Boer-Mulders Functions - A Test of the Assumptions Made in Their Determination

At present, the Boer-Mulders function for a given quark flavour is extracted from data on semi-inclusive deep inelastic scattering using the simplifying assumption that it is proportional to the Sivers function for that flavour. In a recent paper we suggested that the consistency of this assumption could be tested using information on so-called difference asymmetries i.e. the difference between the asymmetries in the production of particles and their anti-particles. Here, using the COMPASS deuteron data on the < cos phi(h)>, < cos 2 phi(h)> and Sivers difference asymmetries, we carry out two independent consistency tests of the assumption of proportionality, but now applied to the sum of the valence-quark contributions. Our analysis shows that such an assumption is compatible with the data. However, we show that the proportionality assumptions made in the existing parametrizations of the Boer-Mulders functions are not compatible with our analysis, which suggests that the published results for the Boer-Mulders functions for individual flavours are unreliable. We have also determined the kinematical Cahn contribution, both directly from a fit to the data (as far as we know for the first time) and from a calculation.