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 $langle Q^2 rangle =2.0; {(text{GeV}/c)^2}$, $langle u rangle = 12.8; {text{GeV}}$, $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 $(8.1 pm 0.9_{text{stat}}{}_{- 1.0}^{+ 1.1}bigrvert_{text{sys}}),{text{nb}}/{(text{GeV}/c)^{2}}$, as well as transverse-transverse and longitudinal-transverse interference contributions of $(-6.0 pm 1.3_{text{stat}}{}_{- 0.7}^{+ 0.7}bigrvert_{text{sys}}),{text{nb}}/{(text{GeV}/c)^{2}}$ and $(1.4 pm 0.5_{text{stat}}{}_{- 0.2}^{+ 0.3}bigrvert_{text{sys}}),{text{nb}}/{(text{GeV}/c)^{2}}$, 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 $overline{E}_T$.
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