Article Dans Une Revue Journal of High Energy Physics Année : 2023

On the Dynamical Origin of the $\eta'$ Potential and the Axion Mass

Résumé

We investigate the dynamics responsible for generating the potential of the $\eta'$, the (would-be) Goldstone boson associated with the anomalous axial $U(1)$ symmetry of QCD. The standard lore posits that pure QCD dynamics generates a confining potential with a branched structure as a function of the $\theta$ angle, and that this same potential largely determines the properties of the $\eta'$ once fermions are included. Here we test this picture by examining a supersymmetric extension of QCD with a small amount of supersymmetry breaking generated via anomaly mediation. For pure $SU(N)$ QCD without flavors, we verify that there are $N$ branches generated by gaugino condensation. Once quarks are introduced, the flavor effects qualitatively change the strong dynamics of the pure theory. For $F$ flavors we find $|N-F|$ branches, whose dynamical origin is gaugino condensation in the unbroken subgroup for $FN+1$. For the special cases of $F = N-1, N, N + 1$ we find no branches and the entire potential is consistent with being a one-instanton effect. The number of branches is a simple consequence of the selection rules of an anomalous $U(1)_R$ symmetry. We find that the $\eta'$ mass does not vanish in the large $N$ limit for fixed $F/N$, since the anomaly is non-vanishing. The same dynamics that is responsible for the $\eta'$ potential is also responsible for the axion potential. We present a simple derivation of the axion mass formula for an arbitrary number of flavors.

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hal-04171358 , version 1 (23-05-2025)

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Csaba Csáki, Raffaele Tito d'Agnolo, Rick S Gupta, Eric Kuflik, Tuhin S Roy, et al.. On the Dynamical Origin of the $\eta'$ Potential and the Axion Mass. Journal of High Energy Physics, 2023, 2023 (10), pp.139. ⟨10.1007/JHEP10(2023)139⟩. ⟨hal-04171358⟩
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