MPI-PHE/96-02 DFTT 1/96 Light Neutralinos as Dark Matter in the Unconstrained Minimal Sup ersymmetric Standard Mo del ay b;c a A. Gabutti , M. Olechowski , S. Cooper , a;c a S. Pokorski , L. Sto dolsky a Max-Planck-Institut fur Physik, Fohringer Ring 6, D-80805 Munc hen, Germany b INFN Sezione di Torino and Dipartamento di Fisica Teorica, UniversitadiTorino, Via P. Giuria 1, 10125 Turin, Italy c Institute of Theoretical Physics, Warsaw University, ul. Hoza 69, 00-681 Warsaw, Poland Abstract The allowed parameter space for the lightest neutralino as the dark matter is explored using the Minimal Sup ersymmetric Standard Mo del as the low-energy ef- fective theory without further theoretical constraints such as GUT. Selecting values of the parameters which are in agreement with present exp erimental limits and applying the additional requirement that the lightest neutralino b e in a cosmolog- ically interesting range, we give limits on the neutralino mass and comp osition. A similar analysis is also p erformed implementing the grand uni cation constraints. 27 The elastic scattering cross section of the selected neutralinos on Al and on other materials for dark matter exp eriments is discussed. Submitted to Astroparticle Physics, 19 Feb. 96 y Corresp onding author, [email protected] 1 1 Intro duction Particle candidates for dark matter are classi ed as hot or cold dep ending on whether they were relativistic or not at the time they decoupled from thermal equilibrium. Any particle candidate for cold dark matter implies an extension of the Standard Mo del. At present the most interesting candidate is the lightest neutralino of the Minimal Sup er- symmetric Standard Mo del (MSSM). Anyweakly interacting massive particle (WIMP) considered as a dark matter candi- date is sub ject to at least two constraints: 1) its relic abundance must b e cosmologicall y 2 interesting, say0:025 < h < 1, in units of the critical density and 2) its existence must b e in accord with present exp erimental limits, provided mainly by the LEP exp eriments. In the standard approach, based in solving the kinetic Boltzman equation, the relic abundance of WIMPs is given roughly by [1]: 37 2 10 cm 2 h (1) h v i ann where h v i is the thermal average at freezeout of the annihilation cross section times the ann 2 relativevelo city in units of c. This is a very remarkable result: h 1 for typical weak cross sections. Supp ose the annihilati on of a WIMP of mass m pro ceeds via the exchange 2 2 2 2 of a particle of mass M (where M = xM ) coupled with the strength g (g = yg ), Z Z where wehaveintro duced the scaling factors x and y to express the mass M and the coupling g in terms of the Z b oson mass and its coupling to neutrinos. Using Eq. (1) and the expressions for h v i which follow from dimensional arguments wehave: ann 2 2 2 4 2 y m y g m Z 37 2 h v i = 0:4 10 cm for m M (2) ann 4 2 2 2 x M 16 x 1 GeV Z 4 2 g m 1 Z 2 37 2 2 = y 0:2 10 cm for m M h v iy ann 2 2 m 16 1TeV 2 and requiring h < 1 leads to a generalized Lee-Weinb erg b ound of: x O(1 GeV) <m<yO(1 TeV) : (3) y This is a useful qualitative constraint on the mass of a WIMP when used together with exp erimental limits on the parameters x and y (of course x and y are also constrained 2 by the requirement that h should not b e to o small). It is convenient to distinguish two cases: a neutrino-like WIMP whichinteracts only via Z -b oson exchange and a non neutrino-like WIMP which can annihilate via exchange of new particles. In the rst case, the presently available exp erimental constraint on the \invisible" width of the Z , = < 0:05 [2], gives y<0:05 (for of course x=1 and m<M =2). inv Z Therefore, from Eq. (3) we obtain m> O(20 GeV ). This is an order of magnitude estimate; in particular we neglect the di erence b etween Ma jorana and Dirac particles. The second case is realized in the Minimal Sup ersymmetric Standard Mo del with the lightest neutralino as the dark matter candidate. Here the analysis is much more involved b ecause of the complexity of the mo del and its large parameter space. A considerable 2 amountofwork has b een devoted to the neutralino as a dark matter candidate [3]. How- ever in most cases several additional theoretical assumptions are used (such as radiative electroweak symmetry breaking and universal b oundary conditions at the GUT scale for the parameters of the soft breaking of sup ersymmetry) whichmay b e to o restrictive and certainly go b eyond the MSSM as the low-energy e ective theory. In view of the dark matter search exp eriments, we explore in Sec. 2 the most general scenario for neutralinos as dark matter within the MSSM as the low-energy e ective theory without any further theoretical constraints such as the grand uni cation constraints (GUT). For completeness, the obtained neutralino masses and comp ositions are compared with the results derived using the GUT constraints. In Sec. 3 we consider the direct detection of neutralino dark matter via elastic scat- tering on nuclei. The dep endence of the axial coupling (spin dep endent) on the nuclear mo del and on the quark spin contents is discussed for selected neutralino comp ositions. In Sec. 4 we calculate the neutralino cross section on some of the nuclei presently used or planned to b e used for dark matter detection. We analyze the low mass region and give the dep endence of the cross section on the neutralino mass and comp osition. Prosp ects for the detection of light neutralinos are discussed in Sec. 5. Our analysis di ers from previous work on neutralino detection [3] b ecause our more general assumptions allow the p ossibili tyofhaving low mass neutralinos as dark matter candidates and weevaluate their cross section on nuclei. In the presentwork neutralinos 2 with relic abundance b elow the cosmological b ound h < 0:025 are not considered as dark matter candidates. This is di erent from the approach used in other work [4] where neutralinos with relic abundance b elow the cosmological b ound are still considered as dark matter candidates and their contribution to the dark matter halo is evaluated by rescaling the lo cal dark matter density. 2 Neutralino in the MSSM as dark matter candidate In the present section we address the question of the most general limits on the lightest neutralino mass and its comp osition which follow only from the two constraints 0:025 < 2 h < 1 and consistency with the present data from accelerator exp eriments, without any further theoretical assumptions. As we shall see, with this approach it is p ossible to obtain quite strong qualitative conclusions. The stable neutralino is the lowest mass sup erp osition of neutral gauginos and higgsi- nos: 0 0 0 ~ ~ ~ ~ = Z B + Z W + Z H + Z H (4) 1 11 12 13 14 1 2 or, in the photino, zino, higgsino basis: 0 0 ~ ~ ~ (5) + Z H = a ~ + bZ + Z H 14 1 13 2 1 0 0 ~ ~ ~ ~ ~ with ~ = cos B + sin W , Z = sin B + cos W and the Weinb erg angle. W W W W W The neutralino comp osition is de ned by the neutralino mass matrix, which in the basis 3 of Eq. (4) is: 1 0 M 0 M cos sin M sin sin 1 Z W Z W C B 0 M M cos cos M sin cos C B 2 Z W Z W C (6) B A @ M cos sin M cos cos 0 Z W Z W M sin sin M sin cos 0 Z W Z W 2.1 Scan of the parameter space The neutralino mass matrix dep ends on several, in general free, parameters of the mo del: the gaugino masses M and M , the higgsino mass parameter , and tan =v =v , 1 2 2 1 where v and v are the vacuum exp ectation values of the two Higgses present in the 1 2 mo del. All of these are indep endent parameters of the low-energy e ective lagrangian. In the present study of the unconstrained low-energy e ective theory, the values of these parameters are chosen randomly in the ranges listed in Tab. 1. The scanning pro cedure is such that log (M ), log (), log (tan ) and the ratio M =M are chosen with at probability. 2 1 2 We restrict our analysis to neutralinos lighter than 100 GeV. Calculations with the grand uni cation constraints are also p erformed using the same 5 2 ranges but with M = M tan ' 0.5M and with M '0.3m .We use for the gluino 1 2 W 2 2 g~ 3 mass m the exp erimental lower b ounds from CDF [5] and D0 [6] resulting in M 50 g~ 2 GeV. It should b e noted that the present exp erimental limits on the gluino mass are derived only for a sp eci c choice of the MSSM parameters. We scan the parameter space incorp orating the following existing exp erimental limits from accelerator exp eriments.