Photon spectra from quark generation by WIMPs
J. A. R. Cembranos, A. de la Cruz-Dombriz, A. Dobado, R. Lineros, A. L. Maroto
PPhoton spectra from quark generation by WIMPs
J. A. R. Cembranos, A. Cruz-Dombriz , A. Dobado, R. Lineros and A. L. Maroto Departamento de Física Teórica I, Universidad Complutense de Madrid, E-28040 Madrid, Spain. also at Department of Mathematics and Applied Mathematics, University of Cape Town, 7700 South Africa. IFIC, CSIC-Universitat de Valencia, Ed. Instituts, Apt. 22085, 46071 Valencia, Spain.
Abstract.
If the present dark matter (DM) in the Universe annihilates into Standard Model (SM) particles, it must contributeto the gamma ray fluxes that are detected on the Earth. The magnitude of such contribution depends on the particular DMcandidate, but certain features of these spectra may be analyzed in a model-independent fashion. In this work we provide thefitting formula valid for the simulated photon spectra from WIMP annihilation into light quark-anti quark ( q ¯ q ) channels in awide range of WIMP masses. We illustrate our results for the c ¯ c channel. Keywords:
Dark matter, indirect searches, WIMPs, photon spectra and quark pairs annihilation.
PACS:
I. INTRODUCTION
According to present observations of large scale struc-tures, CMB anisotropies and light nuclei abundances,DM cannot be accommodated within the SM of elemen-tary particles. Indeed, DM presence is a required com-ponent on cosmological scales, but also to provide a sat-isfactory description of rotational speeds of galaxies, or-bital velocities of galaxies in clusters, gravitational lens-ing of background objects by galaxy clusters and thetemperature distribution of hot gas in galaxies and clus-ters of galaxies. The experimental determination of theDM nature will require the interplay of collider exper-iments and astrophysical observations. These searchesuse to be classified in direct or indirect searches (see [1]and references in Introduction in [2]) . Concerning directones, the elastic scattering of DM particles from nucleishould lead directly to observable nuclear recoil signa-tures although the weak interactions between DM andthe standard matter makes DM direct detection extremelydifficult.On the other hand, DM might be detected indirectly,by observing their annihilation products into standardmodel particles. Thus, even if WIMPs (Weakly Inter-acting Massive Particles) are stable, two of them mayannihilate into ordinary matter such as quarks, leptonsand gauge bosons. Their annihilation in different places(galactic halo, Sun, etc.) produce cosmic rays to be dis-criminated through distinctive signatures from the back-ground. After WIMPs annihilation a cascade process oc-curs. In the end the stable particles: neutrinos, gammarays, antimatter... may be observed through different de-vices. Neutrinos and gamma rays have the advantage ofmaintaining their original direction due to their null elec-tric charges. This communication precisely focuses on photon pro-duction coming from q ¯ q channels (except t ¯ t channel).Photon fluxes in specific DM models are usually ob-tained by software packages such as DarkSUSY and mi-crOMEGAs based on PYTHIA Monte Carlo event gen-erator [3] after having fixed a WIMP mass for the partic-ular SUSY model under consideration. In this sense, theaim of this investigation is to provide fitting functions forthe photon spectra corresponding to each individual an-nihilation q ¯ q channel and, in addition, determine the de-pendence of such spectra on the WIMP mass in a modelindependent way. This would allow to apply the results toalternative DM candidates for which software packageshave not been developed. On the other hand, the infor-mation about channel contribution and mass dependencecan be very useful in order to identify gamma-ray signalsfor specific WIMP candidates and may also provide rel-evant information about the photon energy distributionwhen q ¯ q pairs annihilate.Let us remind that the γ -ray flux from the annihilationof two WIMPs of mass M into two SM particles comingfrom all possible annihilation channels (labelled by thesubindex i ) is given by:d Φ DM γ d E γ = π M ∑ i (cid:104) σ i v (cid:105) d N i γ d E γ × ∆Ω (cid:90) ∆Ω d Ω (cid:90) l . o . s . ρ [ r ( s )] d s , (1)where (cid:104) σ i v (cid:105) holds for the thermal averaged annihilationcross-section of two WIMPs into two ( i th channel) SMparticles and ρ is the DM density. The integral is per-formed along the line of sight (l.o.s.) to the target andaveraged over the detector solid angle ∆Ω . a r X i v : . [ h e p - ph ] N ov ABLE 1. b , n , c , d and p parameters correspond-ing to expression (2) in the c ¯ c channel. Mass indepen-dent parameters in (2) for this channel are a = .
58 ; b = .
90 ; n = .
686 ; c = . q = . · − . M (GeV) b n c d p
50 5.93 2.35 0.239 0.428 210100 5.48 2.08 0.283 0.374 379200 4.98 1.86 0.330 0.330 673500 4.50 1.65 0.378 0.288 12301000 4.00 1.50 0.406 0.264 21102000 3.70 1.35 0.432 0.245 40505000 3.27 1.17 0.470 0.221 80808000 3.08 1.11 0.494 0.208 12000
III. PROCEDURE
We have used the particle physics PYTHIA software [3]to obtain our results. The WIMP annihilation is usuallysplited into two separated processes: The first describesthe annihilation of WIMPs and its SM output. The sec-ond one considers the evolution of the obtained SM un-stable products. Due to the expected velocity dispersionof DM, we expect most of the annihilations to happenquasi-statically. This fact allows to state that by consid-ering different center of mass ( CM ) energies for the ob-tained SM particles pairs from WIMP annihilation pro-cess, we are indeed studying different WIMP masses, i.e. E CM (cid:39) M . The procedure to obtain the photon spectrais thus straightforward: For a given pair of SM particleswhich are produced in the WIMP annihilation, we countthe number of photons in bins for the variable x ≡ E γ / M .Once the PYTHIA simulations have been performed,the required parametrization to fit the data for the q ¯ q channels (except t ¯ t ) may be written as:d N γ d x = a x . exp (cid:16) − b x n − b x n − c x d + c x d (cid:17) + q ln [ p ( − x )] x − x + x (2)The parameters in expression (2) were considered to beWIMP mass dependent. After a fitting process they weredetermined for different WIMP masses, in a range vary-ing from 50 to 7000 (or 8000) GeV. Mass dependencesfor the parameters in (2) were fitted by using power laws. III. c ¯ c CHANNEL
In order to illustrate the explained procedure, we studythe c ¯ c channel. For this channel there are five massdependent parameters in expression (2): b , n , c , d and p presented in Table I. The mass independent parametersare a , b , n , c ( d is thus irrelevant) and q . In Table TABLE 2.
Fitting power laws in c ¯ c channel. Parameter Interval (GeV) Power law(s) b ≤ M ≤ . M − . n ≤ M ≤ . M − . c ≤ M ≤ . M . d ≤ M ≤ . M − . + 0 . M − . p < M ≤ . M . II we present the fitting power laws for mass dependentparameters. Figure 1 presents spectra for four differentWIMP masses whereas Figure 2 shows fitting powerlaws for two mass dependent parameters. The results forthe other q ¯ q channels [2] are completely analogous eventhough for each channel, the parameters which are massdependent may be different to the ones for the c ¯ c channel. IV. CONCLUSIONS
In this work, we have studied the photon spectra comingfrom WIMP pair annihilation into q ¯ q pairs for all thechannels (except t ¯ t ). The covered WIMP mass range wasfrom 50 GeV to 8000 GeV. Simulated spectra coveredthe whole accessible energy interval: from extremelylow energetic photons till photons with one half of theavailable total center of mass energy.Once the spectra were simulated, an analytical expres-sion (2) was proposed to fit the data. This expressiondepends on both WIMP mass dependent and indepen-dent parameters. Our results can both provide a betterunderstanding of the DM annihilation channels into pho-tons and save an important amount of unnecessary MonteCarlo simulations. This fact is particularly important forhigh energy photons, whose production rate is very sup-pressed.Calculations for all q ¯ q channels are availableat the website http://teorica.fis.ucm.es/ ∼ PaginaWeb/downloads.html . This workwas partially supported by MULTIDARK CSD2009-00064.
REFERENCES
1. K. Sigurdson and M. Kamionkowski, PRL , 171302(2004); J. A. R. Cembranos et al. , PRL , 241301 (2003);J. A. R. Cembranos and L. E. Strigari, PRD , 123519(2008); J. A. R. Cembranos, PRL , 141301 (2009).2. J. A. R. Cembranos, A. de la Cruz-Dombriz, A. Dobado,R. A. Lineros, A. L. Maroto, arXiv: hep-ph/1009.4936.3. T. Sjostrand, S. Mrenna and P. Skands, JHEP05 (2006) 026(LUTP 06-13, FERMILAB-PUB-06-052-CD-T). x . d N γ / d x E γ /M WIMP cc channel WIMP annihilation, M
WIMP = 100 GeV
Total fitMontecarlo simulation 0.01 0.1 1 0.001 0.01 x . d N γ / d x E γ /M WIMP x . d N γ / d x E γ /M WIMP cc channel WIMP annihilation, M
WIMP = 200 GeV
Total fitMontecarlo simulation 0.1 1 0.001 0.01 x . d N γ / d x E γ /M WIMP x . d N γ / d x E γ /M WIMP cc channel WIMP annihilation, M
WIMP = 1000 GeV
Total fitMontecarlo simulation 0.1 1 0.001 0.01 x . d N γ / d x E γ /M WIMP x . d N γ / d x E γ /M WIMP cc channel WIMP annihilation, M
WIMP = 5000 GeV
Total fitMontecarlo simulation 0.1 1 0.001 0.01 x . d N γ / d x E γ /M WIMP
FIGURE 1.
Photon spectra for four different WIMP masses (100, 200, 1000 and 5000 GeV) in the c ¯ c annihilation channel. Reddotted points are PYTHIA simulations and solid lines correspond to the proposed fitting functions. P a r a m e t e r d f o r qua r k c ( d i m en s i on l e ss ) WIMP mass (GeV) c channel WIMP annihilation, parameter c Smooth spline curve and power lawc values for quark c P a r a m e t e r b f o r qua r k c ( d i m en s i on l e ss ) WIMP mass (GeV) c channel WIMP annihilation, parameter b linear fit b values for quark c FIGURE 2.
Mass dependence of c and b parameters for cc
Mass dependence of c and b parameters for cc ¯ cc