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arXiv · 2610.00484

Glueballs and fractional anomalous determinants at nonzero $θ$, and the decays of the X(2370)

Francesco Giacosa·Shahriyar Jafarzade·Győző Kovács·Péter Kovács·Robert D. Pisarski·Fabian Rennecke
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Abstract

Using fractional anomalous determinants, we construct a model of the trace and axial anomalies of a $SU(3)$ gauge theory at nonzero $θ$ angle through the couplings to scalar and pseudoscalar glueballs. In the pure gauge theory, we reproduce the $θ$ dependence of the vacuum energy and the scalar-glueball mass from the lattice, and estimate the jump in the topological charge density for the first-order transition at $θ= π$. In QCD, the coupling of a pseudoscalar glueball to fractional anomalous determinants describes all of the four three-pseudoscalar decay channels of the $0^{-+}$ glueball candidate $X(2370)$ measured by the BESIII collaboration. Measuring the decay rates for $ηηη$ and $ηηη'$ can provide a stringent test of the model.

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Francesco Giacosa, Shahriyar Jafarzade, Győző Kovács, Péter Kovács, Robert D. Pisarski, Fabian Rennecke. 2026-09-30. Glueballs and fractional anomalous determinants at nonzero $θ$, and the decays of the X(2370). https://arxiv.org/abs/2610.00484

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