Tests for Sivers, Boer-Mulders and transversity distributions in difference cross sections in SIDIS

Abstract: A major experimental program is presently underway to determine the Sivers, Boer-Mulders and transversity distributions, vital for understanding the internal structure of the nucleon. To this end we consider the Sivers, Boer-Mulders and transversity azimuthal asymmetries of the difference cross sections of hadrons with opposite charges in SIDIS reactions with unpolarized and transversely polarized target l+N\to l'+h+X, h=\pi^\pm, K^\pm, h^\pm. We show that on deuteron target these asymmetries are particularly simple and determine the sum of the valence-quark Q_V=u_V+d_V transverse momentum dependent distributions without any contributions from the strange or other sea-quark functions. At present, data on these asymmetries are presented for the integrated asymmetries i.e. the x_B- and z_h-dependent asymmetries. If data are available in small bins in Q^2, so that Q^2-dependence can be neglected, these expressions simplify dramatically leading to remarkably simple and powerful tests of the simplifying assumptions used in extracting these functions from the data.