A practical approach to the problem of the missing imaginary part of the handbag diagram in the confined Bethe-Salpeter framework

In the confined Bethe-Salpeter (BS) methods, the quark propagator is an entire function. Hence, the imaginary part of the handbag diagram disappears, leading to a problem of the vanishing parton distribution function (PDF). In contrast, the direct calculation of the light-cone (LC) momentum distribution does give a non-vanishing result even in the confined BS framework. We consider their precise relation and difference, and propose to use the latter as a practical approach to this problem. Our formalism is general enough to be applied to various effective models.