Pion Parton Distribution Function in Light-Front Holographic QCD

The valence-quark distribution function of the pion has been of interest for decades; particularly, the profile it should adopt when $x\to 1$ (the large-$x$ behavior) is subject of a long-standing debate. In the light-front holographic QCD (LFHQCD) approach, this behavior is controlled by the so called reparametrization function, $w_{\tau }(x)$, which is not fully determined from first principles. We show that, owing to the flexibility of $w_{\tau }(x)$, the large-$x$ profile $u^{\pi }(x)\sim (1-x{)}^2$ can be contained within the LFHQCD formalism. This is in contrast with a previous LFHQCD study~(Guy F. de Teramond et al., Phys. Rev. Lett., 120(18), 2018) in which $u^{\pi }(x)\sim (1-x{)}^1$ is found instead. Given our observations, augmented by perturbative QCD and recent lattice QCD results, we state that the large-$x$ exponent of “2” cannot be excluded.