Abstract
Light-front wave functions motivated by holographic constructions are used to study Bloom-Gilman duality, a feature of deep inelastic scattering. Separate expressions for structure functions in terms of quark and hadronic degrees of freedom (involving transition form factors) are presented, with an ultimate goal of obtaining a relationship between the two expressions. A specific two-parton model is defined and resonance transition form factors are computed using previously derived light-front wave functions. A new form of global duality (integral over all values of $x$ between 0 and 1) is derived from the valence quark-number sum rule. Using a complete set of hadronic states is necessary for this new global duality to be achieved, and the previous original work does not provide such a set. This feature is remedied by amending the model to include a longitudinal confining potential, and the resulting complete set is sufficient to carry out the study of Bloom-Gilman duality. Specific expressions for transition form factors are obtained and all are shown to fall as $1/{Q}^{2}$, at asymptotically large values. This is because the Feynman mechanism dominates the asymptotic behavior of the model. These transition form factors are used to assess the validity of the global and local duality sum rules, with the result that both are not satisfied within the given model. Evaluations of the hadronic expression for $q(x,{Q}^{2})$ provide more details about this lack. This result is not a failure of the current model because it shows that the observed validity of both global and local forms of duality for deep inelastic scattering must be related to a feature of QCD that is deeper than completeness. Our simple present model suggests a prediction that Bloom-Gilman duality would not be observed if deep inelastic scattering experiments were to be made on the pion. The underlying origin of the duality phenomenon in deep inelastic scattering is deeply buried within the confinement aspects of QCD, and its origin remains a mystery.
Highlights
Two distinct facets of QCD are known
We focus on deep-inelastic scattering from hadrons
Nonrelativistic potential models can describe or represent confining systems with an infinite number of bound states, thereby indicating how it is that Bloom-Gilman scaling may arise, but are not properly relativistic
Summary
Two distinct facets of QCD are known. At asymptotically high energies and momentum transfers Q2 many hadronic observables can be computed using quarks and gluons as degrees of freedom and applying perturbation theory. Nonrelativistic potential models can describe or represent confining systems with an infinite number of bound states, thereby indicating how it is that Bloom-Gilman scaling may arise, but are not properly relativistic This means that none obtain Lorentz invariant quark distributions that have the correct support properties of being nonzero only in the region where Bjorken x varies between 0 and 1. We aim to understand Bloom-Gilman duality by using relativistic light-front wave functions obtained from lightfront holographic QCD, an approach defined in the review [19] that provides a relativistic treatment of confined systems. It is remarkable that in the semiclassical approximation described above, the light-front Hamiltonian has a structure which matches exactly the eigenvalue equations in anti–de Sitter (AdS) space [19] This offers the possibility to explicitly connect the AdS wave function ΦðzÞ to the internal constituent structure of hadrons.
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