Nucleon and pion distribution functions in the valence region

Abstract

We provide an experimental and theoretical perspective on the behavior of unpolarized distribution functions for the nucleon and pion on the valence-quark domain; namely, Bjorken-x > ∼ 0.4. This domain is key to much of hadron physics; e.g., a hadron is defined by its flavor content and that is a valence-quark property. Furthermore, its accurate parametrization is crucial to the provision of reliable input for large collider experiments. We focus on experimental extractions of distribution functions via electron and muon inelastic scattering, and from Drell-Yan interactions; and on theoretical treatments that emphasize an explanation of the distribution functions, providing an overview of major contemporary approaches and issues. Valence-quark physics is a compelling subject, which probes at the heart of our understanding of the Standard Model. There are numerous outstanding and unresolved challenges, which experiment and theory must confront. In connection with experiment, we explain that an upgraded Jefferson Lab facility is well-suited to provide new data on the nucleon, while a future electron ion collider could provide essential new data for the mesons. There is also great potential in using Drell-Yan interactions, at FNAL, J-PARC and GSI, to push into the large-x domain for both mesons and nucleons. We argue furthermore that explanation, in contrast to modeling and parametrization, requires a widespread acceptance of the need to adapt theory: to the lessons learnt already from the methods of nonperturbative quantum field theory; and a fuller exploitation of those methods. * Electronic address: holt@anl.gov † Electronic address: cdroberts@anl.gov

Features and flaws of a contact interaction treatment of the kaon

“…The parameter value c l = 0.095 was chosen in order to satisfy Eq. (10). The lower panel shows that such nonanalyticities rapidly become immaterial when considering the evolution of form factors into the domain Q 2 > 0 [53].…”

“…This window on SU (3)-flavour symmetry breaking therefore provides direct access to both explicit and dynamical effects in a wide variety of domains. For example: the mass formulae for pseudo-Goldstone bosons involve both current-quark masses and order parameters for DCSB [8,9]; and the ratio of kaon and pion valence-u-quark distribution functions provides access to a renormalisation scale invariant ratio of DCSB order parameters [10,11].…”

Confinement contains condensates

“…[25]. Amongst its weaknesses, the model is not Poincaré covariant and hence not symmetry preserving; it is not confining, the understanding of which is critical to the realization of in-hadron condensates; it does not treat mesons and baryons on an equal footing, with, e.g., pseudoscalar and scalar mesons being pointlike but the nucleon having nonzero extent; it is not applicable to all mesons and baryons, e.g., requiring material amendment if a description of vector-and higher-mass-mesons is to be attempted; and it produces valence-quark distribution functions in marked disagreement with QCD [70]. In addition to these factors, the analysis in Ref.…”

“…The DSE framework expresses the results of perturbative QCD and provides a unified treatment of, amongst other things: meson and baryon spectra [43,62]; hadron electromagnetic elastic and transition form factors [63][64][65]; meson-meson scattering [66][67][68]; and the distribution functions that arise in analyses of deep inelastic scattering [69][70][71][72]. The expression and realization of in-hadron condensates has most widely been elucidated within this framework precisely because it is applicable to all hadrons and treats all hadrons equally; viz., as Poincaré-covariant bound-states of confined, dressedpartons.…”

Interplay of threshold resummation and hadron mass corrections in deep inelastic processes

“…As it turns out, it is precisely this region that is particularly relevant at the LHC, when trying to find signals of new physics in, for example, (di-)jet measurements [9]. Furthermore, the large-x region is also interesting as it can provide a window into the non-perturbative dynamics of the color confinement mechanism holding quarks and gluons inside hadrons [10,11].…”