Modelling the nucleon wave function from soft and hard processes

TL;DR

The paper tackles the mismatch between existing nucleon light-cone wave functions and empirical data on the nucleon's Dirac form factor by constructing a soft-overlap–dominated nucleon wave function. It combines a distribution-amplitude structure $\phi_{123}$ with a Gaussian transverse-momentum profile $\Omega$ and fits two parameters, $f_N$ and $a$, to three constraints: the soft contribution to $F_1^N$ in the modest-$Q^2$ regime, consistency with GRV94 valence quark distributions, and the $J/\psi \to N\bar N$ decay width calculated in the modified perturbative approach. The resulting DA is close to the asymptotic shape but with a modest shift, yielding a physical Feynman contribution that aligns with data, a reasonable valence PDF at large $x$, and a $J/\psi$ width compatible with experiment after accounting for electromagnetic contributions. The work argues against COZ- or AS-like DAs, demonstrating that a simple, two-parameter soft wave function can coherently describe multiple hard and soft observables and illuminate the role of end-point effects in nucleon structure.

Abstract

Current light-cone wave functions for the nucleon are unsatisfactory since they are in conflict with the data of the nucleon's Dirac form factor at large momentum transfer. Therefore, we attempt a determination of a new wave function respecting theoretical ideas on its parameterization and satisfying the following constraints: It should provide a soft Feynman contribution to the proton's form factor in agreement with data; it should be consistent with current parameterizations of the valence quark distribution functions and lastly it should provide an acceptable value for the $\jp \to N \bar N$ decay width. The latter process is calculated within the modified perturbative approach to hard exclusive reactions. A simultaneous fit to the three sets of data leads to a wave function whose $x$-dependent part, the distribution amplitude, shows the same type of asymmetry as those distribution amplitudes constrained by QCD sum rules. The asymmetry is however much more moderate as in those amplitudes. Our distribution amplitude resembles the asymptotic one in shape but the position of the maximum is somewhat shifted.

Figures (5)

• Figure 1: Feynman contributions to Dirac form factor $F_1^p$ using the COZ wave function. The solid (dashed, dotted) line is evaluated with $a = 0.99$ (0.60, 0.45) GeV$^{-1}$. Experimental data ($\circ$) are taken from pff.
• Figure 2: Valence Fock state contributions to the valence quark distribution functions of the proton at $Q^2 = 1$ GeV$^{2}$. The open circles represent the parameterization of Ref. GRV94. The solid and dashed lines represent the contributions of the valence Fock state using a wave function composed of the Gaussian (\ref{['BLHMOmega']}) and either the DA (\ref{['phiFIT']}) or the COZ one ($a = 0.60$ GeV$^{-1}$), respectively. The dotted line is obtained from the AS wave function with $f_N$ and $a$ as for the wave function (\ref{['BLHMOmega']}), (\ref{['phiFIT']}).
• Figure 3: Decay graph $J/\psi \to 3g \to 3 q \bar{q}$. The momenta of the quarks are $x_i p+ k_i$ with $k_i = (0,0,{\bf k}_{\perp i})$, and those of the antiquarks are marked by a prime.
• Figure 4: The DA (\ref{['phiFIT']}) as a function of $x_1$ and $x_3$.
• Figure 5: Feynman contribution to the Dirac form factor of the proton (top) and the neutron (bottom) evaluated from the wave function (\ref{['BLHMOmega']}), (\ref{['phiFIT']}). The dashed line in the upper figure is obtained from the AS wave function with $f_N$ and $a$ as for the wave function (\ref{['BLHMOmega']}), (\ref{['phiFIT']}). Data ($\circ$) are taken from Refs. pffnff.