Electroexcitation of nucleon resonances of the $[70,1^{-}]$ multiplet in a light-front relativistic quark model

We utilize the light-front relativistic quark model to predict the $3q$ core contribution to the electroexcitation of nucleon resonances of the $[70,1^{-}]$ multiplet on the proton and neutron at $Q^2<5{\mathrm{GeV}}^2$. The investigation is motivated by new experimental data from continuous electron beam accelerator facility large acceptance spectrometer on meson electroproduction for a wide range of the hadronic invariant mass including the full third nucleon resonance region up to $\sqrt{s}=1.8$ GeV. For the states $N\left(1520\right){\frac{3}{2}}^{-},N\left(1535\right){\frac{1}{2}}^{-}$, and $N\left(1675\right){\frac{5}{2}}^{-}$, experimental results on the electroexcitation amplitudes on the proton are available for a wide range of $Q^2$. This allowed us also to quantify the expected meson-baryon contributions to these amplitudes as a function of $Q^2$.

Figure 1

The ${\gamma }^{*}p\to N\left(1535\right){\frac{1}{2}}^{-}$ transition helicity amplitudes. The solid curves are the LF RQM predictions; the weight factors for the $3q$ contributions to the nucleon and resonance are taken into account according to (50) and (53) with $c_{N^{*}}=0.84$ and 0.94 for the mixing angles ${\theta }_S=-16.6^{\circ }$ and $-{32}^{\circ }$, respectively [see (46) and (47)]. The thin dashed-dotted curves present the inferred meson-baryon contributions (see Sec. 4d). Solid circles are the amplitudes extracted from CLAS pion electroproduction data [1]. The open triangles [19] and open boxes [20] are the amplitudes extracted from the JLab/Hall B $\eta$ electroproduction data; the open circles [21] and open crosses [22] are the amplitudes extracted from the JLab/Hall C $\eta$ electroproduction data; the full triangle at $Q^2=0$ is the Review of Particle Physics (RPP) estimate [42].

Figure 2

The ${\gamma }^{*}n\to N\left(1535\right){\frac{1}{2}}^{-}$ transition helicity amplitudes. The legend for the solid curves is as for Fig. 1. The full triangle at $Q^2=0$ is the RPP estimate [42].

Figure 3

The ${\gamma }^{*}p\to N\left(1650\right){\frac{1}{2}}^{-}$ transition helicity amplitudes. The LF RQM predictions are shown by thin and thick solid lines for the mixing angles ${\theta }_S=0^{\circ }$ and $-16.6^{\circ }$, respectively, and by thick dashed lines for ${\theta }_S=-{32}^{\circ }$ [see (46) and (47)]. The full triangle at $Q^2=0$ is the RPP estimate [42]; open rhombuses are the amplitudes extracted from CLAS $2\pi$ electroproduction data [23].

Figure 4

The ${\gamma }^{*}n\to N\left(1650\right){\frac{1}{2}}^{-}$ transition helicity amplitudes. The legend for the lines is as for Fig. 3. The full triangle at $Q^2=0$ is the RPP estimate [42].

Figure 5

The ${\gamma }^{*}p\to \mathrm{\Delta }\left(1620\right){\frac{1}{2}}^{-}$ transition helicity amplitudes. The solid curves are the LF RQM predictions. The full triangle at $Q^2=0$ is the RPP estimate [42]; open rhombuses are the amplitudes extracted from CLAS $2\pi$ electroproduction data [24].

Figure 6

The ${\gamma }^{*}p\to N\left(1520\right){\frac{3}{2}}^{-}$ transition helicity amplitudes. The solid curves are the LF RQM predictions; the weight factors for the $3q$ contributions to the nucleon and resonance are taken into account according to (50) and (53) with $c_{N^{*}}=0.92$ and 0.94, respectively, for the mixing angles ${\theta }_D=6.3^{\circ }$ and $11.5^{\circ }$ [see (46) and (47)]. The thin dashed curves present our results obtained with $G_3\left(Q^2\right)=0$ (see Sec. 4c). The thin dashed-dotted curves present the inferred meson-baryon contributions (see Sec. 4d). Solid circles are the amplitudes extracted from CLAS pion electroproduction data [1]; open rhombuses are the amplitudes extracted from CLAS $2\pi$ electroproduction data [23, 24, 25]. The full triangles at $Q^2=0$ are the RPP estimates [42].

Figure 7

The ${\gamma }^{*}n\to N\left(1520\right){\frac{3}{2}}^{-}$ transition helicity amplitudes. The legend for the solid and dashed curves is as for Fig. 6. The full triangles at $Q^2=0$ are the RPP estimate [42].

Figure 8

The ${\gamma }^{*}p\to N\left(1700\right){\frac{3}{2}}^{-}$ transition helicity amplitudes. The LF RQM predictions are shown by the thin and thick solid lines for the mixing angles ${\theta }_S=0$ and $11.5^{\circ }$, respectively, and by thick dashed lines for ${\theta }_S=6.3^{\circ }$ [see (46) and (47)]. The full triangles at $Q^2=0$ are the RPP estimates [42].

Figure 9

The ${\gamma }^{*}n\to N\left(1700\right){\frac{3}{2}}^{-}$ transition helicity amplitudes. The legend for the lines and data is as for Fig. 8.

Figure 10

The ${\gamma }^{*}p\to \mathrm{\Delta }\left(1700\right){\frac{3}{2}}^{-}$ transition helicity amplitudes. The solid curves are the LF RQM predictions. The legend for the thin dashed curves is as for Fig. 6. The full triangles at $Q^2=0$ are the RPP estimates [42]; open rhombuses are the amplitudes extracted from CLAS $2\pi$ electroproduction data [23].

Figure 11

The ${\gamma }^{*}p\to N\left(1675\right){\frac{5}{2}}^{-}$ transition helicity amplitudes. The solid curves are the LF RQM predictions. The legend for the thin dashed and dashed-dotted curves is as for Fig. 6. The full triangles at $Q^2=0$ are the RPP estimates [42]; the solid circles are the amplitudes extracted from CLAS $\pi$ electroproduction data [17].

Figure 12

The ${\gamma }^{*}n\to N\left(1675\right){\frac{5}{2}}^{-}$ transition helicity amplitudes. The solid curves are the LF RQM predictions. The legend for the thin dashed curves is as for Fig. 6. The full triangles at $Q^2=0$ are the RPP estimates [42].