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- Title
A Novel Feature of Valence Quark Distributions in Hadrons.
- Authors
Leon, Christopher; Sargsian, Misak M.; Vera, Frank
- Abstract
Examining the evolution of the maximum of valence quark distribution, q V , weighted by Bjorken x, h (x , t) ≡ x q V (x , t) , it is observed that h (x , t) at the peak becomes a one-parameter function; h (x p , t) = Φ (x p (t)) , where x p is the position of the peak, t = log Q 2 , and Q 2 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 x p to the quantum chromodynamics (QCD) evolution equation through the x p derivative of the logarithm of the function Φ (x p (t)) . A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the Φ (x p (t)) = h (x p , t) = C e D x p (t) for leading to next-to-next leading order approximations of PDFs for the range of Q 2 , 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 Q 2 .
- Subjects
VALENCE quark; DEEP inelastic collisions; HADRONS; QUANTUM chromodynamics; FERMIONS
- Publication
Physics (2624-8174), 2021, Vol 3, Issue 4, p913
- ISSN
2624-8174
- Publication type
Article
- DOI
10.3390/physics3040057