Mass spectra in ${\cal N}=1$ SQCD with additional colorless fields. Strong coupling regimes

Abstract

We consider the ${\cal N}=1$ $SU(N_c)$ SQCD-like (direct) theory (and its Seiberg's dual with $SU(N_F-N_c)$ dual colors), and with $N_F$ flavors of light quarks ${\overline Q}_j, Q^i$ with the mass term in the superpotential $m_Q{\rm Tr}({\overline Q} Q),\,\, m_Q\ll\Lambda_Q$. Besides, there are $N_F^2$ additional colorless but flavored fields $\Phi^j_i$ with the large mass parameter $\mu_{\Phi}\gg\Lambda_Q$. But now considered is the region $N_c+1<N_F<3N_c/2$ where the UV free direct $SU(N_c)$ theory is strongly coupled at scales $\mu<\Lambda_Q$. The mass spectra of this direct theory in various vacua and at different values of $\mu_{\Phi}\gg\Lambda_Q$ are calculated within the dynamical scenario introduced by the author in [10]. This scenario assumes that quarks in such ${\cal N}=1$ SQCD-like theories can be in two standard phases only. These are either the HQ (heavy quark) phase where they are confined or the Higgs phase. It is shown that due to the strong power-like RG evolution, the seemingly heavy and dynamically irrelevant at scales $\mu<\Lambda_Q$ fields $\Phi^j_i$ can become light and relevant at lower energies, and there appear then two additional generation of light $\Phi$-particles with masses $\mu_{2,3}^{\rm pole}(\Phi)\ll\Lambda_Q$. The calculated mass spectra of this strongly coupled at $\mu<\Lambda_Q\, SU(N_c)$ theory are compared to those of its weakly coupled at $\mu<\Lambda_Q$ Seiberg's dual $SU(N_F-N_c)$ variant and appeared to be parametrically different. It is worth to recall that the dynamical scenario from [10] used in this article satisfies all those tests which were used as checks of the Seiberg hypothesis about the equivalence of the direct and dual theories. This parametrical difference shows, in particular, that all these tests, although necessary, may well be insufficient.