CERN{TH 95{206 DFTT 47/95 JHU{TIPAC 95020 LNGS{95/51 GEF{Th{7/95 August 1995 Neutralino dark matter in sup ersymmetric mo dels with non{universal scalar mass terms. a b,c d e,c b,c V. Berezinsky , A. Bottino , J. Ellis ,N.Fornengo , G. Mignola f,g and S. Scop el a INFN, Laboratori Nazionali del Gran Sasso, 67010 Assergi (AQ), Italy b Dipartimento di FisicaTeorica, UniversitadiTorino, Via P. Giuria 1, 10125 Torino, Italy c INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy d Theoretical Physics Division, CERN, CH{1211 Geneva 23, Switzerland e Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA. f Dipartimento di Fisica, Universita di Genova, Via Dodecaneso 33, 16146 Genova, Italy g INFN, Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy Abstract Neutralino dark matter is studied in the context of a sup ergravityscheme where the scalar mass terms are not constrained by universality conditions at the grand uni cation scale. We analyse in detail the consequences of the relaxation of this universality assumption on the sup ersymmetric parameter space, on the neutralino relic abundance and on the event rate for the direct detection of relic neutralinos. E{mail: b [email protected], b [email protected], [email protected], [email protected], [email protected], scop [email protected] 1 I. INTRODUCTION The phenomenology of neutralino dark matter has b een studied extensively in the Mini- mal Sup ersymmetric extension of the Standard Mo del (MSSM) [1]. This mo del incorp orates the same gauge group as the Standard Mo del and the sup ersymmetric extension of its parti- cle content. The Higgs sector is slightly mo di ed as compared to that of the Standard Mo del: the MSSM requires two Higgs doublets H and H in order to give mass b oth to down{ and 1 2 up{typ e quarks and to cancel anomalies. After Electro{Weak Symmetry Breaking (EWSB), the physical Higgs elds consist of twocharged particles and three neutral ones: two scalar elds (h and H ) and one pseudoscalar (A). The Higgs sector is sp eci ed at the tree level by two indep endent parameters: the mass of one of the physical Higgs elds and the ratio of the twovacuum exp ectation values, usually de ned as tan = v =v <H >=<H >. 2 1 2 1 The sup ersymmetric sector of the mo del intro duces some other free parameters: the mass parameters M , M and M for the sup ersymmetric partners of gauge elds (gauginos), 1 2 3 the Higgs{mixing parameter and, in general, all the masses of the scalar partners of the fermions (sfermions). In the MSSM it is generally assumed that the gaugino masses are equal at the grand uni cation scale M : M (M ) m and hence are related at lower scales by GU T i GU T 1=2 M : M : M = : : (1) 1 2 3 1 2 3 where the (i=1,2,3) are the coupling constants of the three Standard Mo del gauge groups. i The neutralinos are mass{eigenstate linear sup erp ositions of the two neutral gauginos ( ~ and ~ ~ ~ Z ) and the two neutral higgsinos (H and H ) 1 2 ~ ~ ~ = a ~ + a Z + a H + a H : (2) 1 2 3 1 4 2 The neutralino sector dep ends, at the tree{level, on the following (low{energy) parameters: 2 M =(5=3) tan M , M ' 0:8 m , and tan . Neutralino prop erties are naturally 1 W 2 2 1=2 discussed in the (m , ) plane, for a xed value of tan . As an example, in Fig.1 the lines 1=2 of constant mass for the lightest neutralino (m ) and constant gaugino fractional weight 2 2 (P a + a ) are plotted in the (m , ) plane for tan =8.We observe that the mass of 1=2 1 2 the lightest neutralino increases from the b ottom left to the top right, while the neutralino comp osition changes from higgsino dominance in the top{left region of the plane to gaugino dominance in the b ottom{right. The regions forbidden by accelerator data are also displayed in Fig.1. The low{energy MSSM scheme is a purely phenomenological approach, whose basic idea is to imp ose as few mo del{dep endent restrictions as p ossible. In this approach the lightest neutralino is a favourite candidate for cold dark matter. This scheme has b een employed ex- tensively in the analysis of the size and the relevance of various p ossible signals of neutralino dark matter: direct detection [2{4], signals due to neutralino annihilation in celestial b o dies, 2 namely the Earth and the Sun [5,6], and signals from neutralino annihilation in the galactic halo [7]. The MSSM provides a useful framework in which neutralino phenomenology may b e analysed without strong theoretical prejudices which could, aposteriori, turn out to b e incorrect. This scheme is also frequently employed in analyses of the discovery p otential of future accelerators [8]. At a more fundamental level, it is natural to implement this phenomenological scheme within the sup ergravity framework [9{ 11]. One attractive feature of the ensuing mo del is the connection b etween soft sup ersymmetry breaking and EWSB, whichwould then b e induced radiatively. The essential elements of the mo del are describ ed byaYang{Mills Lagrangian, the sup erp otential, which contains all the Yukawainteractions b etween the standard and sup ersymmetric elds, and by the soft{breaking Lagrangian, which mo dels the breaking of sup ersymmetry. Here we only recall the soft sup ersymmetry breaking terms X 2 2 L = m j j sof t i i i nh i o l l d d u u ~ ~ ~ ~ ~ ~ + A h L H R + A h Q H D + A h Q H U + h.c. BH H + h.c. a 1 b a 1 b a 2 b 1 2 ab ab ab ab ab ab X M ( + ) (3) + i i i i i i where the are the scalar elds, the are the gaugino elds, H and H are the two Higgs i i 1 2 ~ ~ ~ ~ ~ elds, Q and L are the doublet squark and slepton elds, resp ectively, and U , D and R denote the SU (2){singlet elds for the up{squarks, down{squarks and sleptons. In Eq.(3), m and M are the mass parameters of the scalar and gaugino elds, resp ectively, and A i i and B denote trilinear and bilinear sup ersymmetry breaking parameters, resp ectively. The Yukawainteractions are describ ed by the parameters h, which are related to the masses of t the standard fermions by the usual expressions, e.g., m = h v . t 2 The sup ergravity framework is usually implemented with a numb er of restrictive assump- tions ab out uni cation at M : GU T i) Uni cation of the gaugino masses: M (M ) m , i GU T 1=2 ii) Universality of the scalar masses with a common mass denoted by m : m (M ) 0 i GU T m , 0 l d u iii) Universality of the trilinear scalar couplings: A (M )=A (M )=A (M ) GU T GU T GU T A m . 0 0 These conditions have strong consequences for low{energy sup ersymmetry phenomenology, and in particular for the prop erties of the neutralino as dark matter particle. Typically, the lightest neutralino is constrained to regions of gaugino dominance, that entail a large relic 2 abundance (in wide regions of the parameter space h exceeds the cosmological upp er b ound) and a small direct detection rate for neutralino dark matter. Indirect signals from 3 the neutralino, such as high{energy neutrinos from the Earth and Sun, and the pro ducts of annihilatio n in the halo, are practically undetectable [11]. The ab ove assumptions, particularly ii) and iii), are not very solid, since universality may o ccur at a scale higher than M , i.e., the Planck scale or string scale [12], in which GU T case renormalization ab ove M mayweak universality in the m , e.g.,between scalars in GU T i 5 and 10 representations of SU (5) [13]. Moreover, in many string mo dels the m 's are not i universal even at the string scale. In a numb er of recentworks [14,15], deviations from some of the uni cation conditions have b een considered. In particular, in Ref. [14] phenomenological consequences for neu- tralinos of a relaxation of assumption ii) have b een analysed in the regime of large values of tan . It has b een shown that deviations from condition ii) mayentail a changeover in neutralino comp osition from a gaugino{like state to a higgsino{li ke state (or at least to a higgsino{ga ugi no mixed state), with imp ortant consequences for neutralino phenomenology. In this pap er, we rst explore, over the full range of tan , the various scenarios which may o ccur when condition ii) is relaxed, with an approach which is similar to the one adopted in the large{tan analysis of Ref. [14]. We then discuss in detail the ensuing consequences for neutralino dark matter, with particular emphasis for its direct detection. In the following, we rst discuss which constraints can b e applied to the parameters when sp eci c physical requirements are imp osed. In Sect.I I, we summarize the conditions implied by radiative EWSB and de ne the typ e of departure from universality examined in this pap er.