New RG-invariants of Soft Supersymmetry Breaking Parameters

We study new renormalization-group invariant quantities of soft supersymmetry breaking parameters other than the ratio of gaugino mass to gauge coupling squared by using the spurion method. The obtained invariants are useful to probe supersymmetry breaking and μ-term generation mechanisms at high-energy scale. We also discuss the convergence behavior of fixed points of supersymmetry breaking parameters. E-mail address: [email protected] E-mail address: [email protected] Several types of supersymmetry (SUSY) breaking and mediation mechanisms have been studied. Each mechanism leads to a proper structure of SUSY breaking terms. The renormalization group (RG) effects are not negligible to obtain SUSY breaking terms at low energy. It is known that the ratioM/g, whereM is the gaugino mass and g is the gauge coupling, is RG-invariant at one-loop level. For example, if M/g for different gauge groups are measured as similar values in future experiments, that implies the gaugino masses are universal at the unification scale of gauge couplings. On the other hand, when gauge interactions are relevant to the mediation mechanism of SUSY breaking [1], M/g is given by the group-theoretical factors for each gauge group and generally shows disconnected structure with each other. Thus the RG-invariant quantity is important to probe SUSY breaking mechanisms. Recently, the renormalization group equations of soft SUSY breaking parameters have been studied within the spurion formalism [2]-[9]. Renormalization of softly broken SUSY theories can be described by introducing the spurion fields into rigid SUSY theories. That implies the beta-functions of soft SUSY breaking parameters can be written by those of the gauge couplings and anomalous dimensions of the rigid SUSY theories. This aspect has been used to derive several important features and led to interesting applications, e.g. calculations of higher-order beta functions of soft SUSY breaking parameters, finiteness conditions, RG-invariant trajectories and analytical solutions. As another example of applications, in ref. [9] the power-law behavior of running soft SUSY breaking parameters has been derived within the framework of extra dimensions. In this letter, we consider a SUSY gauge-Yukawa system and derive new RG-invariant quantities among soft SUSY breaking parameters through RG-invariants among gauge and Yukawa couplings by use of the spurion technique. The RG invariance holds for any arbitrary value of couplings, not only on a specific RG trajectory. Such invariants of soft SUSY breaking parameters are useful to probe the SUSY breaking mechanisms at high energy. Furthermore we discuss the convergence of infrared fixed points from the obtained RG invariants. Let us consider the N = 1 SUSY gauge theory with the gauge coupling g and the following superpotential, W = yΦ1Φ2Φ3. (1)