At present, the Boer-Mulders (BM) function for a given quark flavor is extracted from data on semi-inclusive deep inelastic scattering (SIDIS) using the simplifying assumption that it is proportional to the Sivers function for that flavor. 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 antiparticles. In this paper, using the SIDIS COMPASS deuteron data on the
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cos
ϕ
h
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,
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2
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h
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and Sivers difference asymmetries, we carry out two independent consistency tests of the assumption of proportionality, but here applied to the sum of the valence-quark contributions. We find that such an assumption is compatible with the data. We also show that the proportionality assumptions made in the existing parametrizations of the BM functions are not compatible with our analysis, which suggests that the published results for the Boer-Mulders functions for individual flavors are unreliable. The
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cos
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and
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cos
2
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h
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asymmetries receive contributions also from the, in principle, calculable Cahn effect. We succeed in extracting the Cahn contributions from experiment (we believe for the first time) and compare with their calculated values, with interesting implications.