Abstract
At present, the Boer-Mulders (BM) function for a given quark flavour 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 flavour. 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 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 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 flavours are unreliable. The $\langle\cos\phi_h\rangle$ and $\langle\cos 2 \phi_h\rangle$ 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.
Highlights
There is a major effort at present to progress beyond a knowledge of collinear parton distribution functions (PDFs) and fragmentation functions (FFs) and to obtain information about the transverse momentum dependent (TMD) versions of these functions
In our recent paper [2], we showed that the difference asymmetries in semiinclusive deep inelastic scattering (SIDIS) allow the determination of the valence quark TMDs in a model-independent way, without any assumptions about the sea quark or gluon densities
We had shown previously [2] that data on difference asymmetries allow one to test the assumed relation of proportionality between the BM and Sivers functions, which is currently used in the extraction of the BM function from data
Summary
There is a major effort at present to progress beyond a knowledge of collinear parton distribution functions (PDFs) and fragmentation functions (FFs) and to obtain information about the transverse momentum dependent (TMD) versions of these functions In extracting these distributions from data, a standard parametrization is usually adopted (see for example [1]), which involves various simplifying assumptions. We use COMPASS SIDIS measurements of the hcos φhi, hcos 2φhi and Sivers asymmetries on a deuteron target to test for the consistency of the assumed relation between BM and Sivers functions. IV, we formulate the two tests for the assumed relation between the BM and Sivers functions They are based on the hcos φhi and hcos 2φhi azimuthal asymmetries of the final hadrons in unpolarized SIDIS, and the Sivers asymmetry for unpolarized leptons on transversely polarized nucleons. V, we apply these tests using the COMPASS SIDIS data on deuterons
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