Theoretical investigation of the decay of the $N\left(2120\right)$ resonance to nucleon resonances near 1.7 GeV

Background: Until now the knowledge about nucleon resonances with a mass higher than 2 GeV has been scarce. Huge amounts of experimental data of the multipion photoproduction have been accumulated, and more can be expected in the future in facilities such as JLab 12 GeV. It makes it possible to investigate the decay of a nucleon resonance into another nucleon resonance.

Purpose: The possibility to research the decay of the $N\left(2120\right)$ to nucleon resonances near 1.7 GeV in the three-pion photoproduction will be explored to provide useful information for future experimental study.

Method: The pion and radiative decay amplitudes of nucleon resonances are studied within the constituent quark model, which is used to calculate the couplings constants, especially for the decay of a nucleon resonance near 2.1 GeV to another nucleon resonance near 1.7 GeV. The three-pion photoproduction off the neutron target, i.e.,$\gamma n\to {\pi }^{-}{\pi }^{-}{\mathrm{\Delta }}^{++}\to {\pi }^{-}{\pi }^{-}{\pi }^{+}p$, is investigated based on the effective Lagrangian method with the coupling constant obtained form the decay amplitudes.

Results: The resonance contribution with a state $N{(}^2{P}_M){\frac{3}{2}}^{-}$ near 2.1 GeV decaying to a state $N{(}^4{P}_M){\frac{5}{2}}^{-}$ near 1.7 GeV, i.e., $N\left(2120\right)\to N\left(1675\right)\pi$, is dominant in the process considered. The total cross section from the resonance contribution is at the order of 1 $\mu \mathrm{b}$ and can be easily distinguished from the background.

Conclusions: Our results suggest it is practicable to research the decay of the $N\left(2120\right)$ to the $N\left(1675\right)$ in experiment.

Figure 1

Feynman diagrams for the resonance contribution of $\gamma n\to {\pi }^{-}{\pi }^{-}{\mathrm{\Delta }}^{++}$ reaction.

Figure 2

Feynman diagrams of background contribution for $\gamma n\to {\pi }^{-}{\pi }^{-}{\mathrm{\Delta }}^{++}$ reaction. (a) $t$ channel, (b) contact term.

Figure 3

The total cross section for $\gamma n\to {\pi }^{-}{\pi }^{-}{\mathrm{\Delta }}^{++}$ from the resonance contributions vs the photon-beam energy $P_{\mathrm{lab}}$. Panels (a) and (c) are obtained with variation of widths of higher resonance from 0.25 to 0.45 GeV with the cutoff $\mathrm{\Lambda }=1.0$ GeV; panels (b) and (d) with variation of the cutoff of higher resonance from 0.7 to 1.3 GeV with width $\mathrm{\Gamma }=0.3$ and 0.15 GeV for the higher and lower resonances, respectively.

Figure 4

The total cross section for $\gamma n\to {\pi }^{-}{\pi }^{-}{\mathrm{\Delta }}^{++}$ with width ${\mathrm{\Gamma }}_{N\left(2120\right)}=0.45$ and $0.25$ GeV and cutoff $\mathrm{\Lambda }=1$ GeV. The solid (red), dashed (black), and dotted (blue) lines are for full model, resonance contribution, and background contribution.

Figure 5

The Dalitz plot for the process $\gamma n\to {\pi }^{-}{\pi }^{-}{\mathrm{\Delta }}^{++}$.