Abstract
The valence-quark distribution function of the pion has been of interest for decades; particularly, the profile it should adopt when (the large-x behavior) has been the subject of a long-standing debate. In the light-front holographic QCD (LFHQCD) approach, this behavior is controlled by the so-called reparametrization function, , which is not fully determined from first principles. We show that, owing to the flexibility of , the large-x profile can be contained within the LFHQCD formalism. This is in contrast to a previous LFHQCD study (Guy F. de Teramond et al., Phys. Rev. Lett., 120(18), 2018) in which was 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.
Highlights
The valence-quark distribution function of the pion has been of interest for decades; the profile it should adopt when x → 1 is subject of a long-standing debate
Those patterns are further supported by perturbative Quantum Chromodynamics [6,7,8]
Given the simplicity of Eq (22), we propose the following rules for the parton distribution function (PDF): Rule-I : (1 − x)2τ−3, with g(τ ) = 2
Summary
The valence-quark distribution function of the pion has been of interest for decades; the profile it should adopt when x → 1 (the large-x behavior) is subject of a long-standing debate. Their findings yielded the so-called Drell-Yan-West relation (DYW), which entails that, when the momentum transfer (−t = Q2) becomes asymptotically large, the proton electromagnetic form factor (EFF) decays as While the corresponding parton distribution function (PDF) exhibits the large-x (i.e., x → 1) behavior of up(x) ∼ (1 − x)2τ−3 .
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