\subsection{Transverse-momentum-dependent effects in SIDIS} In SIDIS on an unpolarised target, hadron azimuthal asymmetries arise that give access to the distribution of intrinsic quark transverse momentum as encoded in the $T$-odd Boer--Mulders function (see also Sect.~\ref{subsec:physics.dy.sidis}) and also to higher-twist effects. The cross section for hadron production in SIDIS of longitudinally polarised leptons on unpolarised nucleons can be written as~\cite{Bacchetta:2006tn} \[ \begin{array}{rcl} \dfrac{\di \sigma}{\di x \di y \di \phi_h} &=& \dfrac{\alpha^2}{xyQ^2} \dfrac{1+(1-y)^2}{2} \left[ F_{UU} + \varepsilon_1 \cos \phi_h F^{\cos \phi_h}_{UU} \right.\\[2ex] & & \left. + \varepsilon_2 \cos 2\phi_h F^{\cos\; 2\phi_h}_{UU} + \lambda_\mu \varepsilon_3 \sin \phi_h F^{\sin \phi_h}_{LU} \right], \end{array} \] where $\phi_h$ is the azimuthal angle of the outgoing hadron in the $\gamma^*$--nucleon system, $\lambda_\mu$ is the value of the longitudinal beam polarisation and the $\varepsilon_i$ are kinematical factors depending on $y$. In the three structure functions $F^{\cos \phi_h}_{UU}$, $F^{\cos\; 2\phi_h}_{UU}$, and $F^{\sin \phi_h}_{LU}$ the first and second subscripts denote beam and target polarisation, respectively, as earlier used in this document. In cross-section asymmetries corresponding azimuthal asymmetries arise which can be extracted by fitting the $ \phi_h$ distribution. At \compass\ energies, the azimuthal asymmetry $A^{\cos \phi_h}$ arises mainly due to the Cahn effect~\cite{Cahn:1978se} describing the non-collinear quark kinematics. It contains information on the mean value on the intrinsic quark transverse momentum~\cite{Anselmino:2005nn}. The Boer--Mulders function is expected to yield an important contribution to the asymmetry $A^{\cos 2\phi_h}$, in which it appears coupled to the Collins fragmentation function that is now known to be different from zero. At hadron transverse momenta smaller than 1~GeV/$c$, the only other relevant contribution to this asymmetry is that from the Cahn effect. The measurement of $A^{\cos 2\phi_h}$ and $A^{\cos \phi_h}$ would thus allow the extraction of the Boer--Mulders function, once the Collins fragmentation function will be known sufficiently well. The third asymmetry involved in this measurement, $A^{\sin \phi_h}$, is expected to contain twist-3 TMDs. In the past, these azimuthal asymmetries were measured by the EMC~\cite{Arneodo:1986cf,Ashman:1991cj}, E665~\cite{Adams:1993hs} and ZEUS~\cite{Breitweg:2000qh} experiments. The precision of these measurements was limited and all results were produced without separating hadrons according to their charge. Recently, \compass\ has produced preliminary results~\cite{Kafer:2008ud} on $A^{\cos \phi_h}$, $A^{\cos 2\phi_h}$ and $A^{\sin \phi_h}$ from data collected with the 160~GeV muon beam and the \mrf{^6LiD} target which essentially mainly of two deuterons and one $\alpha$ particle. For the first time, separate results were given for positive and negative hadrons. The results for $A^{\cos \phi_h}$ and $A^{\cos 2\phi_h}$ as a function of $x$ are shown by the black filled points in Fig.~\ref{unpol_xxx} in the upper and lower rows, respectively. The left (right) panels are for positive (negative) hadrons. The bands show the systematic uncertainties, which are mainly due to the correction for the apparatus acceptance, which is needed for these kind of asymmetries. As can be seen, the asymmetries are different from zero and different for positive and negative hadrons, indicating Boer--Mulders functions being different from zero. The asymmetry $A^{\sin \phi_h}$ (not shown in Fig.~\ref{unpol_xxx}) is consistent with zero. \hermes\ has recently produced preliminary results for charged pions from data collected with $p$ and $d$ targets and a 27.5~GeV electron beam~\cite{Giordano:2009hi}. In their data, the measured values for $A^{\cos \phi_h}$ and $A^{\cos 2\phi_h}$ are quite similar for proton and deuteron. They are different from zero and differ between positive and negative pions. The results on $A^{\cos 2\phi_h}$ from \compass\ and \hermes\ have already been used for a first, model-dependent extraction of the Boer--Mulders functions~\cite{Barone:2009hw}. \begin{figure} \begin{center} \includegraphics[width=0.9\textwidth]{proj_dvcs250cm_cosphi_Xonly_mod}\\ \includegraphics[width=0.9\textwidth]{proj_dvcs250cm_cos2phi_Xonly_mod} \end{center} \caption{ Projected statistical errors (red open squares) for $A_{\cos \phi}$ (upper plots) and $A_{\cos 2\phi}$ asymmetries (lower plots) for positive (left) and negative (right) hadrons for one week of data with the LH target. The black closed spheres with the grey bands for systematic errors correspond to preliminary results on $^6$LiD \cite{Kafer:2008ud}. For the new measurement the systematic errors are expected to be considerably reduced. } \label{unpol_xxx} \end{figure} Given the relevance of TMD effects for the understanding of nucleon structure, measurements of all these azimuthal asymmetries in SIDIS on unpolarised protons at high energies are highly desirable, and only \compass\ could perform them in the near future. The data already collected by \compass\ with the polarised proton target can not be used by averaging the polarisation, since the target material is NH$_3$. In order to study the feasibility of such a measurement in parallel with the GPD programme, we have estimated the expected statistical error for one week of running (corresponding to $6\times 10^{12}$ integrated muons on the target) with the 2.5~m long liquid hydrogen target. The result is shown as red open squares in Fig.~\ref{unpol_xxx}. The estimation is based on the previous analysis~\cite{Kafer:2008ud} and was done assuming the same data selection. This includes the standard DIS cuts ($Q^2 > 1~(\gom)^2$, mass of the hadronic final state $W>5\ \GeV/c^2$, $0.1 < y < 0.9$) and the detection of at least one hadron in the final state with $0.2