We consider the recent limits on dark matter - nucleon elastic scattering cross section from the analysis of CDMS II collaboration using the two signal events observed in CDMS experiment. With these limits we try to interpret the Super-Kamiokande (SK) bounds on the detection rates of up-going muons induced by the neutrinos that are produced in the sun from the decay of annihilation products of dark matter (WIMPs) captured in the solar core. Calculated rates of up-going muons for different annihilation channels at SK using CDMS bounds are found to be orders below the predicted upper limits of such up-going muon rates at SK. Thus there exists room for enhancement (boost) of the calculated rates using CDMS limits for interpreting SK bounds. Such a feature is expected to represent the PAMELA data with the current CDMS limits. We also show the dependence of such a possible enhancement factor (boost) on WIMP mass for different WIMP annihilation channels.
Weakly interacting massive particles (WIMP) as dark matter in our galaxy can be trapped inside massive heavenly bodies like sun due to later's gravity [1]. This gravitational trapping may happen when such dark matter in course of its passage through sun undergoes elastic scattering off the nuclei present in the solar core which causes its final velocity to fall below its velocity of escape from solar gravitational pull. These trapped dark matter may undergo the process of pair-annihilation producing primarily b, c and t quarks, τ leptons, gauge bosons etc. Mass and composition of dark matter determine the annihilation products which in turn produce neutrinos and antineutrinos either through decay or pair annihilation. Such neutrinos from the dark matter annihilation in solar environment have also been studied by previous authors (e.g. [2]). Detection of such solar neutrinos in terrestrial detectors not only provides indirect evidence of dark matter but along with the results from the direct detection experiments of dark matter such as CDMS [3], DAMA [4], XENON [5] etc. provides more insight into the nature of dark matter and its interactions. Analysis of recent observations of two dark matter signal events with the Cryogenic Dark Matter Search experiment (CDMS II) at the Soudan Underground Laboratory combined with all previous CDMS II data has been reported by CDMS collaboration [6]. It sets new upper limits on the WIMP-nucleon elastic scattering cross section (σ χ ) as a function of WIMP mass (m χ ) [6]. The indirect searches for WIMPs through their annihilation in sun, with 1679.6 live days of data from SK detector using neutrino-induced upward through-going muons provide WIMP-induced upward muon flux limits at SK as a function of WIMP mass [7]. In this work we use the 90% Confidence Level (C.L.) limits on σ χ (m χ ) from recent CDMS analysis [6] to calculate corresponding limits on detection rates of up-going muons at SK as a function of WIMP mass (m χ ) and compare them with the results in [7].
The differential flux of neutrinos of type i (i = ν µ , νµ ) at earth from WIMP annihilation products in the sun is given by [8]
where R is sun-earth distance and B F is the annihilation branch for channel F . (dN/dE) F,i is the differential spectrum of neutrinos of type i in the sun for the annihilation channel F . The total rate for WIMP annihilation in the sun, Γ A is given in [10]
where τ ≃ 4.5 Gyr is the age of sun. a = σv /4 √ 2V is a function of the average WIMP annihilation cross section and the effective volume V of WIMPs in the sun [10,11,1,12,13,14]. Under the astrophysical assumptions on density and velocity distribution as mentioned in [10,11] (local dark matter density, ρ χ = 0.3 GeV cm -3 , mean velocity of dark matter, v = 300 km sec -1 , a Maxwellian distribution of velocities etc.) the dark matter capture rate C in the sun is approximated as a function of the ratio of the WIMP-nucleus elastic scattering cross section to the dark matter mass as [10,1]
For such indirect detections of WIMPs at SK, neutrinos are detected through up-going muons produced by charged current interactions of neutrinos with the rock below the detector. With numerical values of this cross section, the muon range in the rock and expressing the energy distribution of neutrino flux in terms of its second moments, the total detection rate at SK detector of up-going muons induced by neutrinos from WIMP annihilation in the sun is given by [8] Γ
where, A ef f (≈ 1200m 2 ) is the muon effective area of the SK detector [15], a i ’s are the neutrino scattering coefficients. The range of neutrino induced muons in the rock are given as the coefficients b i . These coefficients are given by a ν = 6.8,
F,i ’s are the second moments of the spectrum of neutrino type i for the WIMP annihilation channel F in the sun. The N Z 2 F,i for different channels relevant for the present calculations are listed below [8,9].
(a) τ τ channel:
where E inj is the injection energy of the decaying WIMP annihilation product inside the sun, the branching ratio Γ τ →µν ν ≃ 0.18, τ ν (τ ν ) = 1.01 × 10 -3 (3.8 × 10 -4 ) GeV -1 are the stopping coefficients for ν(ν) and
where, the branching ratio Γ b→µνX = 0.103. The hadronization and the decay processes of the quarks from WIMP annihilation in the sun are characterized by the mean energy E d of the hadron,
is the initial hadron energy for quarks injected with energy E inj and Z f (= 0.73) is the quenching fraction for b-quarks to account for the loss of energy during hadronization, The injection energy E inj is the energy with which the WIMP annihilation products b b, τ τ , W and Z etc. are produced. In this work we present our results for two benchmark scenarios namely E inj = m χ and mχ 3 . Recently the CDMS collaboration announced two dark matter signal events with 90% C.L. [6] which set new limits on dark matter-nucleon scattering cross-section σ χ for different m χ ’s [6]. In this work we choose
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