Nucleon to Roper transition amplitudes and electromagnetic form factors

Abstract

The second excitation of the nucleon, the Roper, has properties differentiated from other low-lying nucleon resonances. Their properties challenge our understanding of the structure of the baryons in terms of the degrees of freedom from QCD. In the present work we discuss the properties of the Roper resonance and the nucleon to Roper electromagnetic transition, based on the quark degrees of freedom, that are expected to dominate for large square momentum transfer $Q^2$. We also discuss the analytic structure of the transition amplitudes in the low-$Q^2$ region, and how the contributions of baryon-meson states can help to describe the low and intermediate $Q^2$ data, and the nature of the Roper.

Figures (6)

• Figure 1: $\gamma^\ast N \to N(1440)$ helicity amplitudes. Calculations from covariant spectator quark model N1440 for $M_R=1.440$ GeV (thick solid line) and $M_R= 1.600$ GeV (thin solid line), and holographic model Roper-AdS1 (dashed line). The data are from JLab/CLAS for one pion production (circles) CLAS09 and two pion production (squares) CLAS12CLAS16aMokeev23a, and PDG 2024 (empty circle) PDG2024. For $S_{1/2}$ we include also a data point from MAMI at $Q^2=0.1$ GeV$^2$ (empty square) Stajner17.
• Figure 2: Calculations of the $\gamma^\ast N \to N^\ast$ helicity amplitudes for the first and second radial excitations of the nucleon. The equivalent amplitudes for the nucleon, $N(940)$, are defined in the main text.
• Figure 3: $\gamma^\ast N \to N(1440)$ transition form factors. Calculations from covariant spectator quark model N1440 for $M_R=1.440$ GeV (thick solid line) and $M_R= 1.600$ GeV (thin solid line), and holographic model Roper-AdS1 (dashed line). The data are from JLab/CLAS for one pion production (circles) CLAS09 and two pion production (squares) CLAS12CLAS16aMokeev23a.
• Figure 4: Holographic calculations of the $\gamma^\ast N \to N(1440)$ form factors, in leading order (nucleon and Roper described as $(qqq)$ states). Calculations from Teramond and Brodsky (dashed dotted line) Teramond12a and from Ref. Roper-AdS1 (variation band). The solid line correspond to the holographic parametrization from Ref. Roper-AdS2. The data are described in Fig. \ref{['fig-Roper-FF1']}.
• Figure 5: Parametrizations of the $\gamma^\ast N \to N(1440)$ amplitudes LowQ2param. The solid line represents the original JLab parametrization Blin19aJLab-website. The data are from JLab/CLAS (circles) CLAS09CLAS12CLAS16a (one and two pion production), and MAMI (empty square) for $S_{1/2}$ ($Q^2=0.1$ GeV$^2$) Stajner17. The vertical dotted line represents the photon point ($Q^2=0$).