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At present, the Boer-Mulders (BM) function for a given quark flavour isextracted from data on semi-inclusive deep inelastic scattering (SIDIS) usingthe simplifying assumption that it is proportional to the Sivers function forthat flavour. In a recent paper we suggested that the consistency of thisassumption could be tested using information on so-called differenceasymmetries, i.e. the difference between the asymmetries in the production ofparticles and their anti-particles.  In this paper, using the SIDIS COMPASS deuteron data on the$\langle\cos\phi_h\rangle$, $\langle\cos 2 \phi_h\rangle$ and Sivers differenceasymmetries, we carry out two independent consistency tests of the assumptionof proportionality, but here applied to the sum of the valence-quarkcontributions. We find that such an assumption is compatible with the data. Wealso show that the proportionality assumptions made in the existingparametrizations of the BM functions are not compatible with our analysis,which suggests that the published results for the Boer-Mulders functions forindividual flavours are unreliable.  The $\langle\cos\phi_h\rangle$ and $\langle\cos 2 \phi_h\rangle$ asymmetriesreceive contributions also from the, in principle, calculable Cahn effect. Wesucceed in extracting the Cahn contributions from experiment (we believe forthe first time) and compare with their calculated values, with interestingimplications.

Consistency tests for the extraction of the Boer-Mulders and Sivers functions