KUNS-1370 HE(TH)95/20 hep-ph/9511395 Duality of a Supersymmetric Standard Model without R parity

Recently one of the authors proposed a dual theory of a Supersymmetric Standard Model (SSM), in which it is naturally understood that at least one quark (the top quark) should be heavy, i.e., almost the same order as the weak scale, and the supersymmetric Higgs mass parameter can naturally be expected to be small. Unfortunately, the model cannot possess Yukawa couplings of lepton sector. In this paper, we examine a dual theory of a Supersymmetric Standard Model without R parity. In this scenario, we can introduce Yukawa couplings of lepton sector. In order to induce the enough large Yukawa couplings of leptons, we must introduce fairly large R parity breaking terms, which may be observed in the near future. e-mail: [email protected] e-mail: [email protected] Recently, it has become clear that certain aspects of four dimensional supersymmetric eld theories can be analyzed exactly [1, 2, 3, 4]. By using the innovation, it has been tried to build models in order to solve some phenomenological problems[4, 5, 6, 7]. One of the most interesting aspects is \duality" [1, 3]. By using \duality", we can infer the low energy e ective theory of a strong coupling gauge theory. One of the authors suggested that nature may use this \duality". He discussed a duality of a Supersymmetric Standard Model(SSM). Unfortunately, his model does not possess Yukawa couplings of lepton sector. One possibility to introduce them is to unify quarks and leptons by considering the Pati-Salam gauge group[8] In this paper, we discuss the model with R-parity brealing terms in order to obtain the Yukawa couplings of the lepton sector. First we recaptulate the previous model. Then we discuss the extention of the previous model and see how leptons acquire their mass. Then we give a summary and discussion. To get the point of the previous idea rst we review Seiberg's duality. Following his discussion [1], we examine SU(NC) Supersymmetric(SUSY) QCD with NF avors of chiral super elds, SU(NC) SU(NF )L SU(NF )R U(1)B U(1)R Q NC NF 1 1 (NF NC)=NF Qj NC 1 NF 1 (NF NC)=NF which has the global symmetry SU(NF )L SU(NF )R U(1)B U(1)R. In the case NF NC + 2, Seiberg suggested [1] that at the low energy scale the above theory is equivalent to the following SU( ~ NC) SUSY QCD theory ( ~ NC = NF NC) with NF avors of chiral super elds qi and q j and meson elds T i j , SU( ~ NC) SU(NF )L SU(NF )R U(1)B U(1)R qi ~ NC NF 1 NC=(NF NC) NC=NF q ~ NC 1 NF NC=(NF NC) NC=NF T i j 1 NF NF 0 2(NF NC)=NF and with a superpotential W = qiT i j q j : (1) Then the idea of SSM is the following [5]. We introduce ordinary matter super elds besides Higgs doublets: Q i L = (U i L;D i L) : (3; 2) 1 6 ; U c Ri : ( 3; 1) 2 3 ; D c iR : ( 3; 1) 1 3 L i = (N i L; E i L) : (1; 2) 1 2 ; E c Ri : (1; 1)1; i = 1; 2; 3; (2)