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Recent works argue that the pattern of chiral symmetry breaking in QCD-liketheories can be derived from supersymmetric (SUSY) QCD with perturbation ofanomaly-mediated SUSY breaking (AMSB). Nevertheless, despite the fact that AMSBneeds to be a small (but still exact) perturbation, there are two other majorproblems remaining unsolved: first, in order to derive the chiral symmetrybreaking pattern, one needs to minimize the potential along a certain specificdirection, identifying this direction fully as an outcome is nontrivial giventhe moduli space of degenerate vacua in the SUSY limit; second, when SUSY isbroken, non-holomorphic states might emerge and be relevant for determining thevacuum structure. In this work, we focus on SUSY QCD with $N_f\leq N_c+1$ andperturb the theories using AMSB. Without minimizing the potential along acertain specific direction in the moduli space, we successfully derive theexpected chiral symmetry breaking pattern when $N_f<N_c$. However, when$N_f=N_c$ and $N_f=N_c+1$, we show that tree-level AMSB would induce runawaydirections, along which baryon number is spontaneously broken, and the vacuawith broken baryon number can be deeper while the field values are not far fromthe origin. This implies that phase transitions and/or non-holomorphic physicsare necessary. Moreover, we perform explicit consistency checks on ultravioletinsensitivity for different $N_f$ by adding the holomorphic mass term for thelast flavor, we find that the jump of AMSB potential indeed matches thecontribution from the holomorphic mass term. We also show in general that, whentree-level AMSB is not vanishing, the origin of the moduli space in s-confiningtheories does not persist as a minimum.

On the Derivation of Chiral Symmetry Breaking in QCD-like Theories and S-confining Theories