Table Of ContentScalar dark matter in an extra dimension inspired
model
6 Roberto Lineros1, Fabio Pereira dos Santos2,3
1
1Instituto de F´ısica Corpuscular – CSIC/U. Valencia, Spain
0
2Centro Federal de Educac¸˜ao Tecnolo´gica Celso Suckow da Fonseca, Petro´polis, RJ, Brazil
2
3Departamento de F´ısica, Pontif´ıcia Universidade Cat´olica do Rio de Janeiro, RJ, Brazil
n
a E-mail: [email protected], [email protected]
J
7 Abstract. Inthisworkweconsiderasingletscalarpropagatinginaflatlargeextradimension.
1
The first Kaluza-Klein mode associated to this singlet scalar will be a viable dark matter
candidate. The tower of new particles enriches the calculation of the relic density due effect of
]
h coannihilation. For large mass splitting, the model converges to the predictions of the singlet
p dark matter model. For nearly degenerate mass spectrum, coannihilations increase the cross-
- sections used for direct and indirect dark matter searches. We investigate the impact of the
p
Kaluza-Kleintowerassociatedtosingletscalarforindirectanddirectdetectionofdarkmatter.
e
h
[
1
v
1. Introduction
7
Although the relic density of dark matter can be determined with high precision, a very
4
3 important question still remains without answer, what the nature of dark matter is and also
4 which theory is able to explain it considering all recent observations. In this work we propose a
0
model based on flat extra dimension that is different from the universal extra dimension model
.
1
in the field propagation [1]. We assume that all the standard model particles are confined
0
to a 3-brane and only a singlet scalar (and gravity) can propagate in the 3 + δ space. The
6
1 stabilityofthefirstnonzerostateoftheKKtowerassociatedtothesingletscalarisensuredbya
: remnantU(1)-likesymmetrythatarisesafterintegratingovertheextradimension. Wecalculate
v
i the annihilation cross section and spin independent cross section including coannihilation as a
X
function of dark matter mass. Also, we show that annihilation and spin independent cross
r
a sections of dark matter undergo an increase when we include coannihilation. We include in our
results for annihilation cross section bounds from FERMI-LAT [2], MAGIC [3], and HESS [4]
and for spin independent cross section bounds from XENON100 [5], LUX [6], CDMSlite [7],
CRESST [8], and DAMA/LIBRA [9].
2. The model
In this work we consider a model based on a modified version of the large extra dimension [10].
For our purpose the scalar sector is composed by the the SM higgs doublet H, and by a real
scalar S, which is the only field in the model that depends on the extra dimension y that is
compactified in a circle with radius R. The lagrangian of the scalar sector is divided into three
parts [1]:
L (y) = L +L (y)+L (y) , (1)
scalar H S HS
where the lagrangian for the L ,L (y) and L (y) are:
H S HS
(cid:32) (cid:33)2
m2 v2
L ∝ (D H)†DµH − D H†H − , (2)
H µ 2v2 2
1 m2 λ λ
L (y) = ∂ S(y)∂NS(y)− SS(y)2−µS − 3S(y)3− 4S(y)4 , (3)
S N
2 2 3 4
(cid:32) (cid:33) (cid:32) (cid:33)
v2 v2
L (y) = −λ H†H − S(y)−λ H†H − S(y)2 , (4)
HS H 2H
2 2
√
where in the unitary gauge: HT = (0,(v + h))/ 2. The higgs vacuum expectation value is
v (cid:39) 246 GeV and m the mass term.
D
Due to the circular shape of the extra dimension, the periodic boundary condition for the extra
coordinate can be expressed as S(y) = S(y +2πR). Consequently, the field S(y) appears in a
set of Fourier modes,
S(y) = √ 1 (cid:40)√S0 + (cid:88)∞ S cos(cid:18)ny(cid:19)+ (cid:88)∞ P sin(cid:18)ny(cid:19)(cid:41) , (5)
n n
πRM 2 R R
5 n=1 n=1
whereS andP correspondtotheKKmodesofS(y). Inordertoobtaintheeffectivelagrangean
n n
of the model we integrate over the extra dimension y, the result is:
Leff = 1 (cid:16)∂ S ∂µS −m2S2(cid:17)+ 1 (cid:32)(cid:88)∞ ∂ S ∂µS −(m2 + n2)S2(cid:33)
S 2 µ 0 0 S 0 2 µ n n S R2 n
n=1
+1 (cid:32)(cid:88)∞ ∂ P ∂µP −(m2 + n2)P2(cid:33)− ω3V − ω4V . (6)
2 µ n n S R2 n 3 3 4 4
n=1
The KK modes, S and P , are degenerate in mass as we can realize from equation 6. Hence,
n n
we can define
S +iP S −iP
χ = n√ n and χ∗ = n√ n , (7)
n n
2 2
it reduces the equation 6 to:
Leff = 1 (cid:16)∂ S ∂µS −m2S2(cid:17)+ (cid:88)∞ ∂ χ∗∂µχ −m2 χ∗χ − ω3V − ω4V . (8)
S 2 µ 0 0 S 0 µ n n Sn n n 3 3 4 4
n=1
The interaction terms V and V are, for example:
3 4
(cid:16) (cid:17) (cid:16) (cid:17)
V = S3+3S |χ |2+|χ |2 +3 χ2χ∗+χ χ∗2 , (9)
3 0 0 1 2 1 2 2 1
(cid:16) (cid:17) (cid:16) (cid:17)
V = S4+12S2 |χ |2+|χ |2 +12S χ2χ∗+χ χ∗2
4 0 0 1 2 0 1 2 2 1
(cid:16) (cid:17)
+6 |χ |4+4|χ |2|χ |2+|χ |4 , (10)
1 1 2 2
We can observe that a global U(1) symmetry with charges Q(χ ) = n is present in the la-
n
grangian. So, the lightest KK state, χ , is stable and therefore it is the dark matter candidate.
1
3. Relic abundance and coannihilations
Therelicdensityofadarkmatterparticleisdeterminedbyitsself-annihilationcrosssectionand
also by annihilation processes involving heavier particles. We consider that it was in thermal
equilibrium in the early universe and also decoupled when it was non relativistic. In order to
reproduce the correct dark matter relic density we have to solve the Boltzmann equation
dn (cid:16) (cid:17)
χ +3Hn = −(cid:104)σ v(cid:105) n2 −n2 , (11)
dt χ eff χ eq
where H is the Hubble expansion rate, n is the number density at thermal equilibrium and
eq
(cid:104)σ v(cid:105)isthethermallyaveragedeffectivecrosssectionforannihilationtimestherelativevelocity.
eff
The effective cross section for our model is given by:
n
(cid:88)(1+∆ )3e−2x∆i
i
σ = σ i=1 = σ f(x,∆ ,n), (12)
c 0(cid:34) n (cid:35)2 0 2
(cid:88)(1+∆ )3/2e−x∆i
i
i=1
where the mass splitting between the DM and the i-th KK particles can be written in terms of
∆ :
2
(cid:115)
(i2−1)
∆ = 1+ ∆ (∆ +2)−1, (13)
i 2 2
3
where ∆ ranges between 0 and 1. In this work we parametrize the mass degeneracy as:
2
2 (cid:18)π (cid:19)
ξ = tan ∆ . (14)
KK 2
π 2
In order to be consistent with indirect detection searches that give (cid:104)σv(cid:105) ∼ 10−25cm3/s we
find the mass splitting ξ > 10−3 or in terms of number of KK modes n ∼ 10. The parameter
KK
ξ shows regions where DM phenomenology is affected by coannihilations (see [1] for details).
KK
4. Results and discussions
In order to compute the theoretical prediction of the relic density of our model we use public
software tools LanHEP [11] and MicrOmegas [12].
Figure 1 shows the mass splitting dependence of the annihilation cross section and the spin
independent cross section in terms of mass degeneracy parameter ξ . For lower values of ξ
KK KK
we observe a similar behavior in both cross sections . For ξ < 10−2, i.e. mass splitting of the
KK
order of 1% of the DM mass, the cross sections converge to common values: σ (cid:39) 10−44cm2
SI
and σv (cid:39) 2×10−25cm3/s. In fact, this effect is associated to coannihilations. From figure 2 we
observe that points with σv > 3×10−26cm3/s are in the mass range 150Gev < m < 10TeV.
S1
In the top panel of figure 3 we show the annihilation cross section as a function of dark
matter mass m . The solid red line correponds to the predictions of the inert singlet DM
S1
model . Bounds from FERMI-LAT [2], MAGIC [3], and HESS [4] are displayed in dashed
lines. The color scale correponds to the value of the degeneracy parameter ξ . Smaller values
KK
of ξ lead to enhanced annihilations due to more Kaluza Klein modes were involved in the
KK
early universe. In the bottom panel we show the spin independent cross section versus the
dark matter mass m . Bounds from XENON100 [5], LUX [6], CDMSlite [7], CRESST [8], and
S1
DAMA/LIBRA [9] are also shown. The color bar indicates the value of ξ where for lower
KK
valuesthereisanenhancementofbothcrosssectionsduetocoannihilations. Ontheotherhand,
when ξ is large most of the points fall close to the predictions of the inert singlet DM model.
KK
Figure 1. Annihilation cross section (top) and Spin Independent cross section (bottom) versus
ξ . Both cross sections converge to a fixed value for low values of ξ .
KK KK
Figure 2. Top-panel: ξ versus DM mass. Color scale corresponds to the annihilation cross
KK
section value. Bottom-panel: ξ versus DM mass. Color scale corresponds to the value of
KK
M .
KK
5. Conclusions
The model we present in this work allows us to study the effect of coannihilations when several
particles are quasi degenerate in mass. We found that for a degenerate mass spectrum both
annihilation and spin independent cross section converge to fixed values σ (cid:39) 10−44cm2 and
SI
σv (cid:39) 2×10−25cm3/s. This enhancement can be translated to a mass splitting among the KK
particlessmallerthan100GeV.Forlargermasssplittings,themodelconvergestothepredictions
of the inert scalar DM model.
Figure 3. Annihilation cross section (top-panel) and Spin Independent cross section (bottom-
panel) vs DM mass excluding points that do not satisfy latest LUX bounds [6].
6. Acknowledgments
This work was supported by the Spanish MINECO under grants FPA2014-58183-P,
and MULTIDARK CSD2009-00064 (Consolider-Ingenio 2010 Programme); by Generalitat
Valenciana grant PROMETEOII/2014/084, and Centro de Excelencia Severo Ochoa SEV-2014-
0398 and by Brazilian agencies Capes and CNPq. R.L. is supported by a Juan de la Cierva
contract JCI-2012-12901 (MINECO). We would like to thank you the organizers of the TAUP
2015 for an interesting conference.
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