A major experimental program is presently underway worldwide to determine the fundamental nonperturbative functions, the Sivers, Boer-Mulders and transversity distributions, which are vital for an understanding of the internal structure of the nucleon. However, at present, many simplifying assumptions are used in extracting these functions from the data. We demonstrate that if the binning of the data in $Q^2$ is small enough so that $Q^2$ evolution can be neglected inside a bin, then one can obtain stringent tests of these assumptions. Failure to satisfy these tests implies that the presently extracted nonperturbative functions are unreliable. To this end, we consider the measurement of the Sivers, Boer-Mulders and transversity difference asymmetries for hadrons with opposite charges in SIDIS reactions with unpolarized and transversely polarized deuteron and proton targets: $l+N\to l^{\prime }+h+X$, $h={\pi }^{\pm }$, $K^{\pm }$, $h^{\pm }$. Utilizing only charge and isospin invariance, and applying the above mentioned simplifying assumptions, we obtain several testable relations amongst the measured asymmetries. If these tests are satisfied, then the measured asymmetries determine two different combinations of the valence-quark transverse-momentum-dependent distributions, which can be determined separately without any contributions from the strange and other sea quarks.

• Received 7 July 2015

DOI:https://doi.org/10.1103/PhysRevD.92.114004