Abstract
Examining the evolution of the maximum of valence quark distribution, qV, weighted by Bjorken x, h(x,t)≡xqV(x,t), it is observed that h(x,t) at the peak becomes a one-parameter function; h(xp,t)=Φ(xp(t)), where xp is the position of the peak, t=logQ2, and Q2 is the resolution scale. This observation is used to derive a new model-independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in xp to the quantum chromodynamics (QCD) evolution equation through the xp derivative of the logarithm of the function Φ(xp(t)). A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the Φ(xp(t))=h(xp,t)=CeDxp(t) for leading to next-to-next leading order approximations of PDFs for the range of Q2, covering four orders in magnitude. The exponent, D, of the observed “height-position” correlation function converges with the increase in the order of approximation. This result holds for all the PDF sets considered. A similar relation is observed also for the pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed “height-position” correlation is used also to indicate that no finite number of exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed Q2.
Highlights
Physics 2021, 3, 913–923. https://Valence quarks play a unique role in the quatum chromodynamics (QCD) structure of hadrons
Observation of new properties and relations in valence quark distributions is significant since it allows one to constrain models aimed at describing the dynamics of quantum chromodynamics (QCD) interaction
The observed “height-position” correlation of the peak of the h( x, t) function in the nucleon is a combination of two effects: the dynamics that generate the partonic distribution of valence quarks at given Q2 and the QCD evolution that shifts the strength of the distribution towards smaller x
Summary
Valence quarks play a unique role in the quatum chromodynamics (QCD) structure of hadrons. Even if lattice calculations can reproduce the major characteristics of valence quark distributions, these calculations do not necessarily result in a qualitative understanding of the underlying processes In this respect, observation of new properties and relations in valence quark distributions is significant since it allows one to constrain models aimed at describing the dynamics of QCD interaction. The focus of the present study is on one of the most distinguishable characteristics of valence quarks, which is the distribution, qV ( x, Q2 ), of valence quarks weighted by momentum fraction x, h( x, t) ≡ xqV ( x, t) exhibits a clear peak This peak is a hallmark for the bound system of conserved number fermions (no such peak exists for sea quark distribution) and is characterized by the height, h( x p ), and the position, x p , both of which evolve with the resolution scale, Q2. The implications that Equation (3) may have on partonic distributions of valence quarks is explored
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