, and
In our numerical evaluations all relevant contributions
to the pair annihilation cross–section of light neutralinos
are included. However, an approximate expression for
Ωχh2, valid for very light neutralinos proves very useful
to obtain an analytic formula for the lower bound for the
neutralino mass. Indeed, for mχ<
is dominated by the A–exchange, Ωχh2may be written
as [1]:
∼28 GeV when
?
?σannv?

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3
Ωχh2≃
4.8 · 10−6
GeV2
xf
g⋆(xf)1/2
1
a2
1a2
3tan2βm4
A
[1 − (2mχ)2/m2
m2
A]2
χ]1/2
χ[1 − m2
b/m2
1
(1 + ǫb)2, (3)
where ǫb is a quantity which enters in the relationship
between the b–quark running mass and the correspond-
ing Yukawa coupling (see Ref. [14] and references quoted
therein). For neutralino masses in the range mχ= (10–
20) GeV, g⋆(xf)1/2≃ 2.5. In deriving this expression,
one has taken into account that here the following hier-
archy holds for the coefficients aiof χ [3]:
|a1| > |a3| ≫ |a2|,|a4|,(4)
whenever µ/mχ>
in this regime:
∼a few. In Ref. [3] it is also shown that
a2
1a2
3≃
sin2θW m2
(µ2+ sin2θW m2
Zµ2
Z)2≃
0.19 µ2
(µ2
100
100+ 0.19)2, (5)
where µ100is µ in units of 100 GeV. From this formula
and the LEP lower bound |µ| >
(a2
∼0.13. This upper bound is essentially equiv-
alent to one which can be derived from the upper bound
on the width for the Z–boson decay into a light neutralino
pair: (a2
∼0.12 [3].
∼100 GeV, we obtain
1a2
3)max<
1a2
3)max<
By imposing that the neutralino relic abundance does
not exceed the observed upper bound for cold dark mat-
ter (CDM), i.e. Ωχh2≤ (ΩCDMh2)max, we obtain the
following lower bound on the neutralino mass:
mχ
[1 − m2
[1 − (2mχ)2/m2
b/m2
χ]1/4
A]>
∼17 GeV
?
mA
90 GeV
?2?
15
tanβ
??0.12
a2
1a2
3
?1
2?
0.12
(ΩCDMh2)max
?1
2
. (6)
Here we have taken as default value for (ΩCDMh2)maxthe
numerical value which represents the 2σ upper bound to
(ΩCDMh2)maxderived from the results of Ref. [15]. For
ǫb we have used a value which is representative of the
typical range obtained numerically in our model: ǫb =
−0.08.
B.Neutralino–nucleon elastic cross section
We turn now to the evaluation of the neutralino-
nucleon elastic cross section σ(nucleon)
est here in the comparison of our theoretical evaluations
with the most recent data from experiments of direct
searches for DM particles.
Notice that we consider here only coherent neutralino–
nucleus cross section, thus spin-dependent couplings are
scalar
, since we are inter-
disregarded, and the neutralino–nucleon cross section are
derived from the coherent neutralino–nucleus cross sec-
tion in the standard way.
The neutralino–nucleon scattering then takes contri-
butions from (h,A,H) Higgs boson exchange in the t–
channel and from the squark exchange in the s-channel;
the A–exchange contribution is suppressed by kinematic
effects. In the supersymmetric parameter region consid-
ered in the present paper the contributions from the h
and H exchanges are largely dominant over the squark
exchange, with a sizable dominance of the h exchange
over the H one (a quantitative analysis of this point will
be given in Sect. IIIA in connection with Fig. 4). An
approximate expression for σ(nucleon)
ues of mχ, is obtained by including only the dominant
contribution of the h boson exchange [3]:
scalar
, valid at small val-
σ(nucleon)
scalar
≃ 9.7 × 10−42cm2
?a2
1a2
0.13
3
??tanβ
15
?2?90 GeV
mh
?4?
gd
290 MeV
?2
.(7)
where
gd≡ [md?N|¯dd|N? + ms?N|¯ ss|N? + mb?N|¯bb|N?]. (8)

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4
and the matrix elements ?N|¯ qq|N? denote the scalar
quark densities of the d,s,b quarks inside the nucleon.
In Eq. (7) we have used as reference value for gdthe
value gd,ref = 290 MeV employed in our previous pa-
pers [2, 3]. We recall that this quantity is affected by
large uncertainties [16] with (gd,max/gd,ref)2= 3.0 and
(gd,min/gd,ref)2= 0.12 [2, 3]. Notice that these uncertain-
ties still persist [17, 18]. Our reference value gd,ref= 290
MeV is larger by a factor 1.5 than the central value of
Ref. [19], frequently used in the literature.
By employing Eq. (3) and Eq. (7) we find that any
neutralino configuration, whose relic abundance stays in
the cosmological range for CDM ( i.e. (ΩCDMh2)min≤
Ωχh2≤ (ΩCDMh2)max with (ΩCDMh2)min = 0.098
and (ΩCDMh2)max = 0.12) and passes all particle–
physics constraints, has an elastic neutralino–nucleon
cross–section given approximately by [3]:
σ(nucleon)
scalar
≃ (2.7 − 3.4) × 10−41cm2?
gd
290 MeV
?2?mA
mh
?4
[1 − (2mχ)2/m2
(mχ/(10 GeV)2[1 − m2
A]2
b/m2
χ]1/2.(9)
Notice that in the range 90 GeV ≤ mA≤ 120 GeV the
maximal values of the ratio mA/mh are of order one
within a few percent (see left panel of Fig. 2).
We recall that for neutralino configurations whose relic
abundance stays below the cosmological range for CDM,
i.e. have Ωχh2< (ΩCDMh2)minone has to associate to
σ(nucleon)
scalar
a local density rescaled by a factor ξ = ρχ/ρ0,
as compared to the total local DM density ρχ; ξ is con-
veniently taken as ξ = min{1,Ωχh2/(ΩCDMh2)min} [20].
Furthermore, we note that Eq. (9) is valid when the
A boson exchange is dominating in the neutralino pair
annihilation process (in the s–channel). As mentioned
above, this occurs for mχ<
∼28 GeV. For higher neu-
tralino masses the actual values of σ(nucleon)
what higher than those provided by Eq. (9).
scalar
are some-
C.Constraints
To single out the physical supersymmetric configura-
tions within our LNM the following experimental con-
straints are imposed: accelerators data on supersym-
metric and Higgs boson searches at the CERN e+e−
collider LEP2 [21]; the upper bound on the invisible
width for the decay of the Z–boson into non Standard
Model particles: Γ(Z → χχ) < 3 MeV [22, 23]; mea-
surements of the b → s + γ decay process [24]: 2.89
≤ BR(b → sγ) · 104≤ 4.21 is employed here (this in-
terval is larger by 25% with respect to the experimental
determination [24] in order to take into account theoret-
ical uncertainties in the supersymmetric (SUSY) contri-
butions [25] to the branching ratio of the process (for
the Standard Model calculation, we employ the NNLO
results from Ref. [26])); the measurements of the muon
anomalous magnetic moment aµ≡ (gµ−2)/2: for the de-
viation, ∆aµ≡ aexp
µ
−athe
µ, of the experimental world av-
erage from the theoretical evaluation within the Standard
Model we use here the (2 σ) range 31 ≤ ∆aµ·1011≤ 479,
derived from the latest experimental [27] and theoretical
[28] data (the supersymmetric contributions to the muon
anomalous magnetic moment within the MSSM are eval-
uated here by using the formulae in Ref. [29]); the search
for charged Higgs bosons in top quark decay at the Teva-
tron [30]; the recently improved upper bound (at 95%
C.L.) on the branching ratio for the decay Bs→ µ++µ−:
BR(Bs→ µ+µ−) < 1.08×10−8[31] and the constraints
related to ∆MB,s≡ MBs− M ¯ Bs[32, 33].
A further bound, which plays a most relevant role
in constraining the supersymmetric parameter space, is
represented by the results of searches for Higgs decay
into a tau pair. Indeed colliders have a good sensitiv-
ity to the search for decays (φ → b¯b or φ → τ¯ τ) (where
φ = h,A,H) in the regime of small mAand large tanβ,
because in this region of the supersymmetric parameters
the couplings of one of the neutral Higgs bosons to the
down–fermions are enhanced [34]. This experimental in-
vestigation was thoroughly carried out at the Tevatron
and is now underway at the LHC. No signal for these de-
cays has been found so far, thus successive measurements
have progressively disallowed substantial regions in the
supersymmetric parameters space at small mAand large
tanβ.
However, at present the actual forbidden region is not
yet firmly established. The most stringent bounds pro-
vided in the mA– tanβ plane are reported by the CMS
Collaboration in a preliminary form in Ref. [35] and
Ref. [36]. The first report refers to a luminosity of 1.6
fb−1, the second one to a luminosity of 4.6 fb−1. It is
worth noting that, in the range 90 GeV ≤ mχ ≤ 120
GeV, the bound on tanβ given in the second report is
less stringent than the limit given in the first one by a
factor of (20−40)%. This circumstance suggests to take

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5
FIG. 1: Upper bounds in the mA – tanβ plane, derived from
searches of the neutral Higgs decays into a tau pair at the
LHC. The dot–dashed line denotes the 95% CL upper bound
reported in Ref. [36]. The dashed line displays the expected
upper bound (in case of no positive signal for an integrated
luminosity of 3 fb−1) as evaluated in Refs.
scatter plot denotes configurations of the LNM. The solid lines
(some of which labeled by numbers) denote the cosmological
bound Ωχh2≤ (ΩCDMh2)max for a neutralino whose mass
is given by the corresponding number (in units of GeV), as
obtained by Eqs. (6), with ǫb = −0.08 and (ΩCDMh2)max =
0.12. For any given neutralino mass, the allowed region is
above the corresponding line.
[37, 38]. The
the present constraints with much caution. A conserva-
tive attitude is also suggested by the considerations put
forward in Refs. [37, 38] about the actual role of uncer-
tainties in the derivation of the present bounds.
In Fig. 1, which displays the plane mA– tanβ, we sum-
marize the present situation as far as the constraints from
the collider searches for the neutral Higgs decays into a
tau pair are concerned. The dot–dashed line denotes the
95% CL upper bound reported in Ref. [36], accounting
for a +1σ theoretical uncertainty. The dashed line dis-
plays the expected upper bound (in case of no positive
signal for an integrated luminosity of 3 fb−1) as evalu-
ated in Refs. [37, 38]. We do not mean to attribute to
this expected bound the meaning of the most realistic up-
per limit; we just take it as indicative of a conservative
estimate of the bound, and thus as a reasonable upper
extreme of the physical range to consider in our scan of
the parameter space.
Notice that the regime of small tanβ values is also com-
patible with one of the physical regions selected by the
branching ratio BR(B → τ + ν) (see Fig.16 of Ref. [3]).
Also shown in Fig.1 are the curves which corre-
spond to a fixed value of mχ; these are calculated from
Eq. (6) by replacing the inequality with an equality sym-
bol and setting, for definiteness, to 1 the two last fac-
tors of the right–hand–side.
with different values of (a2
ated to each isomass curve has to be scale up by the
factor (a2
displayed in Fig. 1 and its implications will be discussed
in the next Section.
We recall that also the cosmological constraint Ωχh2≤
(ΩCDMh2)max, discussed in Sect. IIA, is implemented in
our analysis.
The viability of very light neutralinos in terms of var-
ious constraints from collider data, precision observables
and rare meson decays is also considered in Ref. [39].
Perspectives for investigation of these neutralinos at LHC
are analyzed in Ref. [40, 41] and prospects for a very ac-
curate mass measurement at ILC in Ref. [42].
Thus, for configurations
3)1/2, the mχ value associ-
1a2
1a2
3/0.12)1/2. The features of the scatter plot
III. RESULTS
According to the considerations developed up to now,
it is clear that, in order to examine the physical re-
gion relevant for light neutralinos with a sizable elastic
neutralino–nucleon cross section efficiently, one has to set
up a scan of the supersymmetric parameter space focused
on low values of M1, restricted ranges of mAand µ close
to their minimal values as allowed by present experimen-
tal lower bounds, and a range of tanβ delimited from
above by the bounds from the neutral Higgs decays into
a tau pair and from BR(Bs→ µ++ µ−). The LEP lim-
its on tanβ and mAare taken into account through the
bounds derived from the Higgs–strahlung of the Z–boson
[21]. The selection of the parameters ranges has also to
allow small values of the tau slepton, to take care of the
cosmological bound for neutralinos with mχ>
(see previous discussion in Sect. IIA).
For these reasons the scan of the parameter space
adopted in the present paper is the following:
tanβ ≤ 15, 100GeV ≤ µ ≤ 200GeV, 10GeV ≤
M1≤ 100GeV, 100GeV ≤ M2≤ 2000GeV, 700GeV ≤
m˜ q12≤ 2000GeV, 100GeV ≤ m˜ t≤ 1000GeV, 70GeV ≤
m˜l12,L,m˜l12,R,m˜ τL,m˜ τR≤ 150GeV, 90GeV ≤ mA ≤
160GeV, 0.5 ≤ A ≤ 3.
We turn now to the discussion of the physical results as
obtained by our numerical scans of the supersymmetric
parameter space. First we analyze the generic population
of light neutralinos within the LNM which takes into ac-
count all the constraints listed in the previous Sect. IIC,
∼28 GeV
1 ≤

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FIG. 2: Relation among the Higgs masses in the LNM. In the left panel, the correlation between mh and mA is shown. In the
right panel, the correlation between mH and mA is given. The horizontal (red) line and the shaded band around it denote the
value of 126 GeV for the Higgs mass (and the 95 % CL region between 115.5 GeV and 131 GeV) compatible with the excess
of events observed by ATLAS [11] and CMS [12].
then we will discuss the impact of the excess seen by the
ATLAS and CMS Collaborations at the LHC.
A. The light neutralino population within the
LNM
A first result of our scans is shown in Fig. 1. From the
scatter plot displayed here one sees that the lower bound
on the neutralino mass turns out to be about 18 GeV.
The depopulation in the domain with tanβ >
90 GeV <
∼mA<
∼100 GeV with respect to our previous
analyses [3] is due to the new bound BR(Bs→ µ+µ−) <
1.08 × 10−8[31].
In Fig. 2 we display the correlation between mAand
mh,mH, because this will be useful for the discussions to
follow. From the left panel of Fig. 2 one can derive the
values of the ratio mA/mhwhich enters into the approxi-
mate estimate of the neutralino–nucleon elastic cross sec-
tion due to the h–exchange contribution (see Eq. (9).
Figs. 3 and 4 give the size of the various channels
contributing to the neutralino pair annihilation and to
the neutralino–nucleon elastic cross section, respectively.
From Fig. 3 we observe in the neutralino pair annihila-
tion cross section a dominance of the A–exchange contri-
bution for mχ<
∼28 GeV, and a possible dominance of the
˜ τ–exchangefor larger values of mχ, as anticipated in Sect.
IIA (the contribution of the Z–exchange is largely sub-
∼12 and
dominant compared to the other two and is not shown).
Fig. 4 shows that in the direct detection cross section the
contributions from the h and H exchanges are largely
dominant over the squark exchange, with a sizable dom-
inance of the h exchange over the H one.
The scatter plot for the quantity relevant for the com-
parison with the direct detection experimental results,
ξσ(nucleon)
scalar
, is displayed in Fig. 5. It is noticeable that
our population of light neutralinos fits quite well a re-
gion of compatibility of the DAMA/LIBRA data with
the CRESST results in the mχ–ξσ(nucleon)
Some comments are in order here:
a) The scatter plot shown in Fig. 5 is obtained with
a specific set of values for the hadronic quantities which
establish the coupling between the Higgs boson and the
nucleon (i.e. gd= gd,ref = 290 MeV). As mentioned in
Sect.IIB, the quantity gdsuffers from large uncertainties
[19], so that the scatter plot of Fig. 5 could actually move
upwards by a factor 3 or downward by a factor 0.12.
b) The experimental region of each individual exper-
iment is sizeably affected by uncertainties due to the
estimate of the quenching factor.
DAMA/LIBRA experiment the two regions are illustra-
tive (but not exhaustive) of the large effect introduced
by different evaluations of this factor [10].
c) The position of the experimental regions mχ–
ξσ(nucleon)
scalar
strongly depends also on the DM galactic dis-
tribution function (DF) employed in deriving these re-
scalar
plane.
In the case of the

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7
FIG. 3: Fractional relevance of channels in the neutralino self–
annihilation cross section
?
refer to annihilation through A–exchange; (green) crosses to
annihilation through ˜ τ–exchange.
?σannv? appearing in Eq. (2) as a
function of the neutralino mass in the LNM. The (red) points
gions from the experimental rates. Thus, their location
relative to the theoretical scatter plot changes depending
on the galactic DM properties [44]. The domains shown
in Fig. 5 were obtained by using for the DF the standard
isothermal sphere with ρ0 = 0.30 GeV cm−3, v0 = 220
km sec−1, with vesc= 650 km sec−1for DAMA/LIBRA
experiment and vesc= 544 km sec−1for CRESST. The
use of a DF with a larger (smaller) value of ρ0 would
move downward (upward) the experimental regions by
a factor proportional to ρ0. Increasing (decreasing) the
speeds generically produce a displacement towards lower
(higher) masses [44].
In conclusion, by taking into account various sources
of uncertainties, mainly the ones mentioned in the two
last items, the experimental regions shown in Fig. 5 may
change sizably. In the case of the DAMA/LIBRA exper-
iment the regions which encompass the effects of various
uncertainties are plotted in Figs. 1–3 and 7 of Ref. [10].
Negative results reported by other experiments of DM
direct detection [45–47] are in tension with the signals
measured by DAMA/LIBRA and CRESST. It should
however be noted that a number of questions about var-
ious physical and technical features of the specific detec-
tors or of the relevant analyses have been raised [48–50].
One further experiment, CoGeNT [6], reports the mea-
surement of an yearly–modulated signal. If interpreted
in terms of a coherently interacting dark matter parti-
FIG. 4: Fractional relevance of channels in the neutralino–
nucleon elastic–scattering cross section as a function of the
neutralino mass in the LNM. From darker to lighter points:
h–exchange, H–exchange, ˜ q–exchange.
cle, this signal gives a region in the mχ–ξσ(nucleon)
which is approximately located around mχ∼ 10 GeV and
ξσ(nucleon)
scalar
∼ (3 − 10) × 10−41cm2, thus somewhat dis-
placed from the region singled out by the scatter plot of
Fig.6. However, a redetermination of the region towards
smaller σ(nucleon)
scalar
and larger mχis being undertaken by
the CoGeNT Collaboration [51].
scalar
plane,
B.The neutralino subpopulation singled out by a
Higgs at 126 GeV
We turn now to the analysis of a subset of the neu-
tralino population considered in the previous section
which would be selected by an indication of a possible
Higgs signal at the LHC. Actually, the ATLAS Collab-
oration, in a search for a SM Higgs boson, measures an
excess of events around a mass of 126 GeV, and restricts
the most likely mass region (95 % CL) to 115.5–131 GeV
(global statistical significance about 2.3 σ) [11]. Similar
results (with a lower statistical significance) are presented
by CMS [12]. We address the question of what might be
the implications of these measurements (in case the ef-
fect is confirmed in next runs at the LHC) under the
hypothesis that this possible signal is attributed to the
production of the heavier neutral CP–even Higgs boson
H of the MSSM [52].
Within our light neutralino population we select the
subset of configurations with 115 GeV ≤ MH≤ 131 GeV.

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8
FIG. 5: Neutralino–nucleon cross section ξσ(nucleon)
tion of the neutralino mass for the LNM scan and for gd,ref
= 290 MeV. The (red) crosses denote configurations with
a heavy Higgs mass in the range compatible with the AT-
LAS [11] and CMS [12] excess at the LHC. The shaded areas
denote the DAMA/LIBRA annual modulation regions: the
upper area (vertical shade; green) refers to the case where
constant values of 0.3 and 0.09 are taken for the quenching
factors of Na and I, respectively[10]; the lower area (cross
hatched; red) is obtained by using the energy–dependent Na
and I quenching factors as established by the procedure given
in Ref. [43]. The gray regions are those compatible with the
CRESST excess [7]. In all cases a possible channeling effect is
not included.The halo distribution functions used to extract
the experimental regions are given in the text.
scalar
as a func-
These are contained in the band shown in the right panel
of Fig. 2, with values of the mAparameter in the range
90 GeV ≤ MA≤ 129 GeV. This subpopulation of light
neutralinos would have a neutralino–nucleon elastic cross
section in the domain depicted in Fig. 5 by (red) crosses,
and would then be in amazing agreement with the results
of DM direct detection.
The identification of a putative Higgs boson with the
H boson does not seem to be incompatible in terms of
production cross section and branching ratios. Though,
it might happen that imposing restrictive requirements
concerning these quantities would imply some further se-
lection within the neutralino population previously dis-
cussed. A thorough analysis of these aspects is beyond
the scope of the present paper.
IV. CONCLUSIONS
We have reviewed the status of the phenomenology
of light neutralinos in an effective Minimal Supersym-
metric extension of the Standard Model (MSSM) at the
electroweak scale, in light of new results obtained at the
CERN Large Hadron Collider. First we considered the
impact of the new data obtained by the CMS Collabora-
tion on the search for the Higgs boson decay into a tau
pair, and by the CMS and LHCb Collaborations on the
branching ratio for the decay Bs→ µ++µ−, and we es-
tablished that, on the basis of these data, the new value
for the lower bound of the neutralino mass is mχ ≃ 18
GeV.
Then we have examined the possible implications of
the excess of events found by the ATLAS and CMS Col-
laborations in a search for a SM–like Higgs boson around
a mass of 126 GeV, with a most likely mass region (95 %
CL) restricted to 115.5–131 GeV (global statistical sig-
nificance about 2.3 σ). We have derived that the ex-
cess around mSM
H
= 126 GeV, which nevertheless needs
a confirmation by further runs at the LHC, would imply
a neutralino in the mass range 18 GeV <
with neutralino–nucleon elastic cross sections fitting well
the results of the dark matter direct search experiments
DAMA/LIBRA and CRESST.
It is worth stressing that light neutralinos in the mass
range considered here do not appear to be constrained
by DM indirect searches (such as astrophysical gamma
fluxes of diffuse extragalactic origin or from dwarf galax-
ies, and the low–energy cosmic antiproton flux). A de-
tailed investigation of these aspects would however de-
serve a dedicated analysis.
∼mχ<
∼38 GeV,
Acknowledgments
A.B. and N.F. acknowledge Research Grants funded
jointly by Ministero dell’Istruzione, dell’Universit` a e
della Ricerca (MIUR), by Universit` a di Torino and by
Istituto Nazionale di Fisica Nucleare within the As-
troparticle Physics Project (MIUR contract number:
PRIN 2008NR3EBK; INFN grant code: FA51).
acknowledges support by NRF with CQUEST grant
2005-0049049 and by the Sogang Research Grant 2010.
N.F. acknowledges support of the spanish MICINN Con-
solider Ingenio 2010 Programme under grant MULTI-
DARK CSD2009- 00064.
S.S.

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