${\gamma }^{*}N\to N^{*}(1520)$ form factors in the timelike regime

The covariant spectator quark model, tested before in a variety of electromagnetic baryon excitations, is applied here to the ${\gamma }^{*}N\to N^{*}(1520)$ reaction in the timelike regime. The transition form factors are first parametrized in the spacelike region in terms of a valence quark core model together with a parametrization of the meson cloud contribution. The form factor behavior in the timelike region is then predicted, as well as the $N^{*}(1520)\to \gamma N$ decay width and the $N^{*}(1520)$ Dalitz decay, $N^{*}(1520)\to e^{+}{e}^{-}N$. Our results may help in the interpretation of dielectron production from elementary $pp$ collisions and from the new generation of HADES results using a pion beam. In the $q^2=0–1{\mathrm{GeV}}^2$ range, we conclude that the QED approximation (a $q^2$ independent form factor model) underestimates the electromagnetic coupling of the $N^{*}(1520)$ from 1 up to 2 orders of magnitude. We conclude also that the $N^{*}(1520)$ and $\mathrm{\Delta }(1232)$ Dalitz decay widths are comparable.

Figure 1

${\mathrm{\Gamma }}_{\omega }$ as a function of $q$. The $2\pi$, $3\pi$ channels are indicated by the long-dashed and dotted-dashed lines, respectively. The solid line represents the sum of the two channels. The short-dashed vertical and horizontal lines indicate the $\omega$ mass point and the $\omega$-physical width (8.4 MeV).

Figure 2

Electromagnetic interaction (a) with the quark core and (b) with the meson cloud. The intermediate $N^{*}$ is a octet baryon member (spin $1/2$) or a decuplet baryon member (spin $3/2$).

Figure 3

Valence quark core plus meson cloud contributions to the spacelike form factors as a function of $Q^2=-q^2$. Data come from Ref. [48] (the full circles), Ref. [49] (the empty circles), and PDG [50] (the square).

Figure 4

Absolute values of the form factors for $W=1.520$, 1.800, and 2.100 GeV. In the calculations we use the new parametrization and the width ${\mathrm{\Gamma }}_{\omega }(q^2)$ given by Eq. (4.8). The thin lines represent the contribution from the core. For the total result (the thick lines), the lines for $W=1.520\mathrm{GeV}$ coincide with the lines for $W=1.800$ and 2.100 GeV.

Figure 5

Effective contribution of the form factors $|G_T(q^2,W)|$ for $W=1.520$, 1.800, and 2.100 GeV.

Figure 6

Decay width ${\mathrm{\Gamma }}_{\gamma N}$ as function of $W$. The current model ($\mathrm{Valence}+\text{meson cloud}$) is compared with the constant form factor model and with the results obtained for the $\mathrm{\Delta }(1232)$ (see Ref. [7]).

Figure 7

Dalitz decay width ${\mathrm{\Gamma }}_{e^{+}{e}^{-}N}(q^2,W)$ for $W=1.520$, 1.800, and 2.100 GeV.

Figure 8

Results of $\frac{d\mathrm{\Gamma }}{dq}$ for $W=1.520$, 1.800, and 2.100 GeV (the solid lines) compared to the estimate from the constant form factor model (the dotted lines).

Figure 9

$N^{*}(1520)$ Dalitz decay width as a function of $W$. The result of our model (the solid line) is compared to the result of the constant form factor model (the dotted-dashed line).

Figure 10

$N^{*}(1520)$ decay widths as a function of $W$. Photon and Dalitz decays (the solid lines). The results are also compared to the calculation for the $\mathrm{\Delta }(1232)$ case (the dashed lines).