  We report on a measurement of hard exclusive $\pi^0$ muoproduction on the
proton by COMPASS using 160 GeV/$c$ polarised $\mu^+$ and $\mu^-$ beams of the
CERN SPS impinging on a liquid hydrogen target. From the average of the
measured $\mu^+$ and $\mu^-$ cross sections, the virtual-photon proton cross
section is determined as a function of the squared four-momentum transfer
between initial and final proton in the range $0.08\,(\text{GeV/}c)^2 < |t| <
0.64\,(\text{GeV/}c)^2$. The average kinematics of the measurement are $\langle
Q^2 \rangle =2.0\; {(\text{GeV}/c)^2}$, $\langle \nu \rangle = 12.8\;
{\text{GeV}}$, $\langle x_{Bj} \rangle = 0.093 $ and $\langle -t \rangle =
0.256\; {(\text{GeV}/c)^2} $. Fitting the azimuthal dependence reveals a
combined contribution by transversely and longitudinally polarised photons of
$(8.1 \ \pm \ 0.9_{\text{stat}}{}_{- \ 1.0}^{+ \
1.1}\big\rvert_{\text{sys}})\,{\text{nb}}/{(\text{GeV}/c)^{2}}$, as well as
transverse-transverse and longitudinal-transverse interference contributions of
$(-6.0 \pm 1.3_{\text{stat}}{}_{- \ 0.7}^{+ \
0.7}\big\rvert_{\text{sys}})\,{\text{nb}}/{(\text{GeV}/c)^{2}}$ and $(1.4 \pm
0.5_{\text{stat}}{}_{- \ 0.2}^{+ \
0.3}\big\rvert_{\text{sys}})\,{\text{nb}}/{(\text{GeV}/c)^{2}}$, respectively.
Our results provide important input for modelling Generalised Parton
Distributions. In the context of the phenomenological Goloskokov-Kroll model,
the statistically significant transverse-transverse interference contribution
constitutes clear experimental evidence for the chiral-odd GPD
$\overline{E}_T$.
