Interpretation of the unpolarized azimuthal asymmetries in SIDIS

The measurement of azimuthal modulations in hadron leptoproduction on unpolarized nucleons allows to get information on the intrinsic transverse momentum $\langle k_T^2 \rangle$ of quarks in a nucleon through both the Cahn effect and the Boer-Mulders function. We have compared the azimuthal asymmetries in the cross section of $160\, \rm{GeV}/c$ muons scattered off an unpolarised deuteron target as measured by COMPASS with a Monte Carlo program, based on the ${}^3P_0$ model of quark anti-quark pair production at string breaking, which accounts for the Cahn effect. Large differences have been observed between data and Monte Carlo, in particular at large values of the fraction of the longitudinal momentum of the fragmenting quark carried by the produced hadron. We found out that most of these differences are due to pions from exclusive vector mesons contaminating the SIDIS sample, which also exhibit large azimuthal modulations. Using the measurements of the exclusive reaction $\mu N\rightarrow \mu' \, \rho\, N$ we had done in 2006, we can reproduce reasonably well the observed differences. Subtracting the contribution of hadrons produced in the decay of exclusive vector mesons from the SIDIS unpolarised azimuthal asymmetries is therefore a prerequisite condition for extracting $\langle k_T^2 \rangle$ and the Boer-Mulders function.