Probing the Gluon Sivers Function with an Unpolarized Target: GTMD Distributions and the Odderons.

It is commonly believed that the Sivers function has uniquely to do with processes involving a transversely polarized nucleon. In this Letter we show that this is not necessarily the case. We demonstrate that exclusive pion production in unpolarized electron-proton scattering in the forward region is a direct probe of the gluon Sivers function due to its connection to the QCD odderon.