The effective exponential slope, $b_n$, obtained from the fit of double differential photoproduction cross sections ${\rm d^2}\sigma_{\gamma p}/{\rm d}x_L{\rm d}p_{T,n}^2$ to a single exponential function in bins of $x_L$. The first uncertainty represents the fit error from the statistical and uncorrelated systematic uncertainty and the second one is due to the correlated systematic uncertainty.

Energy dependence of the exclusive photoproduction of a $\rho^0$ meson associated with a leading neutron, $\gamma p \to \rho^0 n \pi^+$. The first uncertainty is statistical and the second is systematic. The global normalisation uncertainty of $4.4\%$ is not included. $\Phi_{\gamma}$ is the integral of the photon flux, Eq. (3) of paper, in a given $W_{\gamma p}$ bin.

Differential photoproduction cross section ${\rm d}\sigma_{\gamma p}/{\rm d}\eta$ for the exclusive process $\gamma p \to \rho^0 n \pi^+$ as a function of the $\rho^0$ pseudorapidity in the kinematic range $0.35 < x_L < 0.95$, $\theta_n < 0.75$ mrad and $20 < W_{\gamma p} < 100$ GeV. The statistical, uncorrelated and correlated systematic uncertainties, $\delta_{stat}$, $\delta_{sys}^{unc}$ and $\delta_{sys}^{cor}$ respectively, are given, which does not include the global normalisation error of $4.4\%$.

Differential photoproduction cross section ${\rm d}\sigma_{\gamma p}/{\rm d}t^{\prime}$ for the exclusive process $\gamma p \to \rho^0 n \pi^+$ as a function of the $\rho^0$ four-momentum transfer squared, $t^{\prime}$, in the kinematic range $0.35 < x_L < 0.95$, $\theta_n < 0.75$ mrad and $20 < W_{\gamma p} < 100$ GeV. The statistical, uncorrelated and correlated systematic uncertainties, $\delta_{stat}$, $\delta_{sys}^{unc}$ and $\delta_{sys}^{cor}$ respectively, are given, which does not include the global normalisation error of $4.4\%$.

Exponential slopes, $b_1$ and $b_2$, and the ratio $\sigma_1/\sigma_2$, obtained from the components of fit, Eq. (14) of paper, to the differential cross section ${\rm d}\sigma_{\gamma p}/{\rm d}t^{\prime}$ in bins of $x_L$. The errors represent the statistical and systematic uncertainties added in quadrature.

Exponential slopes, $b_1$ and $b_2$, and the ratio $\sigma_1/\sigma_2$, obtained from the components of fit, Eq. (14) of paper, to the differential cross section ${\rm d}\sigma_{\gamma p}/{\rm d}t^{\prime}$ in bins of $p_{T,n}^2$. The errors represent the statistical and systematic uncertainties added in quadrature.

Energy dependence of elastic $\rho^0$ photoproduction on the pion, $\gamma \pi^+ \to \rho^0 \pi^+$, extracted in the one-pion-exchange approximation using OPE1 sample. The first uncertainty represents the full experimental error and the second is the model error coming from the pion flux uncertainty (see text). $\Gamma_\pi(x_L)$ represents the value of the pion flux, Eqs. (5-6) of paper, integrated over the $p_{T,n}<0.2$ GeV range, at a given $x_L$.

Cross section of elastic $\rho^0$ photoproduction on the pion, $\gamma \pi^+ \to \rho^0 \pi^+$, extracted in the one-pion-exchange approximation using three different samples: full sample, OPE1 and OPE2. The first uncertainty represents the full experimental error and the second is the model error coming from the pion flux uncertainty (see text). $\Gamma_\pi$ represents the value of the pion flux, Eqs. (5-6) of paper, integrated over the corresponding $(x_L,p_{T,n})$ range.

The total inelastic cross section.

The measured differential elastic cross section. In addition to the statistical and total systematic uncertainties, the following 22 systematic shifts are given, which are included in the profile fit with their signs: -- Constraints: Beam optics uncertainty obtained by varying the ALFA constraints in the optics fit -- QScan: Variation by +/- 0.1 % of the quadrupole strength -- Q2: Fit of the strength of Q2 using the best value for the strength of Q1 and Q3 -- Q5Q6: Variation of the strength of Q5 and Q6 by -0.2% as indicated by machine constraints -- MadX: Uncertainty related to the beam transport replacing matrix transport by MadX PTC tracking -- Qmisal: Uncertainty due to the mis-alignment of the quadrupoles in the beam line -- Q1Q3: Propagation of the optics fit uncertainty in the strenght of Q1 and Q3 on the differential elastic cross section -- Aopt: Alignment uncertainty from the optimization procedure -- Offv: Alignment uncertainty related to the vertical beam center offset -- Offh: Alignment uncertainty related to the horizontal beam center offset -- Ang: Alignment uncertainty related to the detector rotation in the x-y plane -- BGn: Uncertainty from the background normalization -- BGs: Uncertainty from the background shape -- MCres: Error from modelling of the detector response -- Slope: Residual dependence on the physics model estimated by varying the nuclear slope in the simulation by +/- 1 GeV^-2 -- Emit: Uncertainty from the emittance used to calculate beam divergence in the simulation -- Unf: Unfolding uncertainty from the data-driven closure test -- Trac: Uncertainty from the variation of the track reconstruction selection cuts -- Xing: Uncertainty from residual crossing angle in the horizontal plane -- Eff: Uncertainty from the reconstruction efficiency -- Lumi: Luminosity uncertainty (+/- 1.5%) -- Ebeam: Uncertainty from the nominal beam energy (+/- 0.65%) Small differences in the values given here compared to the published version are related to insignificant rounding issues.

The statistical covariance matrix for the differential elastic cross section.