AbstractWe study the reaction $$e^+e^-\rightarrow \pi ^0\gamma $$
e
+
e
-
→
π
0
γ
based on a dispersive representation of the underlying $$\pi ^0\rightarrow \gamma \gamma ^*$$
π
0
→
γ
γ
∗
transition form factor. As a first application, we evaluate the contribution of the $$\pi ^0\gamma $$
π
0
γ
channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find $$a_\mu ^{\pi ^0\gamma }\big |_{\le 1.35\,\text {GeV}}=43.8(6)\times 10^{-11}$$
a
μ
π
0
γ
|
≤
1.35
GeV
=
43.8
(
6
)
×
10
-
11
, in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of $$\omega $$
ω
and $$\phi $$
ϕ
. We observe good agreement with the $$e^+e^-\rightarrow 3\pi $$
e
+
e
-
→
3
π
channel, explaining a previous tension in the $$\omega $$
ω
mass between $$\pi ^0\gamma $$
π
0
γ
and $$3\pi $$
3
π
by an unphysical phase in the fit function. Combining both channels we find $${\bar{M}}_\omega =782.736(24)\,\text {MeV}$$
M
¯
ω
=
782.736
(
24
)
MeV
and $${\bar{M}}_\phi =1019.457(20)\,\text {MeV}$$
M
¯
ϕ
=
1019.457
(
20
)
MeV
for the masses including vacuum-polarization corrections. The $$\phi $$
ϕ
mass agrees perfectly with the PDG average, which is dominated by determinations from the $${\bar{K}} K$$
K
¯
K
channel, demonstrating consistency with $$3\pi $$
3
π
and $$\pi ^0\gamma $$
π
0
γ
. For the $$\omega $$
ω
mass, our result is consistent but more precise, exacerbating tensions with the $$\omega $$
ω
mass extracted via isospin-breaking effects from the $$2\pi $$
2
π
channel.
Decays of an exotic
1−+
hybrid meson resonance in QCD