Locality of quark-hadron duality and deviations from quark counting rules above resonance region

We show how deviations from the dimensional scaling laws for exclusive processes may be related to a breakdown in the locality of quark-hadron duality. The essential principles are illustrated in a pedagogic model of a composite system with two spinless charged constituents, for which a dual picture for the low-energy resonance phenomena and high-energy scaling behavior can be established. We introduce the concept of "restricted locality" of quark-hadron duality and show how this results in deviations from the pQCD quark counting rules above the resonance region. In particular it can be a possible source for oscillations about the smooth quark counting rule, as seen e.g. in the 90-degree differential cross sections for $\gamma p\to \pi^+ n$.Comment: The way to present Eqs. (2), (4), (7) are changed while physics contents and calculations are left intact; Additional explanations for the forward and large-angle duality are added; Three more references are included; Version to appear on Phys. Rev. Let

Measurements of the Separated Longitudinal Structure Function FL From Hydrogen and Deuterium Targets at Low Q2

Structure functions, as measured in lepton-nucleon scattering, have proven to be very useful in studying the partonic dynamics within the nucleon. However, it is experimentally difficult to separately determine the longitudinal and transverse structure functions, and consequently there are substantially less data available in particular for the longitudinal structure function. Here, we present separated structure functions for hydrogen and deuterium at low four-momentum transfer squared, Q2 \u3c 1GeV2, and compare them with parton distribution parametrization and kT factorization approaches. While differences are found, the parametrizations generally agree with the data, even at the very low-Q2 scale of the data. The deuterium data show a smaller longitudinal structure function and a smaller ratio of longitudinal to transverse cross section, R, than the proton. This suggests either an unexpected difference in R for the proton and the neutron or a suppression of the gluonic distribution in nuclei

Local Duality Predictions for x ~ 1 Structure Functions

Recent data on the proton F_2 structure function in the resonance region suggest that local quark-hadron duality works remarkably well for each of the low-lying resonances, including the elastic, to rather low values of Q^2. We derive model-independent relations between structure functions at x ~ 1 and elastic electromagnetic form factors, and predict the x -> 1 behavior of nucleon polarization asymmetries and the neutron to proton structure function ratios from available data on nucleon electric and magnetic form factors.Comment: 10 pages, 2 figures, typos in Eq. (2) correcte

The quantum states for Hydrogen atom: spherical harmonics and the orbitals geometrical representation

Our work utilizes the quantum model of the hydrogen atom which is based on the Schrödinger equation with Coulomb potential. Specifically, we concentrate on the angular components of the wave eigenfunctions derived from this model. We consider the quantum states with n ≤ 4. In order to visualize the orbital shapes of these states, we built in the spherical coordinates system their 3D geometric representations. Furthermore, we use the corresponding spherical harmonics, to calculate the θ nodal values that describe the configurations of these orbital states

Separated Kaon Electroproduction Cross Section and the Kaon Form Factor from 6 GeV JLab Data

The $^{1}H$($e,e^\prime K^+$)$\Lambda$ reaction was studied as a function of the Mandelstam variable $-t$ using data from the E01-004 (FPI-2) and E93-018 experiments that were carried out in Hall C at the 6 GeV Jefferson Lab. The cross section was fully separated into longitudinal and transverse components, and two interference terms at four-momentum transfers $Q^2$ of 1.00, 1.36 and 2.07 GeV$^2$. The kaon form factor was extracted from the longitudinal cross section using the Regge model by Vanderhaeghen, Guidal, and Laget. The results establish the method, previously used successfully for pion analyses, for extracting the kaon form factor. Data from 12 GeV Jefferson Lab experiments are expected to have sufficient precision to distinguish between theoretical predictions, for example recent perturbative QCD calculations with modern parton distribution amplitudes. The leading-twist behavior for light mesons is predicted to set in for values of $Q^2$ between 5-10 GeV$^2$, which makes data in the few GeV regime particularly interesting. The $Q^2$ dependence at fixed $x$ and $-t$ of the longitudinal cross section we extracted seems consistent with the QCD factorization prediction within the experimental uncertainty

Off mass shell dual amplitude with Mandelstam analyticity

A model for the $Q^2$-dependent dual amplitude with Mandelstam analyticity (DAMA) is proposed. The modified DAMA (M-DAMA) preserves all the attractive properties of DAMA, such as its pole structure and Regge asymptotics, and leads to a generalized dual amplitude $A(s,t,Q^2)$. This generalized amplitude can be checked in the known kinematical limits, i.e. it should reduce to the ordinary dual amplitude on mass shell, and to the nuclear structure function when $t=0$. In such a way we complete a unified "two-dimensionally dual" picture of strong interaction. By comparing the structure function $F_2$, resulting from M-DAMA, with phenomenological parameterizations, we fix the $Q^2$-dependence in M-DAMA. In all studied regions, i.e. in the large and low $x$ limits as well as in the resonance region, the results of M-DAMA are in qualitative agreement with the experiment.Comment: 20 pages, 3 figures; to appear in Phys.Atom.Nuc

Scaling study of the pion electroproduction cross sections and the pion form factor

The $^{1}$H($e,e^\prime \pi^+$)n cross section was measured for a range of four-momentum transfer up to $Q^2$=3.91 GeV$^2$ at values of the invariant mass, $W$, above the resonance region. The $Q^2$-dependence of the longitudinal component is consistent with the $Q^2$-scaling prediction for hard exclusive processes. This suggests that perturbative QCD concepts are applicable at rather low values of $Q^2$. Pion form factor results, while consistent with the $Q^2$-scaling prediction, are inconsistent in magnitude with perturbative QCD calculations. The extraction of Generalized Parton Distributions from hard exclusive processes assumes the dominance of the longitudinal term. However, transverse contributions to the cross section are still significant at $Q^2$=3.91 GeV$^2$.Comment: 6 pages, 3 figure