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The Dilaton-Dominated Supersymmetry Breaking Scenario in the Context Of View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server SUSX-TH-95/11 January 1995 The dilaton-dominate d sup ersymmetry breaking scenario in the context of the non-minimal sup ersymmetric mo del 1 G. V. KRANIOTIS School of Mathematical and Physical Sciences University of Sussex, Brighton BN1 9QH, United Kingdom ABSTRACT The phenomenological consequences of the dilaton-typ e soft sup ersymmetry breaking terms in the context of the next to minimal sup ersymmetric standard mo del are investigated. We always nd a very low top quark mass. As a consequence such string vacua are excluded by recent exp erimental results. The viability of the solution of the term through the intro duction of a gauge singlet eld is also brie y discussed. processed by the SLAC/DESY Libraries on 30 Jan 1995. 〉 PostScript HEP-PH-9501393 1 e.mail address:[email protected] The Standard Mo del remains unscathed in its confrontation with exp eriment. Furthermore, the compatibility of the mo del with the recent CDF observation [1], is very encouraging and enhances our b elief that we are on the right path towards the realization of the uni cation program. However, in order to talk ab out the uni cation of all the forces wehaveto see the standard mo del as the e ective limit of a more fundamental theory.Today the only theoretical framework which is a strong candidate for the uni cation of all the interactions, including gravity, is heterotic string theory. Sup ersymmetry which is necessary in taming the radiative corrections to the Higgs b oson mass, the only still unseen particle of the standard mo del, is naturally emb edded in string theory. However, sup ersymmetry has to b e softly-broken at an energy of order of the electroweak scale in order to solve the hierarchy problem mentioned ab ove. In the Minimal Sup ersymmetric extension of the Standard Mo del (MSSM) the terms resp onsible for the breaking are customarily parametrized in terms of four universal parameters, M , A, m , B , the universal gaugino mass, the trilinear scalar terms 0 1=2 asso ciated with the trilinear couplings in the sup erp otential, the scalar masses, and the B term asso ciated with the higgs-doublet mixing term in the sup erp otential. In string theory these parameters are in principle, predicted but a de nite answer is at present lacking due to the fact that the sup ersymmetry breaking mechanism in the theory is not well understo o d. Nevertheless progress has taken place at the theoretical level, and therefore we b elieve that it is an appropriate time to use all the present existing knowledge to study string inspired scenarios and confront them with current exp erimental data. In this way phenomenological criteria may help us select the correct string vacuum state among the plethora of equivalent string vacua that app ear at the level of string p ertubation theory, the ma jority of them leading to unacceptable phenomenology. The pro cess of sup ersymmetry breaking has to have a non-p ertubative origin since it is well known that SUSY is preserved order by order in p ertubation theory. However, very little is known ab out non-p ertubative e ects in string theory, partic- ularly in the four-dimensional case. This has led the authors of [3], to parametrize the e ect of SUSY-breaking by the VEVs of the F -terms of the dilaton (S ) and the 2 mo duli (T ) chiral sup er elds generically present in large classes of four-dimensional m sup ersymmetric heterotic strings . In a way, if sup ersymmetry breaking is triggered by these elds (i.e., hF i6=0 or hF i6= 0), this would b e a rather generic prediction S T of string theory. There are various p ossible scenarios for sup ersymmetry breaking which are obtained in this mo del indep endentway.To discriminate among these we consider a simpli ed expression for the scalar masses 2 2 2 m = m (1 + n cos ) (1) i i 3=2 2 In string p ertubation theory, b oth the mo duli and the dilaton are exact at directions of the e ective p otential, leaving their VEVs undetermined. In ref. [3] this p ertubative degeneracy is assumed to b e completely lifted by the non-p ertubative dynamics and VEVs for mo duli and dilaton to b e induced. 1 with tan =hF i/hF i [3]. Here m is the gravitino mass and the n are the mo dular S T i 3=2 weights of the resp ective matter eld. There are twoways in which one can obtain universal scalar masses, as strongly desired phenomenologically to avoid large avor- changing-neutral currents (FCNCs) [4]: (i) setting = =2, that is hF ihF i;or S T (ii) in a mo del where all n are the same, as o ccurs for Z Z orbifolds [3] and free i 2 2 fermionic constructions [5]. In the rst scenario sup ersymmetry breaking is triggered by the dilaton F - term and if the vanishing of the cosmological constant is imp osed as a constraint, this results in a universal scenario for the soft parameters involved [3]. In particular wehave: 1 p A = M ; m = M (2) 1=2 0 1=2 3 As one can see the four-dimensional soft-parameter space is then e ectively two-dimensional. In the strict-dilaton case the B term is no longer an indep endent parameter but is given by 2 p M =2m (3) B = 0 1=2 3 The ab ove universal scenario leads to a natural supression of FCNC. The dilaton dominated scenario has b een studied in the context of the minimal sup ersym- metric mo del [8] and in the context of the ipp ed SU(5) [9]. However, in b oth cases the necessary Higgs mixing term is provided by a bilinear mass term. The relevant term in the sup erp otential is of the form W = H :H : (4) 1 2 The asso ciated soft-breaking term in the scalar p otential will have the form BH :H (5) 1 2 It is well known that, in order to get appropriate SU (2) U(1) breaking, the L parameter has to b e of the same order of magnitude as the SUSY-breaking soft terms. This is in general unexp ected since the -term is a sup ersymmetric term whereas the other soft terms are originated after sup ersymmetry breaking. This is called \the problem", the reason why should b e of the order of the soft terms. Avery attractive solution to the problem [10 ] is to add an extra singlet su- p er eld N which couples with the two Higgs doublets sup er elds. The resulting sup erp otential will contain b esides the usual standard mo del terms the following term. 1 3 W = N H :H + kN (6) N 1 2 3 If, the gauge singlet acquires a vacuum exp ectation value hN i then the role of is played by hN i and the role of B is played by A . The resulting mo del is the so called nonminimal sup ersymmetric standard mo del. We note that such a sup erp otential which contains only trilinear couplings emerges naturally in sup erstrings. 2 It is also very interesting to p oint out that in general the soft terms computed in a general class of string mo dels are complex. The resulting phases, are quite constrained by limits on the electric dip ole moment of the neutron (EDMN), since they give large one-lo op contributions to this CP-violating quantity. In the case of the MSSM, there are three classes of phases asso ciated with the parameters A, M , 1=2 B and which are candidates for CP violation. These are given by = ar g (A = ); A ij k ij k = ar g (B=); B = ar g (M ) (7) C a where M are the masses of the gaugino elds asso ciated with the three gauge group a factors of the MSSM and are the trilinear Yukawa couplings of the chiral su- ij k p er elds of the theory and A the usual trilinear soft terms. However, it has b een ij k shown [6]that after a rede nition there are only two CP violating phases = ar g (AM ); = ar g (BM ) (8) A B 1=2 1=2 These phases are constrained as we mentioned by the electric dip ole moment of the neutron. One has in fact 3 ; 10 (9) A B for sparticle masses around few hundreds GeV. The EDMN receives imp ortant contri- butions from b oth and phases. In the dilaton-dominated scenario in the MSSM A B it has b een shown that the phases for M and A coincide and ! 0 [3]. However, a A is in general large and can b e suciently supressed only if further assumptions B ab out the origin of SUSY-breaking are made [3, 7 ]. In the case of the nonminimal mo del, the dilaton-dominated scenario leads to a natural supression of the EDMN. Indeed, if the problem is solved by the addition of a singlet N , the role of B is played by a trilinear coupling A whose phase is aligned with that of the gauginos and naturally = =0 . Thus the nonminimal mo del A A with sup ersymmetry breaking by the VEV of the dilaton eld is a well motivated scenario that deserves further study.
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