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Implications for Minimal Supersymmetry from Grand Unification and the Neutralino Relic Abundance

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Implications for Minimal Supersymmetry from Grand Unification and the Neutralino Relic Abundance Physics Letters B 309 (1993) 329-336 PHYSICS LETTERS B North-Holland Implications for minimal supersymmetry from grand unification and the neutralino relic abundance R.G. Roberts Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OXl l OQX, UK and Leszek Roszkowski 1 Randall Physics Laboratory, University of Michigan, Ann Arbor, MI 48190, USA Received 25 January 1993; revised manuscript received 17 April 1993 Editor: H. Georgi We examine various predictions of the minimal supersymmetric standard model coupled to minimal supergravity. The previously considered predictions of the model are now extended to include the bottom quark mass and the neutralino relic density which in turn provide stringent bounds on the scale parameters. We find a remarkable consistency among several different constraints only in the region of low-energy supersymmetry, thus avoiding the use of the fine tuning criterion. We find all supersymmetric particle masses preferably within the reach of future supercolliders (LHC and SSC). The requirement that the neutralino be the dominant component of (dark) matter in the flat Universe provides a lower bound on the spectrum of supersymmetric particles beyond the reach of LEP, and most likely also the Tevatron and LEP 200. 1. Introduction symmetric (SUSY) states is completely determined. Even in the simplest SUSY GUT models, like SU (5), The minimal extension of the standard model [ 1 ] one meets some uncertainty related to the presence which corresponds to a softly-broken supersymmetric of the superheavy states around the GUT scale [4- SU ( 3 ) × SU (2) L × U ( I ) r at the GUT scale Mx where 6]. The corresponding threshold corrections depend the gauge couplings unify (as recently confirmed by on which unified group or superstring scenario the LEP [2 ] ) provides a very attractive and economic de- minimal SUSY model is embedded into. These model scription of physics beyond the standard model. It is dependent corrections would weaken the predictive possible to specify a small number of parameters at the power of the theory and, as in a previous paper [6], unification scale and the low energy effective theory is we ignore them. Similarly, the constraint coming from then determined simply by the radiative corrections. the limits on the proton decay [7] depends on the In particular the spontaneous breaking of electroweak choice of a specific GUT model and will not be dis- symmetry is radiately generated due to the presence of cussed here. supersymmetry soft-breaking terms through the mass In this letter, we consider the minimal supergrav- squared of one of the two Higgs doublets being driven ity model without adhering to any specific GUT. We negative at the scale Q ~_ O(rnz ) by the Yukawa top treat corrections from supersymmetric states above quark coupling [3]. In terms of the starting parame- rnz with particular care [6]. Our goal is to explore to ters at the GUT scale a detailed spectrum of the super- what extent the various physical quantities, like as, mt,mb, and the relic density, resulting from GUT- E-mail address: [email protected]. scale assumptions are consistent with each other and 0370-2693/93/$ 06.00 (~) 1993-Elsevier Science Publishers B.V. All rights reserved 329 Volume 309, number 3,4 PHYSICS LETTERS B 15 July 1993 with the notion of low-energy supersymmetry. We do will be discussed in section 3. not use the fine tuning criterion as a constraint. We The LSP for which we find sufficiently large val- extend the previous analysis [6] to properly include ues of the relic abundance to explain at least DM in predictions for the bottom quark mass. We also cal- the galactic halos (I2h 2 > 0.025) invariably comes culate the relic abundance of the lightest neutralino out to be the lightest neutralino, in fact of gaugino- Z which is usually the lightest supersymmetric parti- type (bino-like), consistent with the conclusions of cle (LSP) of the model. The neutralino LSP has long some previous analyses [ 11-13 ]. It was first argued in been identified [8] as one of the leading candidates ref. [ 11 ] that a gaugino-like LSP makes a unique can- for dark matter in the Universe [9,10]. It is neutral, didate for DM. Higgsino-like LSP is somewhat dis- weakly interacting, stable (if R-parity is valid) par- favoured as it corresponds to a high scale of super- ticle and its relic density is typically consistent with symmetry breaking, typically exceeding 1 TeV [ 11 ]. present cosmological expectations. We examine the More recently, it has been shown [13,14] that for predictions for X from the minimal supersymmetric the higgsino-like neutralinos additional effects (co- standard model (MSSM) and compute the annihila- annihilation with the next-to-lightest neutralino and tion cross sections which requires the detailed knowl- the lightest chargino, see section 3) have a dramatic ef- edge of the whole SUSY spectrum. Consequently we fect of reducing the LSP relic abundance below any in- can relate values of the neutralino relic abundance teresting level. Here we find that in addition higgsino- to values of the parameters mu2, m0,/z0 - the com- like LSPs are largely excluded by the current lower mon gaugino mass, the common scalar mass and the bound on the mass of the top quark. higgsino mass at Mx. The lower limit on the age of Overall, the LSP relic abundance constraint, com- the Universe provides an upper bound on the relic bined with the other physical constraints, narrows abundance of matter, and in particular of dark mat- down the allowed ranges of ml/2, m0,/10 considerably. ter which is believed to be a dominant mass compo- We find that the region ml/2 >> m0 is excluded by nent of the Universe. We can therefore use the dark the lower bound on the top mass, while in the re- matter abundance constraint to derive bounds on the gion m~/2 << m0 the LSP relic abundance is too large ranges of rn~/2, mo,#o and in turn get constraints on (12h02 > 1). Furthermore, the requirement that the the masses of all the SUSY particles. LSP provide enough missing mass in the fiat (£2 = 1 ) We combine the dark matter constraint with exper- Universe can be fulfilled only in a relatively narrow imental constraints on as (mz), mt and mb and exam- band of comparable values of ml/2 and m0 and for ine the consistency of trying to satisfy several of these 1 < #o/mo < a few. constraints simultaneously. We conclude that one can In the next section we briefly review the procedure indeed achieve such consistency quite naturally. More used in deriving the low-energy spectrum from a lim- interestingly, we find that this happens for the ranges ited number of basic parameters at the GUT scale. In of the fundamental parameters rn~/2, m0,/~0, and thus section 3 we demonstrate the importance of the neu- also masses of the supersymmetric particles, all prefer- tralino relic density constraint and compare it with ably within the few hundred GeV mass range. We other constraints on the parameter space. We con- thus find that requiring consistency between the cri- clude with final remarks in section 4. teria listed above leads us towards truly low-energy supersymmetry well within the reach of the SSC and the LHC. We also find that the favoured region does 2. Solutions of the MSSM not require any significant amount of fine tuning, ex- pected to avoid the mass hierarchy problem. We em- We follow the procedure of extracting solutions of phasize that our results are consistent with, but not the MSSM consistent with the unification of the gauge constrained by, the fine tuning criterion. couplings at the scale Mx developed in ref. [6]. This We also find that the resulting supersymmetric spec- method takes properly into account the threshold ef- tra lie typically above the reach of LEP, the Tevatron, fects on the running of the gauge couplings due to su- and LEP 200. The lower limit on supersymmetric par- persymmetric states above mz. Each solution is char- ticle masses comes from the dark matter constraint as acterised by the values of a small number of param- 330 Volume 309, number 3,4 PHYSICS LETTERS B 15 July 1993 eters at Q = Mx: m~/2, m0, #0, A0, and B0 which a~ = 0.125+0.002 (expt.)+0.009 (theor.) [19]. Re- determine the masses of the SUSY spectrum at low quiring conservatively as > 0.110 restricts the input energies. Of the Yukawa couplings, in the evolution mass parameters roughly below 5 TeV. of the SUSY masses we keep only ht. Its value hto at We also illustrate in fig. lb the amount of fine tun- Mx must be precisely adjusted to reproduce the cor- ing [6] related to the presented case. Demanding c ~< rect electroweak symmetry breaking, i.e. the value of O(10) would force one to consider only values of Mz, thus leading to a certain degree of"fine tuning", m~ n, mo up to a few hundred GeV [6]. Clearly larger as pointed out in ref. [ 6 ]. values of ml/2 and m0, and correspondingly lower val- This insistence on "naturalness" is essentially a the- ues of as ( < 0.114) are strongly disfavoured by the oretical constraint which rules out large values of m~/2, fine-tuning criterion but cannot be strictly ruled out. m0, #0 and leads to a narrow set of solutions. While To summarise so far, the solutions obtained for it is suggestive, not only is it not a uniquely defined the MSSM with the inclusion of electroweak symme- quantity [15 ] but also its validity depends on ones try allow a fairly restricted region of the parameters personal taste.
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