Tests of the extraction of the Sivers, Boer-Mulders and transversity distributions in SIDIS reactions

A major experimental program is presently underway worldwide to determine the fundamental non-perturbative 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 non-perturbative 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'+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.