Infrared Behaviour of Softly Broken Sqcd and Its Dual

Applying the recently obtained results on the renormalization of soft supersymmetry-breaking parameters, we investigate the infrared behaviour of the softly broken supersymmetric QCD as well as its dual theory in the conformal window. Under general assumptions on βfunctions, it is shown that the soft supersymmetry-breaking parameters asymptotically vanish in the infrared limit so that superconformal symmetry in softly broken supersymmetric QCD and in its dual theory revives at the infrared fixed point, provided the soft scalar masses satisfy certain renormalization group invariant relations. If these relations are not satisfied, there exist marginal operators in both theories that lead to the breaking of supersymmetry and also colour symmetry. Partially supported by the Academy of Finland (no. 37599). On leave from: Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192, Japan ∗∗ Partially supported by the E.C. projects, FMBI-CT96-1212 and ERBFMRXCT960090, the Greek projects, PENED95/1170; 1981. Hunting renormalization group (RG) invariant relations among independent parameters in a given phenomenological model, especially supersymmetric one, has proved in recent years to be successful in predicting, free otherwise, parameters of the model [1]–[4]. These are ranging from the top quark mass, the spectrum of the superpartners to the lightest Higgs mass in N = 1 supersymmetric finite and non-finite Gauge-Yukawa unified models [1]–[4]. The basic idea is based on the principle of coupling reduction proposed in ref. [5]. Most of the practical applications of the principle, however, have been restricted to lower orders in perturbation theory, because the β-functions are mostly known only in lower orders. Parallel to this development, interesting progresses has been made on the renormalization properties of the soft supersymmetry-breaking (SSB) parameters [6]–[9]. In ref. [6] the spurion formalism in a softly-broken supersymmetric gauge theory has been used to derive a certain set of rules to relate the SSB parameters with those of the corresponding supersymmetric theory. Later it has been shown [8, 9] that these rules can be realized by differential operators acting on the anomalous dimensions γi and the gauge coupling β-function βg. As a result, the β-functions of the SSB parameters can be obtained from γi and βg. A consequence is that it has become possible to obtain a closed form for RG invariant relations among the SSB parameters [10]–[13]. Another consequence is that the asymptotic behaviour of the SSB parameters in the ultraviolet (UV) as well as in infrared (IR) limit can be studied by using γi and βg only. If γi and βg are exact, the results on the SSB parameters derived from them are exact, too. The purpose of the present paper is to examine on the light of the above mentioned new development the asymptotic behaviour of softly broken supersymmetric QCD (SQCD) and its dual theory in the IR limit, especially in the regime for which according to Seiberg’s conjecture [14] there would exist a non-trivial IR fixed point if supersymmetry was exact. The existence of a stable IR fixed point in the space of the dimensionless couplings (gauge and Yukawa couplings) of a supersymmetric Yang-Mills theory implies that the β-functions and their derivatives of these couplings should have certain properties in the IR limit. We will use these properties to derive the asymptotic behaviour of the SSB parameters, and will be assuming that the above mentioned perturbative technique to obtain their RG functions is applicable to the problem we are concerned with. Moreover, we assume that the kinetic