Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2001-11-13
Phys.Scripta T99 (2002) 84-95
Physics
High Energy Physics
High Energy Physics - Phenomenology
18 pages, 0 figures, LaTeX with espcrc2.sty
Scientific paper
10.1238/Physica.Topical.099a0008
The radiative decays of the pseudoscalar mesons $P=(\pi^0,\eta,\eta')$ are of special interest as they provide an experimental window on the electromagnetic and colour chiral $U_A(1)$ anomalies. $\pi^0\to\gamma\gamma$ is well described by the electromagnetic $U_A(1)$ anomaly under the assumption that $\pi^0$ is a Goldstone boson for spontaneously broken chiral symmetry, but the analogous results for $\eta'(\eta)\to\gamma\gamma$ are complicated by the colour $U_A(1)$ anomaly in QCD. This paper reviews the theory of $\eta'(\eta)\to\gamma\gamma$ decays, emphasising the role of the colour $U_A(1)$ anomaly and the renormalisation group. The relation to the Witten-Veneziano mass formula for the $\eta'$ and the QCD topological susceptibility is derived. The implications for the phenomenological analysis of $P\to\gamma\gamma$ are described and a proposal is made for a comprehensive re-analysis of existing data on $P\to\gamma\gamma$, $P\to V\gamma$, where $V=(\rho,\omega, \phi)$ is a light $1^-$ meson, $\eta'(\eta)\to \pi\pi\gamma$, $\psi\to\eta'(\eta)\gamma$, etc. Other applications, to the muon anomalous magnetic moment $g_\m-2$ and the determination of the photon structure function $g_1^\gamma$ in polarised deep inelastic scattering, are also briefly discussed.
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