\subsection{A first look at exclusive photon production in 2008} \label{subsec:physics.gpd.validation} Simulations have been performed for the projected DVCS measurements. However, for such complex apparatus like the \compass\ spectrometer, experience has shown that a check with data (whenever available) is mandatory. The precision of the final results will depend on: \bi \item the achievable luminosity, which is a function of the LH target length and the maximum reachable $\mu^+$ and $\mu^-$ beam intensities, \item the global detection efficiency, which includes all possible hardware losses (trigger dead time etc.) and event reconstruction losses, \item the efficiency to identify and possibly reject background, \item how accurately the Bethe--Heitler (BH) contribution, which dominates in certain kinematic regions, can be subtracted, \item how accurately the measured yields can be translated into absolute cross sections. \ei There are common key issues to answer these questions quantitatively, namely: \bi \item how accurately we know the detection efficiencies (absolute, and relative between $\mu^+$ and $\mu^-$) and how well we can monitor their stability versus time, \item what is the ultimate precision for the measurements of the incoming $\mu^+$ and $\mu^-$ flux measurements, which will determine the systematic accurately arising from the combination of both data sets. \ei The set-up used for a part of the \compass\ hadron programme makes use of a 40~cm long LH target, surrounded by a Recoil Proton Detector (RPD). It includes all detectors available including the ECAL1 and ECAL2 electromagnetic calorimeters for photon detection. Apart from the target length and the corresponding RPD length, this set-up has all the features of the one foreseen for the proposed future GPD programme, where the LH target length will be 2.5~m with the RPD length correspondingly adapted. The flexibility of the \cern/SPS M2 beam line allows one to tune either a hadron beam or a polarised muon beam, reaching in both cases the optimum performance within a few hours. This offered an excellent opportunity to perform DVCS test measurements with minimum disturbance of the ongoing hadron programme. Such measurements were performed in 2008 and 2009 using both $\mu^+$ and $\mu^-$ beams of 160~GeV energy, with an intensity of about 1/3 of the maximum in 2008 and close to the maximum intensity in 2009. In 2008, due to the short time slot available, the Beam Momentum Station (BMS) which determines with a precision of a few $10^{-3}$ the incoming beam particle momentum but needs to be removed for running with hadron beam, could not be reinstalled. For the 2009 test run the BMS was reinstalled. %============================================================================== \subsubsection{Overall efficiency and performances to select BH and DVCS events} \label{subsubsec:physics.gpd.validation.effi_perform} % The first results from the 2008 test run on exclusive production of a high-energy single-photon in coincidence with a recoiling proton are presented in Ref.~\cite{first_DVCS_note}. The preselection towards exclusive $\mu p \rightarrow \mu' p \gamma$ events is requiring that: \bi \item there are only two charged tracks ($\mu$, $\mu'$) at the primary vertex, \item there is only one proton candidate in the Recoil Proton Detector (RPD) and it has a momentum of less than $1~\GeV/c$, \item there is only one photon with energy $E_{\gamma} \geq$ 5~GeV in ECAL1 and no other photon with energy $\geq$ 10~GeV in ECAL2, or \item there is only one photon with energy $E_{\gamma} \geq 10~\GeV$ in ECAL2 and no other photon with energy $\geq$ 5~GeV in ECAL1. These conditions correspond to the kinematic domain for DVCS displayed in Fig.~\ref{fig:upgrades.LH2-RPD.Kine_proton_photon}. \ei We note that the events preselected in this way may have additional low-energy photons. At this first step of the analysis, the precise photon timing provided by the ECALs readout electronics to suppress the background was not available. The suppression of the main part of additional photons in this first analysis was accomplished by an appropriate choice of ECAL thresholds. \begin{figure}[tpb] \begin{center} \includegraphics*[width=7.5cm]{gpd_validation_2008_vertex-t} \includegraphics*[width=7.5cm]{gpd_validation_2008_vertex-z} \end{center} \caption{Differences in timing (left) and $Z$ position along the beam direction (right) between the reconstructed $\mu \mu'$ vertex and the single proton detected in the RPD. The resolutions of timing and position difference are better than 1~ns and 4~cm, respectively. } \label{fig:physics.gpd.vertex} \end{figure} In Figure~\ref{fig:physics.gpd.vertex} correlations are illustrated between quantities derived from the particle detected in the RPD and those derived from the muon vertex reconstructed using the incoming and the scattered muons. The left panel shows the time difference $\Delta t = t_{\mu} - t_{RPD}$ between the incoming muon and the RPD particle both evaluated at the muon vertex. The random noise in the 30~ns timing window is less than 2\% and a Gaussian fit gives $\sigma_t \simeq$ 1~ns. The right panel shows $\Delta Z = Z_{\mu \mu' vertex} - Z_{RPD}$, the difference between the longitudinal position of the muon vertex and the RPD particle's point of closest approach to the beam axis. It shows a peak with an approximately 8~cm width at half maximum and a tail present in the left part of the $\Delta Z$ distribution; a Gaussian fit gives $\sigma_Z \simeq$ 4~cm. No cuts are applied yet since most of the events in this tail will be removed by the further application of exclusivity cuts. \begin{figure}[tpb] \begin{center} \includegraphics*[width=7cm]{gpd_validation_2008_delta-pPerp} \\ \includegraphics*[width=7cm]{gpd_validation_2008_phi-vs-phi} \includegraphics*[width=7cm]{gpd_validation_2008_delta-phi} \end{center} \caption{Top panel: $\Delta P_{\perp} = |\vec{P}^{\perp}_{miss}| - |\vec{P}^{\perp}_{RPD}|$. Bottom left: correlation between $\phi_{miss}$ and $\phi_{RPD}$. Bottom right: $\Delta \phi = \phi_{miss} - \phi_{RPD}$. } \label{fig:physics.gpd.Transverse} \end{figure} In the absence of the BMS, the momentum of the incoming muon is not precisely known while its direction is well determined, hence it is relevant to work in the transverse plane. One can build the missing momentum $\vec{P}_{miss}= \vec{P}_{\mu} - \vec{P}_{\mu'} - \vec{P}_{\gamma}$ and compare its projection in the transverse plane with the projection of $\vec{P}_{proton}$. This is shown in Fig.~\ref{fig:physics.gpd.Transverse} together with correlation and difference between the azimuthal angles $\phi_{miss}$ and $\phi_{RPD}$. % \begin{figure}[tbp] \begin{center} \includegraphics*[width=7.5cm] {gpd_validation_2008_phi-physics-allQ2-beforecuts} \includegraphics*[width=7.5cm] {gpd_validation_2008_phi-physics-allQ2} \end{center} \caption{Azimuthal distribution in $\phi$ of the measured exclusive $\mu p \rightarrow \mu' p \gamma$ events before (left) and after (right) exclusivity cuts. This angular distribution exhibits a peak at $\phi$ = 0, which is a characteristic feature of BH dominance at small $x_B$. } \label{fig:physics.gpd.phiBH_allQ2} \end{figure} Two exclusivity cuts, $|\Delta P_{\perp}| < 0.2~\GeV$ and $\Delta \phi < 36^{\circ} $ (\ie\ 3~$\sigma$), are derived using these distribution and applied to improve the rejection of non-exclusive background. Assuming now that the selected events have a pure 3-particle final state $\mu p \rightarrow \mu' p \gamma$, one can calculate the azimuthal angle $\phi$ between the lepton plane spanned by the incoming and scattered muons and the ``hadron'' plane spanned by recoiling proton and produced photon, as illustrated in Fig.~\ref{fig:physics.gpd.phi_angle}. Results are shown in Fig.~\ref{fig:physics.gpd.phiBH_allQ2} where the peak at $\phi = 0$ is a characteristic feature of BH events which are dominant at small $x_B$ (as shown in the left panel of Fig.~\ref{fig:dvcs_bh_int_mc_2009}). Applying the two previous exclusivity cuts $|\Delta P_{\perp}| < 0.2~$GeV and $\Delta \phi < 36^{\circ}$ reduces significantly the constant (non-exclusive) background, as illustrated in the right panel of Fig.~\ref{fig:physics.gpd.phiBH_allQ2}. \begin{figure}[tbp] \begin{center} \includegraphics*[width=9cm]{gpd_validation_2008_phi-physics} \end{center} \caption{Azimuthal distribution in $\phi$ of the measured exclusive $\mu p \rightarrow \mu' p \gamma$ events for $Q^2 > 1$~GeV$^2$ and comparison with simulation. This distribution is rather similar to the distribution dominated by the BH contribution at small $x_B$ (left panel of Fig.~\ref{fig:dvcs_bh_int_mc_2009}). In total, 51 events are selected. } \label{fig:physics.gpd.phiBH_highQ2} \end{figure} Reliable simulations for the hard exclusive DVCS process are restricted to sufficiently large photon virtualities, $Q^2 > 1~\GeV^2$. This restriction does not apply to the BH bremsstrahlung process, which dominates this sample of events at low values of $x_B$. Awaiting a simulation for BH production for this full kinematical phase space, a standard ``2-Gaussian + constant'' fit is applied to the background, as shown in Fig.~\ref{fig:physics.gpd.phiBH_allQ2}. In order to compare with available simulations, a cut $Q^2 > 1~\GeV^2$ is eventually applied. The resulting $\phi$ distribution is shown in Fig.~\ref{fig:physics.gpd.phiBH_highQ2}, where 51 events are finally selected. We note that among the 51 selected events, 36 have an additional cluster with energy below 1~GeV in ECAL1 or below 2~GeV in ECAL2. Calculating the $M_{\gamma \gamma}$ for the corresponding photon pair leads to an upper limit for a possible $\pi^0$ contamination of the selected sample of $16 \pm 6\%$. We can now compare to the prediction for single-photon production which is still dominated, for this restricted kinematic region, by the BH process. The relative normalisation factor of the two distributions produced for equal luminosities provides the overall detection efficiency $\epsilon= 0.32 \pm 0.13$. The final global efficiency incorporates several additional factors which amount to $\epsilon_{Add} \sim 0.4$. Combining the two numbers provides the global efficiency $\epsilon_{global}= 0.13 \pm 0.05$. The value of 0.1 that was given in the Letter of Intent~\cite{LoI2009} to the SPSC is in excellent agreement with this first direct estimate. %========================================================================= \subsubsection{Improved analysis of single-photon production using ECAL timing information} % \label{subsubsec:physics.gpd.validation.improved_analysis} % Following the first analysis step described in the previous section, the 2008 DVCS test data were reproduced providing an improved cluster reconstruction and a precise cluster timing information from the ECALs. The issue of background from additional photons was solved in the new production as described in Ref.~\cite{second_DVCS_note}. The reduction of additional photons was accomplished by imposing a cut on the ECALs' timing information, and also by a general improvement of the ECAL reconstruction software and calibration algorithm. Given the timing resolution for all photons in the ECALs, the optimum cut was found to be $|t-t_0| \leq 3.5 \; \sigma_t$ with $\sigma_t \sim 1.5$~ns and $t_0$ the offset of the distribution from zero. This cut, which simultaneously maximises the number of selected events and drastically decreases the average multiplicities of the additional clusters, is a major improvement that opened the way to select exclusive single-photon events without applying any threshold on $E_{\gamma}$ (besides the necessary hardware thresholds). \begin{figure}[tbp] \begin{center} \includegraphics*[width=9cm] {gpd_validation_2008_phi-physics_timing} \end{center} \caption{Same distribution as shown in Fig.~\ref{fig:physics.gpd.phiBH_highQ2} but from the new analysis with photon timing. In total, 52 purely exclusive single-photon events are selected. } \label{fig:physics.gpd.newprod_with_tc} \end{figure} In Figure~\ref{fig:physics.gpd.newprod_with_tc} is shown the azimuthal distribution of the final 52 exclusive $\mu p \rightarrow \mu' p \gamma$ events which are obtained for $Q^2 > 1$~GeV$^2$ from the improved analysis using the photon timing information, \ie\ without additional low-energy clusters. Possible reasons for any remaining $\pi^0$ contamination in this sample are that one of the two photons is not detected in the ECALs or has an energy below the hardware threshold. %=========================================================================== \subsection{A first hint of ``pure'' DVCS events from the 2009 test run} % \label{subsec:physics.gpd.validation.first_hint} % One of the main goals of the DVCS test run performed in 2009 was to provide a first evaluation of the relative contributions of the $|DVCS|^2$ and $|BH|^2$ terms, and of the DVCS-BH interference term at \compass\ kinematics. In comparison to the shorter 2008 test run, the 2009 test run was improved in several aspects: \bi \item higher statistics, \item the three inclusive triggers (Middle, Ladder and Outer) were added to the trigger in coincidence with the RPD, \item the beam momentum station was reinstalled to measure the momentum of the incoming muon, \item the $\mu$ beam intensity was increased by a factor of three, \item the data were taken with both $\mu^+$ and a $\mu^-$ beam. \ei \begin{figure}[tbp] \begin{center} \includegraphics*[width=150mm,angle=0.]{gpd_validation_2009_res09-final} \end{center} \caption{Distribution in the azimuthal angle $\phi$ for measured exclusive single-photon events, $\mu p \rightarrow \mu' p \gamma$ with $Q^2 > 1~\GeV^2$, in the same three $x_{B}$ bins as in Fig.~\ref{fig:dvcs_bh_int_mc_2009}. %for three bins in $x_B$: $0.005 < x_{B} < 0.01$ (left), $0.01 < x_{B} < 0.03$ %(middle) and $0.03 < x_{B}$ (right). Shown here is a Monte Carlo simulation of only the BH process $(\rm |BH|^2)$ and of both the BH and DVCS processes $(\rm |BH + DVCS|^2)$. } \label{fig:dvcs_bh_2009} \end{figure} % %\medskip % %\begin{figure}[tbp] %\begin{center} %\includegraphics*[width=150mm,angle=0.]{gpd_validation_2009_res09-mc-final} %\end{center} %\caption{Monte Carlo simulation of the exclusive process %$\mu^+ p \rightarrow \mu'^{+} p \gamma$ for $Q^2 > 1~\GeV^2$, showing the %$\phi$ angle distribution in the same three $x_{B}$ bins as in %Fig.~\ref{fig:dvcs_bh_2009} for pure BH $(\rm |BH|^2)$, pure DVCS %$(\rm |DVCS|^2)$, DVCS-BH interference, and the sum of all %contributions $(\rm |BH + DVCS|^2)$. %} %\label{fig:dvcs_bh_int_mc_2009} %\end{figure} \noindent The selection of exclusive single-photon production events and the use of the precise photon timing were performed as for the 2008 data analysis (see Sects.~\ref{subsubsec:physics.gpd.validation.effi_perform} and \ref{subsubsec:physics.gpd.validation.improved_analysis}). Figure~\ref{fig:dvcs_bh_2009} shows, for three bins in $x_{B}$ and after applying the cut $Q^2 > 1~$GeV$^2$, the $\phi$ distribution for a sample of exclusive single-photon events obtained with the $\mu^+$ beam. In the low-$x_{B}$ bin we observe 278 events with a $\phi$ distribution compatible with a BH-dominated sample. In the high-$x_{B}$ bin we observe 54 events. An extrapolation of the BH yield from the low-$x_{B}$ bin to the high-$x_{B}$ bin leads to $\sim 10$ BH events, which suggests a significant contribution of DVCS events in the high-$x_{B}$ bin. This figure has to be compared to Fig.~\ref{fig:dvcs_bh_int_mc_2009} that shows, in the same lay-out, a simulation of all contributions to hard exclusive single-photon production, namely pure BH ($\rm |BH|^2$), pure DVCS ($\rm |DVCS|^2$), DVCS-BH interference term and the resulting sum ($\rm |BH + DVCS|^2$). %We note that the interference terms remains sizable even when DVCS has a %negligible contribution. This is expected, as the BH process acts as %'amplifier' in probing the DVCS process. Another goal of the 2009 DVCS test run is to learn about the possible limitations to reach a level of accuracy of a few percent, to which the overall luminosity, including acceptances and efficiencies, has to be controlled. This is a severe requirement for this physics programme and the study involves the use of inclusive $\mu p \rightarrow \mu' X$ and semi-inclusive $\mu p \rightarrow \mu' \pi^+(\pi^-)(\pi^0)X$ channels as well as exclusive channels with a recoil proton detected, including $\mu p \rightarrow \mu' p \gamma$.