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

## TL;DR

This paper calculates and compares the mass spectra of ${
m f N}=1$ SQCD-like theories with additional fields, revealing new phenomena and differences between direct and dual theories in various regimes.

## Contribution

It provides the first direct calculation of mass spectra in ${
m f N}=1$ SQCD-like theories with additional fields across different vacua and regimes, highlighting differences between direct and dual theories.

## Key findings

- Mass spectra are explicitly calculated in different vacua.
- Discrepancies are found between direct and dual theories' spectra.
- New light $\

## Abstract

Considered is the ${\cal N}=1$ 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 $N^2_F$ 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 $U(N_F)\rightarrow U(n_1)\times U(n_2)$. 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 $\mu^{\rm pole}(\Phi)\ll\Lambda_Q$. Also considered is the $X$-theory which is the ${\cal N}=2$ SQCD with $SU(N_c)$ colors and $0< N_F<2N_c$ flavors of light quarks, broken down to ${\cal N}=1$ 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.