Mass spectra in softly broken ${\cal N}=2$ SQCD

TL;DR

This paper analyzes the vacuum structure, low energy spectra, and condensates in softly broken ${ m extbf{N}=2}$ SQCD with gauge group $SU(N_c)$ or $U(N_c)$, highlighting differences from previous studies and providing detailed calculations of power corrections.

Contribution

It provides a comprehensive analysis of vacua with unbroken discrete symmetry and calculates power corrections, clarifying discrepancies with prior research.

Findings

Identifies various vacua with unbroken $Z_{2N_c-N_F}$ symmetry.

Calculates power corrections confirming the consistency of the low energy approach.

Highlights key differences from recent related works.

Abstract

Considered are ${\cal N}=2\, SU(N_c)$ or $U(N_c)$ SQCD with $N_F<2N_c-1$ quark flavors with the quark mass term $m{\rm Tr}\,({\bar Q} Q)$ in the superpotential. ${\cal N}=2$ supersymmetry is softly broken down to ${\cal N}=1$ by the mass term $\mu_{\rm x}{\rm Tr}\,(X^2)$ of colored adjoint scalar partners of gluons, $\mu_{\rm x}\ll\Lambda_2$ ($\Lambda_2$ is the scale factor of the $SU(N_c)$ gauge coupling). There is a large number of different types of vacua in these theories with both unbroken and spontaneously broken flavor symmetry, $U(N_F)\rightarrow U({\rm n}_1)\times U({\rm n}_2)$. We consider in this paper the large subset of these vacua with the unbroken nontrivial $Z_{2N_c-N_F\geq 2}$ discrete symmetry, at different hierarchies between the Lagrangian parameters $m\gtrless\Lambda_2,\,\, \mu_{\rm x}\gtrless m$. The forms of low energy Lagrangians, quantum numbers of light particles and mass spectra are described in the main text for all these vacua. The calculations of power corrections to the leading terms of the low energy quark and dyon condensates are presented in two important Appendices. These calculations confirm additionally in a non-trivial way a self-consistency of the whole approach. Our results differ essentially from corresponding results in recent related papers arXiv:1304.0822, arXiv:1403.6086, and arXiv:1704.06201 of M.Shifman and A.Yung (and in a number of their numerous previous papers on this subject), and we explain in the text the reasons for these differences (see also the extended critique of a number of results of these authors in section 8 of arXiv:1308.5863).