# Consistency tests for the extraction of the Boer-Mulders and Sivers functions

## TL;DR

This paper tests the common assumption that Boer-Mulders functions are proportional to Sivers functions in SIDIS data, finding that while the assumption holds for valence-quark sums, existing flavor-specific parametrizations are inconsistent with the data.

## Contribution

It introduces two independent consistency tests for the proportionality assumption of Boer-Mulders and Sivers functions using COMPASS data, and challenges the reliability of existing flavor-specific Boer-Mulders parametrizations.

## Key findings

- Proportionality assumption is compatible with valence-quark sum data.
- Existing flavor-specific Boer-Mulders parametrizations are inconsistent with the data.
- First extraction of Cahn contributions from SIDIS asymmetries with comparison to calculations.

## 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.