Measurement of the cross section for hard exclusive ${\pi }^0$ leptoproduction

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/}$c)^2$\mathrm{.}Theaveragekinematicsofthemeasurementare$\langle Q^2 \rangle =2.0; {($\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 ${\bar{E}}_T$.