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Definition of angles in the process $\mu N \to \mu' N' \rho ^0$ with $\rho ^0 \to \pi^+ \pi^- $. Here, $\Phi$ is the angle between the $\rho ^0$ production plane and the lepton scattering plane in the centre-of-mass system of the virtual photon and the target nucleon, while $\phi$ is the angle between the $\rho ^0$ production and decay planes. The variable $\Theta$ is the polar angle of the decay $\pi ^+$ in the $\rho ^0$ meson rest frame.

Definition of angles in the process $\mu N \to \mu' N' \rho ^0$ with $\rho ^0 \to \pi^+ \pi^- $. Here, $\Phi$ is the angle between the $\rho ^0$ production plane and the lepton scattering plane in the centre-of-mass system of the virtual photon and the target nucleon, while $\phi$ is the angle between the $\rho ^0$ production and decay planes. The variable $\Theta$ is the polar angle of the decay $\pi ^+$ in the $\rho ^0$ meson rest frame.

\small{ Distribution of the $\pi ^+ \pi ^-$ invariant mass for experimental data (shaded histogram) and HEPGEN MC (open histogram). The invariant mass distribution from HEPGEN is normalised to the data in the region 0.75 GeV/$c^2$ < $M_{\pi^{+}\pi^{-}}$ < 0.77 GeV/$c^2$. The vertical lines indicate the applied limits. }

\small{ Distribution of the $\pi ^+ \pi ^-$ invariant mass for experimental data (shaded histogram) and HEPGEN MC (open histogram). The distributions are obtained applying all event selections except the selection on the invariant mass. The invariant mass distribution from HEPGEN is normalised to the data in the region 0.75 GeV/$c^2$ < $M_{\pi^{+}\pi^{-}}$ < 0.77 GeV/$c^2$. The vertical lines indicate the applied limits. }

The missing-energy distribution from experimental data (red points) compared to the distribution of SIDIS events from a LEPTO MC simulation (blue points). The MC distribution is normalised to the data in the region 7~GeV $< E_{\rm miss} < 20$~GeV. The background-corrected distribution for the data is shown as shaded histogram. The vertical lines at $|E_{\rm miss}| =$ 2.5 GeV indicate the limits of the exclusive region. Each LEPTO MC event is reweighted by a $E_{\rm miss}$-dependent weight that is calculated using both experimental and simulated data with same-charge hadron pairs. See text for a detailed explanation.

The missing-energy distribution from experimental data (red points) compared to the distribution of SIDIS events from a LEPTO MC simulation (blue points). Each LEPTO MC event is reweighted by a $E_{\rm miss}$-dependent weight that is calculated using both experimental and simulated data with same-charge hadron pairs. See text for a detailed explanation. The reweighted MC distribution is normalised to the data in the region 7~GeV $< E_{\rm miss} < 20$~GeV. The SIDIS-background-corrected distribution for the data is shown as shaded histogram. The vertical lines at $|E_{\rm miss}| =$ 2.5 GeV indicate the limits of the exclusive region. The shown distributions are obtained using all event selections except the selection on $E_{\rm miss}$.

The 23 SDMEs for exclusive $\rho ^0$ leptoproduction extracted in the entire COMPASS kinematic region with $ \langle Q^2 \rangle = 2.40$~(GeV/$c$)$^2$, $\langle W\rangle =9.9$~GeV/$c^2$, $ \langle p^{2}_{\rm T}\rangle = 0.18$ (GeV/$c$)$^2$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature. Unpolarised (polarised) SDMEs are displayed in unshaded (shaded) areas.

The 23 SDMEs for exclusive $\rho ^0$ leptoproduction extracted in the entire COMPASS kinematic region with $ \langle Q^2 \rangle = 2.40$~(GeV/$c$)$^2$, $\langle W\rangle =9.9$~GeV/$c^2$, $ \langle p^{2}_{\rm T}\rangle = 0.18$ (GeV/$c$)$^2$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature. Unpolarised (polarised) SDMEs are displayed in unshaded (shaded) areas.

$Q^2$ dependence of the measured 23 SDMEs. The capital letters A to E denote the class, to which the SDME belongs. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$Q^2$ dependence of the measured 23 SDMEs. The capital letters A to E denote the class, to which the SDME belongs. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$p^{2}_{\rm{T}}$ dependence of the measured 23 SDMEs. The capital letters A to E denote the class, to which the SDME belongs. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$p^{2}_{\rm{T}}$ dependence of the measured 23 SDMEs. The capital letters A to E denote the class, to which the SDME belongs. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$W$ dependence of the measured 23 SDMEs. The capital letters A to E denote the class, to which the SDME belongs. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$W$ dependence of the measured 23 SDMEs. The capital letters A to E denote the class, to which the SDME belongs. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$Q^{2}$, $p^{2}_{\rm{T}}$ and $W$ dependences of $\tau_{01}$, $\tau_{10}$, $\tau_{1-1}$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$Q^{2}$, $p^{2}_{\rm{T}}$ and $W$ dependences of $\tau_{01}$, $\tau_{10}$, $\tau_{1-1}$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$Q^{2}$, $p^{2}_{\rm{T}}$, and $W$ dependences of $u_{1}$, $u_{2}$, $u_{3}$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$Q^{2}$, $p^{2}_{\rm{T}}$, and $W$ dependences of $u_{1}$, $u_{2}$, $u_{3}$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$Q^{2}$, $p^{2}_{\rm{T}}$ and $W$ dependences of the NPE-to-UPE asymmetry of the transverse cross section for the transition $\gamma^*_T \rightarrow V_T$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$Q^{2}$, $p^{2}_{\rm{T}}$ and $W$ dependences of the NPE-to-UPE asymmetry of the transverse cross section for the transition $\gamma^*_T \rightarrow V_T$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature.

$Q^{2}$, $p^{2}_{\rm{T}}$ and $W$ dependences of two estimates, $R'$ and $\widetilde{R}$, of the longitudinal-to-transverse cross-section ratio $R$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature. For better visibility the data points for $\widetilde{R}$ are presented with a small horizontal off-set.

$Q^{2}$, $p^{2}_{\rm{T}}$ and $W$ dependences of two estimates, $R'$ and $\widetilde{R}$, of the longitudinal-to-transverse cross-section ratio $R$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature. For better visibility the data points for $\widetilde{R}$ are presented with a small horizontal off-set.

Comparison of the 23 SDMEs for exclusive $\rho ^0$ leptoproduction on the proton extracted in the entire kinematic regions of the HERMES and COMPASS experiments. For HERMES the average kinematic values are $ \langle Q^2 \rangle = 1.96$~(GeV/$c$)$^2$, $\langle W\rangle =4.8$~GeV/$c^2$, $ \langle |t'| \rangle = 0.13$, while those for COMPASS are $ \langle Q^2 \rangle = 2.40$~(GeV/$c$)$^2$, $\langle W\rangle =9.9$~GeV/$c^2$, $ \langle p^{2}_{\rm T}\rangle = 0.18$ (GeV/$c$)$^2$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature. Unpolarised (polarised) SDMEs are displayed in unshaded (shaded) areas.

Comparison of the 23 SDMEs for exclusive $\rho ^0$ leptoproduction on the proton extracted in the entire kinematic regions of the HERMES and COMPASS experiments. For HERMES the average kinematic values are $ \langle Q^2 \rangle = 1.96$~(GeV/$c$)$^2$, $\langle W\rangle =4.8$~GeV/$c^2$, $ \langle |t'| \rangle = 0.13$, while those for COMPASS are $ \langle Q^2 \rangle = 2.40$~(GeV/$c$)$^2$, $\langle W\rangle =9.9$~GeV/$c^2$, $ \langle p^{2}_{\rm T}\rangle = 0.18$ (GeV/$c$)$^2$. Inner error bars represent statistical uncertainties and outer ones statistical and systematic uncertainties added in quadrature. Unpolarised (polarised) SDMEs are displayed in unshaded (shaded) areas.

The ratio $R = \sigma_L/\sigma_T$ as a function of $Q^2$. For comparison measurements of exclusive $\rho ^0$ leptoproduction by fixed target experiments (HERMES~\cite{DC-24}, NMC~\cite{NMC}, E665~\cite{E665}) and by HERA collider experiments (ZEUS~\cite{zeus-2007}, H1~\cite{h1-2010}, H1 SV~\cite{h1-2000}) are also shown.

The ratio $R = \sigma_L/\sigma_T$ as a function of $Q^2$. For comparison measurements of exclusive $\rho ^0$ leptoproduction by fixed target experiments (HERMES~\cite{DC-24}, NMC~\cite{NMC}, E665~\cite{E665}) and by HERA collider experiments (ZEUS~\cite{zeus-2007}, H1~\cite{h1-2010}, H1 SV~\cite{h1-2000}) are also shown.