Form factors in the quark resonance model

Vector and axial form factors in the quark resonance model are analyzed with a combination of theoretical and phenomenological arguments. The new form of form factors is deduced from $\Delta (1232)$ excitation models and available data. The vector part is shown to agree with the resonant contribution to electron-proton inclusive $F_2$ data. The axial part is obtained by finding a simultaneous fit to ANL and BNL $\frac{d\sigma }{d{Q}^2}$ neutrino scattering data. The best fit corresponds to $C_5^A(0)=0.88$ in the Rarita-Schwinger formalism.

Figure 1

Fits to $C_5^A(Q^2)$ with the ANL (black squares) and the BNL (white squares) experimental points. The analytical form of fits are given in Eqs. (52, 53). The fitting procedure is explained in the text.

Figure 2

In the top predictions for $F_2$ for $ep$ scattering in the original FKR model and in the model of this paper for $Q^2=0.225{\mathrm{GeV}}^2$ and $Q^2=1.025{\mathrm{GeV}}^2$ are shown. The data is taken from 26. In the bottom the fractions of the measured strength predicted by both models are presented.

Figure 3

Differential (left and middle figures) $d\sigma /d{Q}^2$ and total cross sections (right figure) for $\nu +p\to {\mu }^{-}+p+{\pi }^{+}$ scattering. In the first figure the data (black squares) is from the ANL experiment [15]. In the second figure the data (white squares) is from the BNL experiment [16, 17]. Theoretical curves are obtained with form factors (58) where $C_5^A(Q^2)$ is given by (53) (solid line) and by (52) (dotted line). The cross sections calculated based on original form factors (57) with $M_A=1.1\mathrm{GeV}$ are denoted by dashed lines. For the differential cross sections the cut on the invariant hadronic mass is imposed $W<1.4\mathrm{GeV}$ whereas for the total cross sections $W<2\mathrm{GeV}$.

Figure 4

Total cross sections for SPP in NC neutrino-nucleon scattering. The data is from the experiments: GGM [33] (black squares) and ANL [34] (white squares). Theoretical curves are obtained with form factors (58) and $C_5^A(Q^2)$ given by (53) (solid line) or by (52) (dotted line). The cross sections calculated based on the original RS form factors (57) with $M_A=1.1\mathrm{GeV}$ are denoted by dashed lines. The cut on the invariant hadronic mass $W<2\mathrm{GeV}$ is imposed.