Describing the nucleon and its form factors at high q**2

TL;DR

This paper investigates the calculation of nucleon form factors at high momentum transfer using non-relativistic quark models, emphasizing numerical methods' reliability and the asymptotic behavior of form factors.

Contribution

It compares hyperspherical and Faddeev approaches, highlighting the importance of including sufficient partial waves to accurately reproduce the expected asymptotic behavior.

Findings

Faddeev solutions yield the correct q^{-8} behavior.

Hypercentral approximation leads to q^{-7} behavior.

Convergence issues affect results at high q^2.

Abstract

The nucleon form factors are calculated using a non-relativistic description in terms of constituent quarks. The emphasis is put on the reliability of present numerical methods used to solve the three-body problem in order to correctly reproduce the expected asymptotic behavior of form factors. Nucleon wave functions obtained in the hyperspherical formalism or employing Faddeev equations have been considered. While a q**(-8) behavior is expected at high q for a quark-quark force behaving like 1/r at short distances, it is found that the hypercentral approximation in the hyperspherical formalism (K=0) leads to a q**(-7) behavior. An infinite set of waves is required to get the correct behavior. Solutions of the Faddeev equations lead to the q**(-8) behavior. The amplitude of the corresponding term however depends on the number of partial waves retained in the Faddeev amplitude. The convergence to the asymptotic behavior has also been studied. Sizeable departures are observed in some cases at squared momentum transfers as high as 50 (GeV/c)**2. It is not clear whether these departures are of the order 1/q or 1/q**2 log q relatively to the dominant contribution and whether the bad convergence results from truncations in the calculations. From a comparison with the most complete Faddeev results, a q**2 validity range is obtained for the calculation made in the hyperspherical formalism or in the Faddeev approach with the minimum number of amplitudes.