Parton distribution functions from reduced Ioffe-time distributions

We show that the correct way to extract parton distribution functions from the reduced Ioffe-time distribution, a ratio of the Ioffe-time distribution for a moving hadron and a hadron at rest, is through a factorization formula. This factorization exists because, at small distances, forming the ratio does not change the infrared behavior of the numerator, which is factorizable. We illustrate the effect of such a factorization by applying it to results in the literature.

Figure 1

Valence distribution $u_v(x)-d_v(x)$ extracted from the data in Ref. [56]. The solid blue curve is the CJ15 global fit [66], and the dashed green curve is the result of Ref. [56] by a fitting to the RITD $M(\nu ,z^2,\mu )$, where the authors ignored the factorization converting $M(\nu ,z^2,\mu )$ to $M(\nu ,0,\mu )$. The dashed red curve is the result obtained using the factorization formula, Eq. (10). The data points we use are extracted from the figures of Ref. [56].