Research ArticleDark Atoms and the Positron-Annihilation-Line Excessin the Galactic Bulge
J-R Cudell1 M Yu Khlopov234 and Q Wallemacq1
1 IFPA ldquoDepartement drsquoAGOrdquo Universite de Liege Sart Tilman 4000 Liege Belgium2National Research Nuclear University ldquoMoscow Engineering Physics Instituterdquo Moscow 115409 Russia3 Centre for Cosmoparticle Physics ldquoCosmionrdquo 115409 Moscow Russia4APC Laboratory 10 rue Alice Domon et Leonie Duquet 75205 Paris Cedex 13 France
Correspondence should be addressed to Q Wallemacq quentinwallemacqulgacbe
Received 25 November 2013 Accepted 13 January 2014 Published 25 February 2014
Academic Editor Chris Kouvaris
Copyright copy 2014 J-R Cudell et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited Thepublication of this article was funded by SCOAP3
It was recently proposed that stable particles of charge minus2 Ominusminus can exist and constitute dark matter after they bind with primordialhelium in O-helium (OHe) atoms We study here in detail the possibility that this model provides an explanation for the excessof gamma radiation in the positron-annihilation line from the galactic bulge observed by INTEGRAL This explanation assumesthat OHe excited to a 2s state through collisions in the central part of the Galaxy deexcites to its ground state via an 1198640 transitionemitting an electron-positron pair The cross-section for OHe collisions with excitation to 2s level is calculated and it is shownthat the rate of such excitations in the galactic bulge strongly depends not only on the mass of O-helium which is determined bythe mass of Ominusminus but also on the density and velocity distribution of dark matter Given the astrophysical uncertainties on thesedistributions this mechanism constrains the Ominusminus mass to lie in two possible regions One of these is reachable in the experimentalsearches for stable multicharged particles at the LHC
1 Introduction
According to modern cosmology dark matter correspondsto 25 of the total cosmological density is nonbaryonicand consists of new stable particles Such particles (see [1ndash6] for reviews and references) should be stable providethe measured dark-matter density and be decoupled fromplasma and radiation at least before the beginning of thematter-dominated era It was recently shown that heavy stableparticles of charge minus2 Ominusminus bound to primordial heliumin OHe atoms can provide an interesting explanation forcosmological dark matter [6 7] It should also be notedthat the nuclear cross-section of the O-helium interactionwith matter escapes the severe constraints [8ndash10] on stronglyinteracting dark-matter particles (SIMPs) [8ndash16] imposed bythe XQC experiment [17 18]
The hypothesis of composite O-helium dark matter firstconsidered to provide a solution to the puzzles of direct dark-matter searches can offer an explanation for another puzzle
of modern astrophysics [6 7 19] this composite dark-mattermodel can explain the excess of gamma radiation in theelectron-positron-annihilation line observed by INTEGRALin the galactic bulge (see [20] for a review and references)The explanation assumes that OHe provides all the galacticdark matter and that its collisions in the central part ofthe Galaxy result in 2s-level excitations of OHe which aredeexcited to the ground state by an 1198640 transition in which anelectron-positron pair is emitted If the 2s level is excited pairproduction dominates over the two-photon channel in thedeexcitation because electrons are much lighter than heliumnuclei and positron production is not accompanied by astrong gamma-ray signal
According to [21] the rate of positron production 3 sdot
10
42 sminus1 is sufficient to explain the excess in the positron-annihilation line from the bulge measured by INTEGRAL Inthe present paper we study the process of 2s-level excitationof OHe from collisions in the galactic bulge and determinethe conditions under which such collisions can provide
Hindawi Publishing CorporationAdvances in High Energy PhysicsVolume 2014 Article ID 869425 5 pageshttpdxdoiorg1011552014869425
2 Advances in High Energy Physics
the observed excess Inelastic interactions of O-helium withmatter in interstellar space and subsequent deexcitation cangive rise to radiation in the range from a few keV to afew MeV In the galactic bulge with radius 119903
119887
sim 1 kpcthe number density of O-helium can be of the order of119899
119900
asymp 3 sdot 10
minus3
119878
3
cmminus3 or larger and the collision rate of O-helium in this central region was estimated in [19] 119889119873119889119905 =
119899
2
119900
120590Vℎ
4120587119903
3
119887
3 asymp 3 sdot 10
42
119878
minus2
3
sminus1 with 119878
3
= 119898OHe1TeV At thevelocity of V
ℎ
sim 3 sdot 10
7 cms energy transfer in such collisionsis Δ119864 sim 1MeV119878
3
These collisions can lead to excitation ofO-helium If OHe levels with nonzero angular momentumare excited gamma lines should be observed from transitions(119899 gt 119898) 119864
119899119898
= 1598MeV(1119898
2
minus 1119899
2
) (or from similartransitions corresponding to the case 119868
119900
= 1287MeV) at thelevel 3 sdot 10
minus4
119878
minus2
3
(cm2 sMeV ster)minus1
2 Collisional Excitation Cross-Section
The studied reaction is the collision between two OHe atomsboth being initially in their ground state |1s⟩ giving rise tothe excitation of one of them to a |119899s⟩ state while the otherremains in its ground state
OHe (1s) +OHe (1s) 997888rarr OHe (1s) +OHe (119899s) (1)
If we work in the rest frame of the OHe that gets excitedand if we neglect its recoil after the collision the differentialcross-section of the process is given by
119889120590 (1s 997888rarr 119899s) = 2120587
1003816
1003816
1003816
1003816
1003816
⟨119899s
119901
1015840
|119880|1s
119901⟩
1003816
1003816
1003816
1003816
1003816
2
times 120575(
119901
10158402
2119872
+ 119864
119899s minus119901
2
2119872
minus 119864
1s)119889
3
119901
1015840
(2120587)
3
(2)
where 119872 is the mass of OHe
119901 and
119901
1015840 are the momenta ofthe incident OHe before and after the collision 119864
1s and 119864
119899sare the ground-state and excited-state energies of the targetOHe and 119880 is the interaction potential between the incidentand the target OHersquos
Wewill neglect the internal structure of the incidentOHeso that its wave functions are plane waves120595
119901
is normalized toobtain a unit incident current density and the normalisationof 120595
119901
1015840 is chosen for it to be pointlike that is the Fouriertransform of 120575(3)( 119903) [22]
120595
119901
= radic
119872
119901
119890
119894
119901sdot 119903
120595
119901
1015840 = 119890
119894
119901
1015840sdot 119903
(3)
where 119903 is the position vector of the incidentOHe and119901 = |
119901|In the following we will be led to consider Ominusminus masses
which are much larger than themass of helium or the bound-state energies Therefore the origin of the rest frame of thetarget OHe coincides with the position of its Ominusminus componentand its reduced mass 120583 can be taken as the mass of helium119872He
The OHe that gets excited is described as a hydrogen-likeatom with energy levels 119864
119899s = minus05119872He(119885He119885O120572)2
119899
2 andinitial and final bound-state wave functions 120595
1s and 120595
119899s of ahydrogenoid atom with a Bohr radius 119886
0
= (119872He119885He119885O120572)minus1
The incident OHe interacts with the Ominusminus and heliumcomponents in the target OHe so that the interactionpotential 119880 is the sum of the two contributions 119880O and 119880He
119880 (119903) = 119880O (
119903) + 119880He ( 119903 minus 119903He) (4)
where 119903He is the position vector of the helium componentThe first term119880O gives a zero contribution to the integral
of expression (2) since the states 1205951s and 120595
119899s are orthogonalFor the second term we treat the incident OHe as a heavyneutron colliding on a helium nucleus through short-rangenuclear forces The interaction potential can then be writtenin the form of a contact term
119880He ( 119903 minus 119903He) = minus
2120587
119872He119886
0
120575 ( 119903 minus 119903He) (5)
where we have normalised the delta function to obtain anOHe-helium elastic cross-section equal to 4120587119886
2
0
Going to spherical coordinates for
119901
1015840 and integrating over119901
1015840
= |
119901
1015840
| in the differential cross-section (2) together withthe previous expressions (3) (4) and (5) we get
119889120590 (1s 997888rarr 119899s) = (
119872
119872He)
2
119886
2
0
(
119901
1015840
119901
)
times
1003816
1003816
1003816
1003816
1003816
1003816
1003816
int 119890
minus119894 119902 119903He120595
lowast
119899s1205951s1198893
119903He1003816
1003816
1003816
1003816
1003816
1003816
1003816
2
119889Ω
(6)
where 119902 =
119901
1015840
minus
119901 is the transferred momentum and 119889Ω is thesolid angle From the integration over the delta function in(2) we have obtained the conservation of energy during theprocess
119901
10158402
= 119901
2
+ 2119872(119864
1s minus 119864
119899s) (7)
It leads to the threshold energy corresponding to 119901
10158402
= 0 andto aminimum incident velocity Vmin =
radic2(119864
119899s minus 119864
1s)119872Theprevious expression for 119901
1015840 allows us to express the squaredmodulus of 119902 as
119902
2
= 2 (119901
2
+ 119872(119864
1s minus 119864
119899s)
minus119901
radic
119901
2
+ 2119872(119864
1s minus 119864
119899s) cos 120579)
(8)
where 120579 is the deviation angle of the incident OHe withrespect to the collision axis in the rest frame of the targetOHe
119890
+
119890
minus pairs will be dominantly produced if OHe is excitedto a 2s state since the only deexcitation channel is in this casefrom 2s to 1s As 119890
+
119890
minus pair production is the only possiblechannel the differential pair-production cross-section 119889120590
119890119890
isequal to the differential collisional excitation cross-sectionBy particularizing expression (6) to the case 119899 = 2 one finallygets
119889120590
119890119890
119889 cos 120579= 512
2
(
2120587119872
2
119872
2
He)119886
6
0
(
119901
1015840
119901
)
119902
4
2(4119886
2
0
119902
2
+ 9)
6
(9)
Advances in High Energy Physics 3
3 The 119890
+
119890
minus Pair-Production Rate in theGalactic Bulge
The total 119890+119890minus pair-production rate in the galactic bulge isgiven by
119889119873
119889119905
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816119890119890
= int
119881
119887
120588
2
DM (
119877)
119872
2
⟨120590
119890119890
V⟩ (
119877) 119889
119877
(10)
where119881119887
is the volume of the galactic bulge which is a sphereof radius 119877
119887
= 15 kpc 120588DM is the energy density distributionof dark matter in the galactic halo and ⟨120590
119890119890
V⟩ is the pair-production cross-section 120590
119890119890
times relative velocity V aver-aged over the velocity distribution of dark-matter particlesThe total pair-production cross-section 120590
119890119890
is obtained byintegrating (9) over the diffusion angle Its dependence on therelative velocity V is contained in1199011199011015840 and 119902 through119901 = 119872Vand the expressions (7) and (8) of 1199011015840 and 119902 in terms of 119901
We use a Burkert [23 24] flat cored dark-matter densityprofile known to reproduce well the kinematics of disksystems in massive spiral galaxies and supported by recentsimulations including supernova feedback and radiationpressure of massive stars [25] in response to the cuspy haloproblem
120588DM (119877) = 120588
0
119877
3
0
(119877 + 119877
0
) (119877
2
+ 119877
2
0
)
(11)
where 119877 is the distance from the galactic center The centraldark-matter density 120588
0
is left as a free parameter and 119877
0
isdetermined by requiring that the local dark-matter density at119877 = 119877
⊙
= 8 kpc is 120588⊙
= 03GeVcm3 The dark-matter massenclosed in a sphere of radius 119877 is therefore given by
119872DM (119877) = 120588
0
120587119877
3
0
log(119877
2
+ 119877
2
0
119877
2
0
)
+2 log(119877 + 119877
0
119877
0
) minus 2 arctan(
119877
119877
0
)
(12)
For the baryons in the bulge we use an exponential profile[26] of the form
120588
119887
(119877) =
119872bulge
8120587119877
3
119887
119890
minus119877119877
119887 (13)
where 119872bulge = 10
10
119872
⊙
[27] is the mass of the bulge Thisgives the baryonic mass distribution in the galactic bulge
119872
119887
(119877) = 119872bulge 1 minus 119890
minus119877119877
119887(1 +
119877
119877
119887
+
119877
2
119877
2
119887
) (14)
We assume a Maxwell-Boltzmann velocity distributionfor the dark-matter particles of the galactic halo with avelocity dispersion 119906(119877) and a cutoff at the galactic escapevelocity Vesc(119877)
119891 (119877 Vℎ
) =
1
119862 (119877)
119890
minusV2ℎ119906
2(119877)
(15)
where Vℎ
is the velocity of the dark-matter particles in theframe of the halo and 119862(119877) = 120587119906
2
(radic120587119906 erf(Vesc119906) minus
2Vesc119890minusV2esc119906
2
) is a normalization constant such thatint
Vesc(119877)0
119891(119877 Vℎ
)119889Vℎ
= 1The radial dependence of the velocity dispersion is
obtained via the virial theorem
119906 (119877) =
radic
119866119872tot (119877)
119877
(16)
where119872tot = 119872DM + 119872
119887
while Vesc =
radic
2119906Using the velocity distribution (15) going to center-of-
mass and relative velocities VCM and V and performing theintegrals over VCM we obtain for the mean pair-productioncross-section times relative velocity
⟨120590
119890119890
V⟩ =
1
119906
2
radic
2120587119906 erf (radic2Vesc119906) minus 4Vesc119890minus2V2esc119906
2
(radic120587119906 erf (Vesc119906) minus 2Vesc119890minusV2
esc1199062
)
2
times int
2Vesc
0
120590
119890119890
(V) V3119890minusV22119906
2
119889V
(17)
which is also a function of 119877 through 119906 and Vesc Putting (9)(11) (12) (14) (16) and (17) together allows us to compute thepair-production rate in the galactic bulge defined in (10) as afunction of 120588
0
and119872
4 Results
The rate of excessive 119890+119890minus pairs to be generated in the galacticbulge was estimated in [21] to be 119889119873119889119905|obs = 3 times 10
42 sminus1We computed 119889119873119889119905|
119890119890
for a large range of central dark-matter densities going from 03GeVcm3 to an ultimateupper limit of 10
4 GeVcm3 [28] For each value of 120588
0
wesearched for themass119872 ofOHe that reproduces the observedrate The results are shown in Figure 1
The observed rate can be reproduced from a value of120588
0
≃ 115GeVcm3 corresponding to an OHe mass of 119872 ≃
125TeV As 120588
0
gets larger two values of 119872 are possiblewith the lower one going from 125TeV to 130GeV and theupper one going from 125 to 130TeV as 120588
0
goes from 115 to10
4 GeVcm3
5 Conclusion
The existence of heavy stable particles is one of the mostpopular solutions for the dark- matter problem Usually theyare considered to be electrically neutral But dark mattercan potentially be made of stable heavy charged particlesbound in neutral atom-like states by Coulomb attractionAn analysis of the cosmological data and of the atomiccomposition of theUniverse forces the particle to have chargeminus2 Ominusminus is then trapped by primordial helium in neutral O-helium states and this avoids the problem of overproductionof anomalous isotopes which are severely constrained byobservations Here we have shown that the cosmologicalmodel of O-helium dark matter can explain the puzzle ofpositron line emission from the center of our Galaxy
4 Advances in High Energy Physics
1000100101
10000
1000
100001 01
1205880(GeV
cm
3)
M (TeV)
Figure 1 Values of the central dark-matter density 120588
0
(GeVcm3)and of the OHe mass 119872 (TeV) reproducing the excess of 119890+119890minus pairsproduction in the galactic bulge Below the red curve the predictedrate is too low
The proposed explanation is based on the assumptionthat OHe dominates the dark-matter sector Its collisionscan lead to 1198640 deexcitations of the 2s states excited by thecollisionsThe estimated luminosity in the electron-positron-annihilation line strongly depends not only on the mass ofOminusminus but also on the density profile and velocity distribution ofdarkmatter in the galactic bulge Note that the density profilewe considered is used only to obtain a reasonable estimatefor the uncertainties on the density in the bulge It indeedunderestimates the mass of the Galaxy but it shows thatthe uncertainties on the astrophysical parameters are largeenough to reproduce the observed excess for a rather widerange of masses of Ominusminus For a fixed density profile and a fixedvelocity distribution only two values of the Ominusminus mass leadto the necessary rate of positron production The lower valueof this mass which does not exceed 125TeV is within thereach of experimental searches for multicharged stable heavyparticles at the LHC
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors express their gratitude to A S Romaniouk fordiscussions
References
[1] M Yu Khlopov Cosmoparticle Physics World Scientific Singa-pore 1999
[2] M Yu Khlopov ldquoCosmoarcheology Direct and indirect astro-physical effects of hypothetical particles and fieldsrdquo inCosmion-94 M Yu Khlopov M E Prokhorov A A Starobinsky and J
Tran Thanh Van Eds pp 67ndash76 Editions Frontieres QuebecCanada 1996
[3] M Y Khlopov ldquoProceedings to the 9th workshop lsquowhat comesbeyond the standard modelsrsquordquo Bled Workshops in Physics vol 7no 2 p 51 2006
[4] M Y Khlopov ldquoProceedings to the 10th workshop lsquowhat comesbeyond the standard modelsrsquordquo Bled Workshops in Physics vol 8no 2 p 114 2007
[5] M Yu Khlopov Fundamentals of Cosmoparticle Physics CISP-Springer Cambridge UK 2012
[6] M Yu Khlopov ldquoFundamental particle structure in the cosmo-logical dark matterrdquo International Journal of Modern Physics Avol 28 no 29 Article ID 1330042 60 pages 2013
[7] M Yu Khlopov ldquoPhysics of dark matter in the light of darkatomsrdquoModern Physics Letters A vol 26 no 38 Article ID 28232011
[8] B D Wandelt R Dave G R Farrar P C McGuire D NSpergel and P J Steinhardt ldquoSelf-interacting dark matterrdquohttparxivorgabsastro-ph0006344
[9] P C McGuire and P J Steinhardt ldquoCracking open the windowfor strongly interacting massive particles as the halo darkmatterrdquo httparxivorgabsastro-ph0105567
[10] G Zaharijas and G R Farrar ldquoWindow in the dark matterexclusion limitsrdquo Physical Review D vol 72 no 8 Article ID083502 11 pages 2005
[11] C B Dover et al ldquoCosmological constraints on new stablehadronsrdquo Physical Review Letters vol 42 no 17 pp 1117ndash11201979
[12] S Wolfram ldquoAbundances of new stable particles produced inthe early universerdquo Physics Letters B vol 82 no 1 pp 65ndash681979
[13] G D Starkman A Gould R Esmailzadeh and S DimopoulosldquoOpening the window on strongly interacting dark matterrdquoPhysical Review D vol 41 no 12 pp 3594ndash3603 1990
[14] D Javorsek D Elmore E Fischbach et al ldquoNew experimentallimits on strongly interactingmassive particles at the TeV scalerdquoPhysical Review Letters vol 87 no 23 Article ID 231804 2001
[15] S Mitra ldquoUranusrsquos anomalously low excess heat constrainsstrongly interacting dark matterrdquo Physical Review D vol 70 no10 Article ID 103517 2004
[16] G D Mack J F Beacom and G Bertone ldquoTowards closingthe window on strongly interacting dark matter far-reachingconstraints from Earthrsquos heat flowrdquo Physical Review D vol 76no 4 Article ID 043523 2007
[17] D McCammon R Almy S Deiker et al ldquoA soundingrocket payload for X-ray astronomy employing high-resolutionmicrocalorimetersrdquoNuclear Instruments andMethods in PhysicsResearch Section A vol 370 no 1 pp 266ndash268 1996
[18] D McCammon R Almy E Apodaca et al ldquoA high spectralresolution observation of the soft X-ray diffuse backgroundwith thermal detectors rdquoThe Astrophysical Journal vol 576 no1 p 188 2002
[19] M Yu Khlopov ldquoComposite dark matter from stable chargedconstituentsrdquo httparxivorgabs08063581
[20] B J Teegarden K Watanabe P Jean et al ldquoINTEGRAL SPIlimits on electron-positron annihilation radiation from thegalactic planerdquoThe Astrophysical Journal vol 621 no 1 p 2962005
[21] D P Finkbeiner and N Weiner ldquoExciting dark matter and theINTEGRALSPI 511 keV signalrdquo Physical Review D vol 76 no8 Article ID 083519 2007
Advances in High Energy Physics 5
[22] LD Landau andEM LifshitzQuantumMechanics PergamonPress Elmsford NY USA 1965
[23] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquo IAU Symposia vol 171 p 175 1996
[24] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquoThe Astrophysical Journal vol 447 no 1 p L25 1995
[25] A V Maccio G Stinson C B Brook et al ldquoHALO Expansionin cosmological hydro simulations toward a baryonic solutionof the cuspcore problem in massive spiralsrdquo The AstrophysicalJournal Letters vol 744 no 1 p L9 2012
[26] O Y Gnedin A V Kravtsov A A Klypin and D NagaildquoResponse of dark matter halos to condensation of Baryonscosmological simulations and improved adiabatic contractionmodelrdquoThe Astrophysical Journal vol 616 no 1 p 16 2004
[27] H Mo F van den Bosch and S White Galaxy Formation andEvolution Cambridge University Press Cambridge UK 2010
[28] X Hernandez and W H Lee ldquoAn upper limit to the centraldensity of dark matter haloes from consistency with the pres-ence ofmassive central black holesrdquoMonthlyNotices of the RoyalAstronomical Society vol 404 no 1 p L10 2010
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
2 Advances in High Energy Physics
the observed excess Inelastic interactions of O-helium withmatter in interstellar space and subsequent deexcitation cangive rise to radiation in the range from a few keV to afew MeV In the galactic bulge with radius 119903
119887
sim 1 kpcthe number density of O-helium can be of the order of119899
119900
asymp 3 sdot 10
minus3
119878
3
cmminus3 or larger and the collision rate of O-helium in this central region was estimated in [19] 119889119873119889119905 =
119899
2
119900
120590Vℎ
4120587119903
3
119887
3 asymp 3 sdot 10
42
119878
minus2
3
sminus1 with 119878
3
= 119898OHe1TeV At thevelocity of V
ℎ
sim 3 sdot 10
7 cms energy transfer in such collisionsis Δ119864 sim 1MeV119878
3
These collisions can lead to excitation ofO-helium If OHe levels with nonzero angular momentumare excited gamma lines should be observed from transitions(119899 gt 119898) 119864
119899119898
= 1598MeV(1119898
2
minus 1119899
2
) (or from similartransitions corresponding to the case 119868
119900
= 1287MeV) at thelevel 3 sdot 10
minus4
119878
minus2
3
(cm2 sMeV ster)minus1
2 Collisional Excitation Cross-Section
The studied reaction is the collision between two OHe atomsboth being initially in their ground state |1s⟩ giving rise tothe excitation of one of them to a |119899s⟩ state while the otherremains in its ground state
OHe (1s) +OHe (1s) 997888rarr OHe (1s) +OHe (119899s) (1)
If we work in the rest frame of the OHe that gets excitedand if we neglect its recoil after the collision the differentialcross-section of the process is given by
119889120590 (1s 997888rarr 119899s) = 2120587
1003816
1003816
1003816
1003816
1003816
⟨119899s
119901
1015840
|119880|1s
119901⟩
1003816
1003816
1003816
1003816
1003816
2
times 120575(
119901
10158402
2119872
+ 119864
119899s minus119901
2
2119872
minus 119864
1s)119889
3
119901
1015840
(2120587)
3
(2)
where 119872 is the mass of OHe
119901 and
119901
1015840 are the momenta ofthe incident OHe before and after the collision 119864
1s and 119864
119899sare the ground-state and excited-state energies of the targetOHe and 119880 is the interaction potential between the incidentand the target OHersquos
Wewill neglect the internal structure of the incidentOHeso that its wave functions are plane waves120595
119901
is normalized toobtain a unit incident current density and the normalisationof 120595
119901
1015840 is chosen for it to be pointlike that is the Fouriertransform of 120575(3)( 119903) [22]
120595
119901
= radic
119872
119901
119890
119894
119901sdot 119903
120595
119901
1015840 = 119890
119894
119901
1015840sdot 119903
(3)
where 119903 is the position vector of the incidentOHe and119901 = |
119901|In the following we will be led to consider Ominusminus masses
which are much larger than themass of helium or the bound-state energies Therefore the origin of the rest frame of thetarget OHe coincides with the position of its Ominusminus componentand its reduced mass 120583 can be taken as the mass of helium119872He
The OHe that gets excited is described as a hydrogen-likeatom with energy levels 119864
119899s = minus05119872He(119885He119885O120572)2
119899
2 andinitial and final bound-state wave functions 120595
1s and 120595
119899s of ahydrogenoid atom with a Bohr radius 119886
0
= (119872He119885He119885O120572)minus1
The incident OHe interacts with the Ominusminus and heliumcomponents in the target OHe so that the interactionpotential 119880 is the sum of the two contributions 119880O and 119880He
119880 (119903) = 119880O (
119903) + 119880He ( 119903 minus 119903He) (4)
where 119903He is the position vector of the helium componentThe first term119880O gives a zero contribution to the integral
of expression (2) since the states 1205951s and 120595
119899s are orthogonalFor the second term we treat the incident OHe as a heavyneutron colliding on a helium nucleus through short-rangenuclear forces The interaction potential can then be writtenin the form of a contact term
119880He ( 119903 minus 119903He) = minus
2120587
119872He119886
0
120575 ( 119903 minus 119903He) (5)
where we have normalised the delta function to obtain anOHe-helium elastic cross-section equal to 4120587119886
2
0
Going to spherical coordinates for
119901
1015840 and integrating over119901
1015840
= |
119901
1015840
| in the differential cross-section (2) together withthe previous expressions (3) (4) and (5) we get
119889120590 (1s 997888rarr 119899s) = (
119872
119872He)
2
119886
2
0
(
119901
1015840
119901
)
times
1003816
1003816
1003816
1003816
1003816
1003816
1003816
int 119890
minus119894 119902 119903He120595
lowast
119899s1205951s1198893
119903He1003816
1003816
1003816
1003816
1003816
1003816
1003816
2
119889Ω
(6)
where 119902 =
119901
1015840
minus
119901 is the transferred momentum and 119889Ω is thesolid angle From the integration over the delta function in(2) we have obtained the conservation of energy during theprocess
119901
10158402
= 119901
2
+ 2119872(119864
1s minus 119864
119899s) (7)
It leads to the threshold energy corresponding to 119901
10158402
= 0 andto aminimum incident velocity Vmin =
radic2(119864
119899s minus 119864
1s)119872Theprevious expression for 119901
1015840 allows us to express the squaredmodulus of 119902 as
119902
2
= 2 (119901
2
+ 119872(119864
1s minus 119864
119899s)
minus119901
radic
119901
2
+ 2119872(119864
1s minus 119864
119899s) cos 120579)
(8)
where 120579 is the deviation angle of the incident OHe withrespect to the collision axis in the rest frame of the targetOHe
119890
+
119890
minus pairs will be dominantly produced if OHe is excitedto a 2s state since the only deexcitation channel is in this casefrom 2s to 1s As 119890
+
119890
minus pair production is the only possiblechannel the differential pair-production cross-section 119889120590
119890119890
isequal to the differential collisional excitation cross-sectionBy particularizing expression (6) to the case 119899 = 2 one finallygets
119889120590
119890119890
119889 cos 120579= 512
2
(
2120587119872
2
119872
2
He)119886
6
0
(
119901
1015840
119901
)
119902
4
2(4119886
2
0
119902
2
+ 9)
6
(9)
Advances in High Energy Physics 3
3 The 119890
+
119890
minus Pair-Production Rate in theGalactic Bulge
The total 119890+119890minus pair-production rate in the galactic bulge isgiven by
119889119873
119889119905
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816119890119890
= int
119881
119887
120588
2
DM (
119877)
119872
2
⟨120590
119890119890
V⟩ (
119877) 119889
119877
(10)
where119881119887
is the volume of the galactic bulge which is a sphereof radius 119877
119887
= 15 kpc 120588DM is the energy density distributionof dark matter in the galactic halo and ⟨120590
119890119890
V⟩ is the pair-production cross-section 120590
119890119890
times relative velocity V aver-aged over the velocity distribution of dark-matter particlesThe total pair-production cross-section 120590
119890119890
is obtained byintegrating (9) over the diffusion angle Its dependence on therelative velocity V is contained in1199011199011015840 and 119902 through119901 = 119872Vand the expressions (7) and (8) of 1199011015840 and 119902 in terms of 119901
We use a Burkert [23 24] flat cored dark-matter densityprofile known to reproduce well the kinematics of disksystems in massive spiral galaxies and supported by recentsimulations including supernova feedback and radiationpressure of massive stars [25] in response to the cuspy haloproblem
120588DM (119877) = 120588
0
119877
3
0
(119877 + 119877
0
) (119877
2
+ 119877
2
0
)
(11)
where 119877 is the distance from the galactic center The centraldark-matter density 120588
0
is left as a free parameter and 119877
0
isdetermined by requiring that the local dark-matter density at119877 = 119877
⊙
= 8 kpc is 120588⊙
= 03GeVcm3 The dark-matter massenclosed in a sphere of radius 119877 is therefore given by
119872DM (119877) = 120588
0
120587119877
3
0
log(119877
2
+ 119877
2
0
119877
2
0
)
+2 log(119877 + 119877
0
119877
0
) minus 2 arctan(
119877
119877
0
)
(12)
For the baryons in the bulge we use an exponential profile[26] of the form
120588
119887
(119877) =
119872bulge
8120587119877
3
119887
119890
minus119877119877
119887 (13)
where 119872bulge = 10
10
119872
⊙
[27] is the mass of the bulge Thisgives the baryonic mass distribution in the galactic bulge
119872
119887
(119877) = 119872bulge 1 minus 119890
minus119877119877
119887(1 +
119877
119877
119887
+
119877
2
119877
2
119887
) (14)
We assume a Maxwell-Boltzmann velocity distributionfor the dark-matter particles of the galactic halo with avelocity dispersion 119906(119877) and a cutoff at the galactic escapevelocity Vesc(119877)
119891 (119877 Vℎ
) =
1
119862 (119877)
119890
minusV2ℎ119906
2(119877)
(15)
where Vℎ
is the velocity of the dark-matter particles in theframe of the halo and 119862(119877) = 120587119906
2
(radic120587119906 erf(Vesc119906) minus
2Vesc119890minusV2esc119906
2
) is a normalization constant such thatint
Vesc(119877)0
119891(119877 Vℎ
)119889Vℎ
= 1The radial dependence of the velocity dispersion is
obtained via the virial theorem
119906 (119877) =
radic
119866119872tot (119877)
119877
(16)
where119872tot = 119872DM + 119872
119887
while Vesc =
radic
2119906Using the velocity distribution (15) going to center-of-
mass and relative velocities VCM and V and performing theintegrals over VCM we obtain for the mean pair-productioncross-section times relative velocity
⟨120590
119890119890
V⟩ =
1
119906
2
radic
2120587119906 erf (radic2Vesc119906) minus 4Vesc119890minus2V2esc119906
2
(radic120587119906 erf (Vesc119906) minus 2Vesc119890minusV2
esc1199062
)
2
times int
2Vesc
0
120590
119890119890
(V) V3119890minusV22119906
2
119889V
(17)
which is also a function of 119877 through 119906 and Vesc Putting (9)(11) (12) (14) (16) and (17) together allows us to compute thepair-production rate in the galactic bulge defined in (10) as afunction of 120588
0
and119872
4 Results
The rate of excessive 119890+119890minus pairs to be generated in the galacticbulge was estimated in [21] to be 119889119873119889119905|obs = 3 times 10
42 sminus1We computed 119889119873119889119905|
119890119890
for a large range of central dark-matter densities going from 03GeVcm3 to an ultimateupper limit of 10
4 GeVcm3 [28] For each value of 120588
0
wesearched for themass119872 ofOHe that reproduces the observedrate The results are shown in Figure 1
The observed rate can be reproduced from a value of120588
0
≃ 115GeVcm3 corresponding to an OHe mass of 119872 ≃
125TeV As 120588
0
gets larger two values of 119872 are possiblewith the lower one going from 125TeV to 130GeV and theupper one going from 125 to 130TeV as 120588
0
goes from 115 to10
4 GeVcm3
5 Conclusion
The existence of heavy stable particles is one of the mostpopular solutions for the dark- matter problem Usually theyare considered to be electrically neutral But dark mattercan potentially be made of stable heavy charged particlesbound in neutral atom-like states by Coulomb attractionAn analysis of the cosmological data and of the atomiccomposition of theUniverse forces the particle to have chargeminus2 Ominusminus is then trapped by primordial helium in neutral O-helium states and this avoids the problem of overproductionof anomalous isotopes which are severely constrained byobservations Here we have shown that the cosmologicalmodel of O-helium dark matter can explain the puzzle ofpositron line emission from the center of our Galaxy
4 Advances in High Energy Physics
1000100101
10000
1000
100001 01
1205880(GeV
cm
3)
M (TeV)
Figure 1 Values of the central dark-matter density 120588
0
(GeVcm3)and of the OHe mass 119872 (TeV) reproducing the excess of 119890+119890minus pairsproduction in the galactic bulge Below the red curve the predictedrate is too low
The proposed explanation is based on the assumptionthat OHe dominates the dark-matter sector Its collisionscan lead to 1198640 deexcitations of the 2s states excited by thecollisionsThe estimated luminosity in the electron-positron-annihilation line strongly depends not only on the mass ofOminusminus but also on the density profile and velocity distribution ofdarkmatter in the galactic bulge Note that the density profilewe considered is used only to obtain a reasonable estimatefor the uncertainties on the density in the bulge It indeedunderestimates the mass of the Galaxy but it shows thatthe uncertainties on the astrophysical parameters are largeenough to reproduce the observed excess for a rather widerange of masses of Ominusminus For a fixed density profile and a fixedvelocity distribution only two values of the Ominusminus mass leadto the necessary rate of positron production The lower valueof this mass which does not exceed 125TeV is within thereach of experimental searches for multicharged stable heavyparticles at the LHC
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors express their gratitude to A S Romaniouk fordiscussions
References
[1] M Yu Khlopov Cosmoparticle Physics World Scientific Singa-pore 1999
[2] M Yu Khlopov ldquoCosmoarcheology Direct and indirect astro-physical effects of hypothetical particles and fieldsrdquo inCosmion-94 M Yu Khlopov M E Prokhorov A A Starobinsky and J
Tran Thanh Van Eds pp 67ndash76 Editions Frontieres QuebecCanada 1996
[3] M Y Khlopov ldquoProceedings to the 9th workshop lsquowhat comesbeyond the standard modelsrsquordquo Bled Workshops in Physics vol 7no 2 p 51 2006
[4] M Y Khlopov ldquoProceedings to the 10th workshop lsquowhat comesbeyond the standard modelsrsquordquo Bled Workshops in Physics vol 8no 2 p 114 2007
[5] M Yu Khlopov Fundamentals of Cosmoparticle Physics CISP-Springer Cambridge UK 2012
[6] M Yu Khlopov ldquoFundamental particle structure in the cosmo-logical dark matterrdquo International Journal of Modern Physics Avol 28 no 29 Article ID 1330042 60 pages 2013
[7] M Yu Khlopov ldquoPhysics of dark matter in the light of darkatomsrdquoModern Physics Letters A vol 26 no 38 Article ID 28232011
[8] B D Wandelt R Dave G R Farrar P C McGuire D NSpergel and P J Steinhardt ldquoSelf-interacting dark matterrdquohttparxivorgabsastro-ph0006344
[9] P C McGuire and P J Steinhardt ldquoCracking open the windowfor strongly interacting massive particles as the halo darkmatterrdquo httparxivorgabsastro-ph0105567
[10] G Zaharijas and G R Farrar ldquoWindow in the dark matterexclusion limitsrdquo Physical Review D vol 72 no 8 Article ID083502 11 pages 2005
[11] C B Dover et al ldquoCosmological constraints on new stablehadronsrdquo Physical Review Letters vol 42 no 17 pp 1117ndash11201979
[12] S Wolfram ldquoAbundances of new stable particles produced inthe early universerdquo Physics Letters B vol 82 no 1 pp 65ndash681979
[13] G D Starkman A Gould R Esmailzadeh and S DimopoulosldquoOpening the window on strongly interacting dark matterrdquoPhysical Review D vol 41 no 12 pp 3594ndash3603 1990
[14] D Javorsek D Elmore E Fischbach et al ldquoNew experimentallimits on strongly interactingmassive particles at the TeV scalerdquoPhysical Review Letters vol 87 no 23 Article ID 231804 2001
[15] S Mitra ldquoUranusrsquos anomalously low excess heat constrainsstrongly interacting dark matterrdquo Physical Review D vol 70 no10 Article ID 103517 2004
[16] G D Mack J F Beacom and G Bertone ldquoTowards closingthe window on strongly interacting dark matter far-reachingconstraints from Earthrsquos heat flowrdquo Physical Review D vol 76no 4 Article ID 043523 2007
[17] D McCammon R Almy S Deiker et al ldquoA soundingrocket payload for X-ray astronomy employing high-resolutionmicrocalorimetersrdquoNuclear Instruments andMethods in PhysicsResearch Section A vol 370 no 1 pp 266ndash268 1996
[18] D McCammon R Almy E Apodaca et al ldquoA high spectralresolution observation of the soft X-ray diffuse backgroundwith thermal detectors rdquoThe Astrophysical Journal vol 576 no1 p 188 2002
[19] M Yu Khlopov ldquoComposite dark matter from stable chargedconstituentsrdquo httparxivorgabs08063581
[20] B J Teegarden K Watanabe P Jean et al ldquoINTEGRAL SPIlimits on electron-positron annihilation radiation from thegalactic planerdquoThe Astrophysical Journal vol 621 no 1 p 2962005
[21] D P Finkbeiner and N Weiner ldquoExciting dark matter and theINTEGRALSPI 511 keV signalrdquo Physical Review D vol 76 no8 Article ID 083519 2007
Advances in High Energy Physics 5
[22] LD Landau andEM LifshitzQuantumMechanics PergamonPress Elmsford NY USA 1965
[23] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquo IAU Symposia vol 171 p 175 1996
[24] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquoThe Astrophysical Journal vol 447 no 1 p L25 1995
[25] A V Maccio G Stinson C B Brook et al ldquoHALO Expansionin cosmological hydro simulations toward a baryonic solutionof the cuspcore problem in massive spiralsrdquo The AstrophysicalJournal Letters vol 744 no 1 p L9 2012
[26] O Y Gnedin A V Kravtsov A A Klypin and D NagaildquoResponse of dark matter halos to condensation of Baryonscosmological simulations and improved adiabatic contractionmodelrdquoThe Astrophysical Journal vol 616 no 1 p 16 2004
[27] H Mo F van den Bosch and S White Galaxy Formation andEvolution Cambridge University Press Cambridge UK 2010
[28] X Hernandez and W H Lee ldquoAn upper limit to the centraldensity of dark matter haloes from consistency with the pres-ence ofmassive central black holesrdquoMonthlyNotices of the RoyalAstronomical Society vol 404 no 1 p L10 2010
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Advances in High Energy Physics 3
3 The 119890
+
119890
minus Pair-Production Rate in theGalactic Bulge
The total 119890+119890minus pair-production rate in the galactic bulge isgiven by
119889119873
119889119905
1003816
1003816
1003816
1003816
1003816
1003816
1003816
1003816119890119890
= int
119881
119887
120588
2
DM (
119877)
119872
2
⟨120590
119890119890
V⟩ (
119877) 119889
119877
(10)
where119881119887
is the volume of the galactic bulge which is a sphereof radius 119877
119887
= 15 kpc 120588DM is the energy density distributionof dark matter in the galactic halo and ⟨120590
119890119890
V⟩ is the pair-production cross-section 120590
119890119890
times relative velocity V aver-aged over the velocity distribution of dark-matter particlesThe total pair-production cross-section 120590
119890119890
is obtained byintegrating (9) over the diffusion angle Its dependence on therelative velocity V is contained in1199011199011015840 and 119902 through119901 = 119872Vand the expressions (7) and (8) of 1199011015840 and 119902 in terms of 119901
We use a Burkert [23 24] flat cored dark-matter densityprofile known to reproduce well the kinematics of disksystems in massive spiral galaxies and supported by recentsimulations including supernova feedback and radiationpressure of massive stars [25] in response to the cuspy haloproblem
120588DM (119877) = 120588
0
119877
3
0
(119877 + 119877
0
) (119877
2
+ 119877
2
0
)
(11)
where 119877 is the distance from the galactic center The centraldark-matter density 120588
0
is left as a free parameter and 119877
0
isdetermined by requiring that the local dark-matter density at119877 = 119877
⊙
= 8 kpc is 120588⊙
= 03GeVcm3 The dark-matter massenclosed in a sphere of radius 119877 is therefore given by
119872DM (119877) = 120588
0
120587119877
3
0
log(119877
2
+ 119877
2
0
119877
2
0
)
+2 log(119877 + 119877
0
119877
0
) minus 2 arctan(
119877
119877
0
)
(12)
For the baryons in the bulge we use an exponential profile[26] of the form
120588
119887
(119877) =
119872bulge
8120587119877
3
119887
119890
minus119877119877
119887 (13)
where 119872bulge = 10
10
119872
⊙
[27] is the mass of the bulge Thisgives the baryonic mass distribution in the galactic bulge
119872
119887
(119877) = 119872bulge 1 minus 119890
minus119877119877
119887(1 +
119877
119877
119887
+
119877
2
119877
2
119887
) (14)
We assume a Maxwell-Boltzmann velocity distributionfor the dark-matter particles of the galactic halo with avelocity dispersion 119906(119877) and a cutoff at the galactic escapevelocity Vesc(119877)
119891 (119877 Vℎ
) =
1
119862 (119877)
119890
minusV2ℎ119906
2(119877)
(15)
where Vℎ
is the velocity of the dark-matter particles in theframe of the halo and 119862(119877) = 120587119906
2
(radic120587119906 erf(Vesc119906) minus
2Vesc119890minusV2esc119906
2
) is a normalization constant such thatint
Vesc(119877)0
119891(119877 Vℎ
)119889Vℎ
= 1The radial dependence of the velocity dispersion is
obtained via the virial theorem
119906 (119877) =
radic
119866119872tot (119877)
119877
(16)
where119872tot = 119872DM + 119872
119887
while Vesc =
radic
2119906Using the velocity distribution (15) going to center-of-
mass and relative velocities VCM and V and performing theintegrals over VCM we obtain for the mean pair-productioncross-section times relative velocity
⟨120590
119890119890
V⟩ =
1
119906
2
radic
2120587119906 erf (radic2Vesc119906) minus 4Vesc119890minus2V2esc119906
2
(radic120587119906 erf (Vesc119906) minus 2Vesc119890minusV2
esc1199062
)
2
times int
2Vesc
0
120590
119890119890
(V) V3119890minusV22119906
2
119889V
(17)
which is also a function of 119877 through 119906 and Vesc Putting (9)(11) (12) (14) (16) and (17) together allows us to compute thepair-production rate in the galactic bulge defined in (10) as afunction of 120588
0
and119872
4 Results
The rate of excessive 119890+119890minus pairs to be generated in the galacticbulge was estimated in [21] to be 119889119873119889119905|obs = 3 times 10
42 sminus1We computed 119889119873119889119905|
119890119890
for a large range of central dark-matter densities going from 03GeVcm3 to an ultimateupper limit of 10
4 GeVcm3 [28] For each value of 120588
0
wesearched for themass119872 ofOHe that reproduces the observedrate The results are shown in Figure 1
The observed rate can be reproduced from a value of120588
0
≃ 115GeVcm3 corresponding to an OHe mass of 119872 ≃
125TeV As 120588
0
gets larger two values of 119872 are possiblewith the lower one going from 125TeV to 130GeV and theupper one going from 125 to 130TeV as 120588
0
goes from 115 to10
4 GeVcm3
5 Conclusion
The existence of heavy stable particles is one of the mostpopular solutions for the dark- matter problem Usually theyare considered to be electrically neutral But dark mattercan potentially be made of stable heavy charged particlesbound in neutral atom-like states by Coulomb attractionAn analysis of the cosmological data and of the atomiccomposition of theUniverse forces the particle to have chargeminus2 Ominusminus is then trapped by primordial helium in neutral O-helium states and this avoids the problem of overproductionof anomalous isotopes which are severely constrained byobservations Here we have shown that the cosmologicalmodel of O-helium dark matter can explain the puzzle ofpositron line emission from the center of our Galaxy
4 Advances in High Energy Physics
1000100101
10000
1000
100001 01
1205880(GeV
cm
3)
M (TeV)
Figure 1 Values of the central dark-matter density 120588
0
(GeVcm3)and of the OHe mass 119872 (TeV) reproducing the excess of 119890+119890minus pairsproduction in the galactic bulge Below the red curve the predictedrate is too low
The proposed explanation is based on the assumptionthat OHe dominates the dark-matter sector Its collisionscan lead to 1198640 deexcitations of the 2s states excited by thecollisionsThe estimated luminosity in the electron-positron-annihilation line strongly depends not only on the mass ofOminusminus but also on the density profile and velocity distribution ofdarkmatter in the galactic bulge Note that the density profilewe considered is used only to obtain a reasonable estimatefor the uncertainties on the density in the bulge It indeedunderestimates the mass of the Galaxy but it shows thatthe uncertainties on the astrophysical parameters are largeenough to reproduce the observed excess for a rather widerange of masses of Ominusminus For a fixed density profile and a fixedvelocity distribution only two values of the Ominusminus mass leadto the necessary rate of positron production The lower valueof this mass which does not exceed 125TeV is within thereach of experimental searches for multicharged stable heavyparticles at the LHC
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors express their gratitude to A S Romaniouk fordiscussions
References
[1] M Yu Khlopov Cosmoparticle Physics World Scientific Singa-pore 1999
[2] M Yu Khlopov ldquoCosmoarcheology Direct and indirect astro-physical effects of hypothetical particles and fieldsrdquo inCosmion-94 M Yu Khlopov M E Prokhorov A A Starobinsky and J
Tran Thanh Van Eds pp 67ndash76 Editions Frontieres QuebecCanada 1996
[3] M Y Khlopov ldquoProceedings to the 9th workshop lsquowhat comesbeyond the standard modelsrsquordquo Bled Workshops in Physics vol 7no 2 p 51 2006
[4] M Y Khlopov ldquoProceedings to the 10th workshop lsquowhat comesbeyond the standard modelsrsquordquo Bled Workshops in Physics vol 8no 2 p 114 2007
[5] M Yu Khlopov Fundamentals of Cosmoparticle Physics CISP-Springer Cambridge UK 2012
[6] M Yu Khlopov ldquoFundamental particle structure in the cosmo-logical dark matterrdquo International Journal of Modern Physics Avol 28 no 29 Article ID 1330042 60 pages 2013
[7] M Yu Khlopov ldquoPhysics of dark matter in the light of darkatomsrdquoModern Physics Letters A vol 26 no 38 Article ID 28232011
[8] B D Wandelt R Dave G R Farrar P C McGuire D NSpergel and P J Steinhardt ldquoSelf-interacting dark matterrdquohttparxivorgabsastro-ph0006344
[9] P C McGuire and P J Steinhardt ldquoCracking open the windowfor strongly interacting massive particles as the halo darkmatterrdquo httparxivorgabsastro-ph0105567
[10] G Zaharijas and G R Farrar ldquoWindow in the dark matterexclusion limitsrdquo Physical Review D vol 72 no 8 Article ID083502 11 pages 2005
[11] C B Dover et al ldquoCosmological constraints on new stablehadronsrdquo Physical Review Letters vol 42 no 17 pp 1117ndash11201979
[12] S Wolfram ldquoAbundances of new stable particles produced inthe early universerdquo Physics Letters B vol 82 no 1 pp 65ndash681979
[13] G D Starkman A Gould R Esmailzadeh and S DimopoulosldquoOpening the window on strongly interacting dark matterrdquoPhysical Review D vol 41 no 12 pp 3594ndash3603 1990
[14] D Javorsek D Elmore E Fischbach et al ldquoNew experimentallimits on strongly interactingmassive particles at the TeV scalerdquoPhysical Review Letters vol 87 no 23 Article ID 231804 2001
[15] S Mitra ldquoUranusrsquos anomalously low excess heat constrainsstrongly interacting dark matterrdquo Physical Review D vol 70 no10 Article ID 103517 2004
[16] G D Mack J F Beacom and G Bertone ldquoTowards closingthe window on strongly interacting dark matter far-reachingconstraints from Earthrsquos heat flowrdquo Physical Review D vol 76no 4 Article ID 043523 2007
[17] D McCammon R Almy S Deiker et al ldquoA soundingrocket payload for X-ray astronomy employing high-resolutionmicrocalorimetersrdquoNuclear Instruments andMethods in PhysicsResearch Section A vol 370 no 1 pp 266ndash268 1996
[18] D McCammon R Almy E Apodaca et al ldquoA high spectralresolution observation of the soft X-ray diffuse backgroundwith thermal detectors rdquoThe Astrophysical Journal vol 576 no1 p 188 2002
[19] M Yu Khlopov ldquoComposite dark matter from stable chargedconstituentsrdquo httparxivorgabs08063581
[20] B J Teegarden K Watanabe P Jean et al ldquoINTEGRAL SPIlimits on electron-positron annihilation radiation from thegalactic planerdquoThe Astrophysical Journal vol 621 no 1 p 2962005
[21] D P Finkbeiner and N Weiner ldquoExciting dark matter and theINTEGRALSPI 511 keV signalrdquo Physical Review D vol 76 no8 Article ID 083519 2007
Advances in High Energy Physics 5
[22] LD Landau andEM LifshitzQuantumMechanics PergamonPress Elmsford NY USA 1965
[23] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquo IAU Symposia vol 171 p 175 1996
[24] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquoThe Astrophysical Journal vol 447 no 1 p L25 1995
[25] A V Maccio G Stinson C B Brook et al ldquoHALO Expansionin cosmological hydro simulations toward a baryonic solutionof the cuspcore problem in massive spiralsrdquo The AstrophysicalJournal Letters vol 744 no 1 p L9 2012
[26] O Y Gnedin A V Kravtsov A A Klypin and D NagaildquoResponse of dark matter halos to condensation of Baryonscosmological simulations and improved adiabatic contractionmodelrdquoThe Astrophysical Journal vol 616 no 1 p 16 2004
[27] H Mo F van den Bosch and S White Galaxy Formation andEvolution Cambridge University Press Cambridge UK 2010
[28] X Hernandez and W H Lee ldquoAn upper limit to the centraldensity of dark matter haloes from consistency with the pres-ence ofmassive central black holesrdquoMonthlyNotices of the RoyalAstronomical Society vol 404 no 1 p L10 2010
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
4 Advances in High Energy Physics
1000100101
10000
1000
100001 01
1205880(GeV
cm
3)
M (TeV)
Figure 1 Values of the central dark-matter density 120588
0
(GeVcm3)and of the OHe mass 119872 (TeV) reproducing the excess of 119890+119890minus pairsproduction in the galactic bulge Below the red curve the predictedrate is too low
The proposed explanation is based on the assumptionthat OHe dominates the dark-matter sector Its collisionscan lead to 1198640 deexcitations of the 2s states excited by thecollisionsThe estimated luminosity in the electron-positron-annihilation line strongly depends not only on the mass ofOminusminus but also on the density profile and velocity distribution ofdarkmatter in the galactic bulge Note that the density profilewe considered is used only to obtain a reasonable estimatefor the uncertainties on the density in the bulge It indeedunderestimates the mass of the Galaxy but it shows thatthe uncertainties on the astrophysical parameters are largeenough to reproduce the observed excess for a rather widerange of masses of Ominusminus For a fixed density profile and a fixedvelocity distribution only two values of the Ominusminus mass leadto the necessary rate of positron production The lower valueof this mass which does not exceed 125TeV is within thereach of experimental searches for multicharged stable heavyparticles at the LHC
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The authors express their gratitude to A S Romaniouk fordiscussions
References
[1] M Yu Khlopov Cosmoparticle Physics World Scientific Singa-pore 1999
[2] M Yu Khlopov ldquoCosmoarcheology Direct and indirect astro-physical effects of hypothetical particles and fieldsrdquo inCosmion-94 M Yu Khlopov M E Prokhorov A A Starobinsky and J
Tran Thanh Van Eds pp 67ndash76 Editions Frontieres QuebecCanada 1996
[3] M Y Khlopov ldquoProceedings to the 9th workshop lsquowhat comesbeyond the standard modelsrsquordquo Bled Workshops in Physics vol 7no 2 p 51 2006
[4] M Y Khlopov ldquoProceedings to the 10th workshop lsquowhat comesbeyond the standard modelsrsquordquo Bled Workshops in Physics vol 8no 2 p 114 2007
[5] M Yu Khlopov Fundamentals of Cosmoparticle Physics CISP-Springer Cambridge UK 2012
[6] M Yu Khlopov ldquoFundamental particle structure in the cosmo-logical dark matterrdquo International Journal of Modern Physics Avol 28 no 29 Article ID 1330042 60 pages 2013
[7] M Yu Khlopov ldquoPhysics of dark matter in the light of darkatomsrdquoModern Physics Letters A vol 26 no 38 Article ID 28232011
[8] B D Wandelt R Dave G R Farrar P C McGuire D NSpergel and P J Steinhardt ldquoSelf-interacting dark matterrdquohttparxivorgabsastro-ph0006344
[9] P C McGuire and P J Steinhardt ldquoCracking open the windowfor strongly interacting massive particles as the halo darkmatterrdquo httparxivorgabsastro-ph0105567
[10] G Zaharijas and G R Farrar ldquoWindow in the dark matterexclusion limitsrdquo Physical Review D vol 72 no 8 Article ID083502 11 pages 2005
[11] C B Dover et al ldquoCosmological constraints on new stablehadronsrdquo Physical Review Letters vol 42 no 17 pp 1117ndash11201979
[12] S Wolfram ldquoAbundances of new stable particles produced inthe early universerdquo Physics Letters B vol 82 no 1 pp 65ndash681979
[13] G D Starkman A Gould R Esmailzadeh and S DimopoulosldquoOpening the window on strongly interacting dark matterrdquoPhysical Review D vol 41 no 12 pp 3594ndash3603 1990
[14] D Javorsek D Elmore E Fischbach et al ldquoNew experimentallimits on strongly interactingmassive particles at the TeV scalerdquoPhysical Review Letters vol 87 no 23 Article ID 231804 2001
[15] S Mitra ldquoUranusrsquos anomalously low excess heat constrainsstrongly interacting dark matterrdquo Physical Review D vol 70 no10 Article ID 103517 2004
[16] G D Mack J F Beacom and G Bertone ldquoTowards closingthe window on strongly interacting dark matter far-reachingconstraints from Earthrsquos heat flowrdquo Physical Review D vol 76no 4 Article ID 043523 2007
[17] D McCammon R Almy S Deiker et al ldquoA soundingrocket payload for X-ray astronomy employing high-resolutionmicrocalorimetersrdquoNuclear Instruments andMethods in PhysicsResearch Section A vol 370 no 1 pp 266ndash268 1996
[18] D McCammon R Almy E Apodaca et al ldquoA high spectralresolution observation of the soft X-ray diffuse backgroundwith thermal detectors rdquoThe Astrophysical Journal vol 576 no1 p 188 2002
[19] M Yu Khlopov ldquoComposite dark matter from stable chargedconstituentsrdquo httparxivorgabs08063581
[20] B J Teegarden K Watanabe P Jean et al ldquoINTEGRAL SPIlimits on electron-positron annihilation radiation from thegalactic planerdquoThe Astrophysical Journal vol 621 no 1 p 2962005
[21] D P Finkbeiner and N Weiner ldquoExciting dark matter and theINTEGRALSPI 511 keV signalrdquo Physical Review D vol 76 no8 Article ID 083519 2007
Advances in High Energy Physics 5
[22] LD Landau andEM LifshitzQuantumMechanics PergamonPress Elmsford NY USA 1965
[23] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquo IAU Symposia vol 171 p 175 1996
[24] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquoThe Astrophysical Journal vol 447 no 1 p L25 1995
[25] A V Maccio G Stinson C B Brook et al ldquoHALO Expansionin cosmological hydro simulations toward a baryonic solutionof the cuspcore problem in massive spiralsrdquo The AstrophysicalJournal Letters vol 744 no 1 p L9 2012
[26] O Y Gnedin A V Kravtsov A A Klypin and D NagaildquoResponse of dark matter halos to condensation of Baryonscosmological simulations and improved adiabatic contractionmodelrdquoThe Astrophysical Journal vol 616 no 1 p 16 2004
[27] H Mo F van den Bosch and S White Galaxy Formation andEvolution Cambridge University Press Cambridge UK 2010
[28] X Hernandez and W H Lee ldquoAn upper limit to the centraldensity of dark matter haloes from consistency with the pres-ence ofmassive central black holesrdquoMonthlyNotices of the RoyalAstronomical Society vol 404 no 1 p L10 2010
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Advances in High Energy Physics 5
[22] LD Landau andEM LifshitzQuantumMechanics PergamonPress Elmsford NY USA 1965
[23] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquo IAU Symposia vol 171 p 175 1996
[24] A Burkert ldquoThe structure of dark matter haloes in dwarfgalaxiesrdquoThe Astrophysical Journal vol 447 no 1 p L25 1995
[25] A V Maccio G Stinson C B Brook et al ldquoHALO Expansionin cosmological hydro simulations toward a baryonic solutionof the cuspcore problem in massive spiralsrdquo The AstrophysicalJournal Letters vol 744 no 1 p L9 2012
[26] O Y Gnedin A V Kravtsov A A Klypin and D NagaildquoResponse of dark matter halos to condensation of Baryonscosmological simulations and improved adiabatic contractionmodelrdquoThe Astrophysical Journal vol 616 no 1 p 16 2004
[27] H Mo F van den Bosch and S White Galaxy Formation andEvolution Cambridge University Press Cambridge UK 2010
[28] X Hernandez and W H Lee ldquoAn upper limit to the centraldensity of dark matter haloes from consistency with the pres-ence ofmassive central black holesrdquoMonthlyNotices of the RoyalAstronomical Society vol 404 no 1 p L10 2010
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
High Energy PhysicsAdvances in
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
FluidsJournal of
Atomic and Molecular Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Condensed Matter Physics
OpticsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstronomyAdvances in
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Superconductivity
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Statistical MechanicsInternational Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
GravityJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
AstrophysicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Physics Research International
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Solid State PhysicsJournal of
Computational Methods in Physics
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Soft MatterJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
AerodynamicsJournal of
Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
PhotonicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Biophysics
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ThermodynamicsJournal of