A smooth massless limit for supersymmetric QCD

TL;DR

This paper investigates the behavior of supersymmetric QCD with fewer flavors than colors, focusing on the massless limit, and explores the spontaneous breaking of flavor symmetry and the associated Goldstone modes.

Contribution

It provides a detailed analysis of the low-energy spectrum, decay constants, and the singular behavior in the massless limit of supersymmetric QCD, including the role of Nambu-Goldstone variables.

Findings

Mass spectrum and decay constants are consistent with decoupling and current algebra.

Massless limit involves spontaneous flavor symmetry breaking with Goldstone modes.

Interactions between chiral superfields turn off in the massless limit.

Abstract

We analyse in detail the behaviour of supersymmetric QCD with a number of flavours M smaller than the number of colours N, for quark masses smaller than the dynamically generated scale. In this regime, we find it useful to move from meson superfields to Nambu-Goldstone-like variables. In particular we work out the mass spectrum and the set of decay constants that specify the interactions of the low-energy theory. We explicitly check that masses and decay constants have a consistent behaviour under decoupling and that they satisfy current algebra requirements. Finally we speculate about the massless limit. For vanishing quark masses, and only in this case, the relation between mesons and Nambu-Goldstone variables becomes singular. When analysed in terms of the Nambu-Goldstone superfields, the massless limit exhibits a spontaneous breaking of the flavour symmetry, with massless Goldstone modes embedded in an M^2-dimensional complex moduli space. The symmetry-breaking order parameter is formally infinite, but this has the only effect of turning off the interactions between the chiral superfields.