Mass spectra in $\mathcal{N}=1SQCD$ with additional colorless but flavored fields

Abstract

Considered is the $\mathcal{N}=1$ SQCD-like theory with $SU(N_c)$ colors and $0<N_F<2N_c$ flavors of equal mass $0<m_Q\ll {\Lambda }_Q$ quarks. Besides, it includes $N_F^2$ additional colorless but flavored fields ${\Phi }_i^j$, with the large mass parameter ${\mu }_{\Phi }\gg {\Lambda }_Q$. The mass spectra of this $\Phi$-theory are first directly calculated at $0<N_F<N_c$ where the quarks are weakly coupled, in all different vacua with the unbroken or spontaneously broken flavor symmetry $U(N_F)\to U(n_1)\times U(n_2)$. Further, the mass spectra of this direct $\Phi$-theory and its Seiberg's dual variant, the $d\Phi$-theory, are calculated at $3N_c/2<N_F<2N_c$ and various values of ${\mu }_{\Phi }/{\Lambda }_Q\gg 1$ (in strong coupling regimes), using the dynamical scenario introduced by the author in his previous article \cite{ch3}. This scenario assumes that quarks can be in two different standard phases only: either this is the HQ (heavy quark) phase where they are confined, or they are higgsed. Within the used dynamical scenario, it is shown that mass spectra of the direct $\Phi$ and dual $d\Phi$ - theories are parametrically different. Besides it is shown in the direct $\Phi$-theory that a qualitatively new phenomenon takes place: under appropriate conditions, the seemingly heavy and dynamically irrelevant fields $\Phi$ 'return back' and there appear two additional generations of light $\Phi$-particles with small masses ${\mu }^{\mathrm{pole}}(\Phi )\ll {\Lambda }_Q$. Also considered is the $X$-theory which is the $\mathcal{N}=2$ SQCD with $SU(N_c)$ colors and $0<N_F<2N_c$ flavors of light quarks, broken down to $\mathcal{N}=1$ by the large mass parameter of the adjoint scalar superfield $X,{\mu }_X\gg {\Lambda }_2$. The tight interrelations between these $X$ and $\Phi$ theories are described, in particular, the conditions under which they are equivalent.

Comments: 54 pages, published version. arXiv admin note: substantial text overlap with arXiv:1205.0410, arXiv:1211.1487