Search for WIMPS using Upward-Going Muons in MACRO

We present updated results on the search for a neutrino signal from the core of the Earth and of the Sun induced by Weakly Interacting Massive Particles (WIMPs). In this paper we concentrate on neutralinos as WIMP candidates. The 971 and 642 events used respectively for the search from the Sun and from the Earth are compatible with the background of atmospheric neutrinos. Consequently we calculate flux limits for various search cones around these sources. Limits as a function of the neutralino mass are given and compared to the supersymmetric (SUSY) models. 1 WIMPs from the Earth and the Sun: We describe an indirect method to look for non-baryonic dark matter WIMPs. The best WIMP candidate is the lightest SUSY particle (LSP) which in the Minimal Supersymmetric Standard Model (MSSM) is expected to be stable if R-parity is conserved and hence should be present in the Universe as a cosmological relic from the Big Bang. The linear combination of Higgsinos and gauginos, the neutralino χ, is currently considered the best candidate for cold dark matter since its couplings and mass range naturally give the relic density required to explain halo dark matter. Neutralinos are described by 3 parameters in the MSSM assuming the GUT relation between gaugino masses: one of the gaugino masses, the Higgsino mass parameter μ and the ratio of the Higgs doublet vacuum expectation values tan β. Moreover, if universality is assumed, the MSSM phenomenology is described by these parameters, the universal trilinear scalar coupling A, the degenerate scalar mass m0 and the mass of the pseudoscalar neutral Higgs mA. Experimental searches at LEP set a lower limit on mχ at ∼ 32 GeV and suggest an upper limit at ∼ 600 GeV if one requires that the neutralino cosmological abundance Ωχh ≤ 0.3 (Ellis, 1999). This upper limit is not yet achievable by the forthcoming LEP and Tevatron runs. Direct and indirect searches at underground detectors explore SUSY parameters and are complementary to the future LHC measurements. Direct searches look for a signature of a direct scattering of a WIMP from a nucleus in the detector. The DAMA experiment (∼ 100 Kg NaI(Tl)) sees an indication of an annual modulation of the rate which could be due to the Earth’s motion around the Sun and the change of the Earth’s velocity relative to the incident WIMP. The 19511 kg day data favor at 99.6% c.l. the presence of an annual modulation signal which, if interpreted in terms of WIMPs, implies a mass of mW = (59 +17 −14) GeV (Bernabei et al., 1999). This indication should be checked using different techniques, such as the indirect detection of trapped WIMPs inside the core of the Earth and of the Sun. The signature would be an excess of neutrino events resulting from WIMP-WIMP annihilations around the direction of the vertical of the apparatus and of the Sun beyond the known atmospheric ν background (Jungman, Kamionkowski & Griest, 1996). MACRO measures neutrinos indirectly as upward-going muons and has presented results of the WIMP search in Ambrosio et al., 1998a, to which we refer for details. We update this search including the data collected during Mar. 98-Feb. 99. 2 MACRO Updated Results on WIMPs: The MACRO detector at the Gran Sasso Laboratories, with overall dimensions of 12×76.6×9 m, detects upward-going muons through the time-of-flight measurement using 600 tons of liquid scintillator inside 12 m long boxes (time resolution ∼ 500 psec). A system of around 20, 000 m of streamer tubes reconstructs tracks with angular resolution ≤ 1. The lower part of the apparatus is filled with rock absorber setting a 1 GeV threshold for vertical μs. The upward-going muon measurement relative to the construction period of MACRO (Mar. 89 Apr. 94: 1.38 yr of running of 1/6 of the lower apparatus and 0.41 yr of the lower detector, inefficiencies included) is described in Ahlen et al., 1995. Since then, MACRO is in its full configuration (3.93 yr, inefficiencies included) and further results are in Ambrosio et al., 1998a and Ambrosio et al., 1998b. For the WIMP search for the Earth we use the sample of 642 throughgoing upward muons selected with the requirement that the track crosses at least 200 g/cm in the MACRO rock absorber, which reduces the background due to soft πs produced at large angles by downward-going μs to ∼ 1% (Ambrosio et al., 1998c). Releasing this cut, we use 971 upward-going μs for the search for the Sun because background rejection is not so critical for moving sources and the increase in exposure offsets the slight increase in background. For the Earth, the expected background due to interactions of atmospheric νs in the rock below MACRO is evaluated with a full Monte Carlo described in Ambrosio et al., 1998b using the Bartol ν flux (Agrawal et al., 1996), the GRV(94) DIS parton distributions (Glück, Reya & Vogt, 1995) and the muon energy loss as in Lohmann et al., 1985. We estimate a toEARTH SUN HalfData BackNorm. Flux Limit Data BackFlux Limit cone ground factor (Eμ > 1.5 GeV) ground (Eμ > 2 GeV) events (cm s) events (cm s) 30◦ 102 150.2 0.83 2.01 ×10 69 58.9 6.38 ×10 24◦ 70 96.2 0.80 1.56 ×10 41 37.3 4.06 ×10 18◦ 44 53.0 0.78 1.28 ×10 22 20.9 2.77 ×10 15◦ 32 36.8 0.77 1.03 ×10 14 14.5 2.07 ×10 9◦ 12 13.7 0.77 6.58 ×10 5 5.3 1.42 ×10 6◦ 4 6.2 0.77 5.07 ×10 2 2.3 1.07 ×10 3◦ 0 1.6 0.77 2.89 ×10 2 0.6 1.35 ×10 Table 1: Observed and atmospheric ν-induced background and 90% c.l. μ flux limits as a function of halfcone angles around the Earth core and the Sun. For the Earth, the expected background events are multiplied by the ratio of observed to expected events outside each cone. The Earth results are for the no oscillation scenario. The average exposure for the Earth is 3272 m yr and for the Sun 1116 m yr. tal uncertainty in the calculation of upward-going muon fluxes of 17%. For the Earth we have even considered a νμ → ντ oscillation scenario with parameters ∆m = 0.0025 eV, sin 2Θ = 1 as suggested by the flux measurement reported at this conference (Ronga et al., 1999). For the Earth search, the expected number of atmospheric induced events in the no oscillation scenario is (including the contribution due to ν-interactions inside the bottom part of the apparatus which are selected as throughgoing muons) 835 ± 142 and in the oscillation scenario 581 ± 99. For the Sun we have compared the 971 measured events with a different simulation with respect to that used for the Earth. This is obtained by mixing randomly the local coordinates of measured upward-going events and times gathered during the entire data-taking. This method takes into account the contribution of events produced by internal ν-interactions in the MACRO absorber. In Fig. 1(a) we show the angular distributions of the measured and expected events from atmospheric neutrinos for the Earth and the Sun. For the Sun this distribution depends strongly on time due to the motion of the Sun. In Fig. 1(b) we show the muon flux limits for 10 search cones from 3 to 10. In the case of the Earth, the expectation from atmospheric νs in the region of interest for the signal is larger than the data; we then evaluate flux limits multiplying the expected number of events by the ratio of the data to the expectation outside the cone where we look for the signal. This normalization is motivated by the high uncertainty in the normalization of upward-going muon flux calculations, whereas the shape error in the flux distribution is a few percent only. Moreover, since the number of detected events is less than the normalized expected events, we set conservative flux limits assuming that the number of measured events equals the number of expected ones (Caso et al., 1998). With this normalization, Earth limits considering ν-oscillations agree with the ones in the case of no oscillations within 7%. On the other hand, for the Sun, having used data to evaluate the expected numbers from atmospheric νs, oscillation effects are automatically included in the given limits. In Table 1 we show measured and expected events and flux limits for some of the cones calculated assuming a minimum μ energy of 1.5 GeV and 2 GeV for the Earth and the Sun, respectively. The minimum energy for the Sun is higher because tracks pointing toward it are more slanted than vertical tracks pointing to the core of the Earth and hence cross a larger amount of MACRO absorber. The average exposures (live-time times detector area in the direction of the expected signal from the source of WIMP annihilation) for cones between 3◦ and 30◦ is 3272 m yr for the Earth and 1116 m yr for the Sun. We estimate a maximum error of 5% on flux limits assuming these minimum energies for flux limit calculation with respect to a calculation which takes into account the dependence of the acceptance of the apparatus and of the neutrino fluxes from χ− χ̄ annihilation. 0 20 40 60 80 100 120 140 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 cos θ U p g o in g m u o n s 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2