Roper Resonance Structure and Exploration of Emergent Hadron Mass from CLAS Electroproduction Data

TL;DR

The paper investigates the N(1440)1/2^+ (Roper) resonance using exclusive CLAS electroproduction data to test how hadron mass and resonance structure emerge from QCD. It uses independent analyses of $ ext{πN}$ and $ ext{π}^+ ext{π}^-p$ channels within the Continuum Schwinger Method, revealing a two-component structure: a three-dressed-quark core plus a meson–baryon cloud, with the quark core dominating the $Q^2>2$ GeV$^2$ regime. It shows resonance parameters extracted from $ ext{π}^+ ext{π}^-p$ fits are $Q^2$-independent, consistent with an $s$-channel quark-core excitation, while dynamical-generation pictures from HEFT+LQCD remain contentious. The work demonstrates that more than $98 ext{%}$ of hadron mass is emergent from strong QCD dynamics and maps the $Q^2$ evolution of the dressed-quark mass function, guiding prospects for CLAS12 and a CEBAF upgrade to extend measurements up to $Q^2\,\sim\$30 GeV$^2$.

Abstract

The $N(1440)1/2^+$ nucleon resonance, first identified in 1964 by L.D. Roper and collaborators in analyses of $πN$ hadroproduction data have continued to provide pivotal insights that serve to advance our understanding of nucleon excited states. In this contribution, we present results from studies of the structure of the Roper resonance based on exclusive $πN$ and $π^+π^-p$ electroproduction data measured with the CLAS detector at Jefferson Lab. These analyses have revealed the Roper resonance as a complex interplay between an inner core of three dressed quarks and an external meson--baryon cloud. Analyses of the CLAS results on the evolution of the Roper resonance electroexcitation amplitudes with photon virtuality $Q^2$, within the framework of the Continuum Schwinger Method, have conclusively demonstrated the capability to gain insight into the strong interaction dynamics responsible for generating more than 98\% of hadron mass. Further extension of such studies to higher $Q^2$--through experiments currently underway with the CLAS12 detector and in the future with a potential CEBAF energy upgrade to 22 GeV--offers the only foreseeable opportunity to explore the full range of distances where the dominant portion of hadron mass and resonance structure emerges.

Figures (8)

• Figure 1: The $\gamma_vpN^*$ electrocouplings for the $N(1440)1/2^+$ obtained from independent studies of $\pi N$ (red circles) Aznauryan:2011qjAznauryan:2009mx and $\pi^+\pi^-p$ (green triangles and magenta diamonds) Mokeev:2015ldaMokeev:2012vsa electroproduction off protons. The photocouplings (in blue) are taken from Refs. CLAS:2009tyzParticleDataGroup:2024cfk.
• Figure 2: Comparison of the $A_{1/2}$ electrocouplings of the $N(1440)1/2^+$ (see Fig. \ref{['roper_coupl_exp']} for details) to the computation from CSM Segovia:2015hra (black solid line). The descriptions achieved within light--front quark models are also shown that i) implement a phenomenological momentum--dependent dressed quark mass Aznauryan:2018okk (black dashed line) and ii) account for both an inner core of three constituent quarks and an external meson--baryon cloud Obukhovsky:2011sc (blue dashed line).
• Figure 3: Faddeev equation for computation of the masses and wavefunctions of the quark core of the ground and excited states of the nucleon. The kernel for the matrix--valued integral equations is represented by the blue area.
• Figure 4: (Left) CSM predictions for the momentum ($k=\sqrt{k^2}$) dependence of the dressed gluon (solid blue curve) and quark (dot--dashed green) mass functions in the chiral limit Roberts:2020hiwRoberts:2021xnzRoberts:2021nhw. For the quark, the associated band expresses existing uncertainties in the CSM predictions. (Right) CSM prediction Cui:2019dwv for the momentum dependence of the process--independent QCD running coupling, $\hat{\alpha}(k)$ (purple curve and associated uncertainty band, which includes uncertainties associated with the gluon mass function) compared with empirical results Deur:2022msf for the process--dependent effective charge defined via the Bjorken sum rule. The vertical yellow band marks the window of sQCD $\leftrightarrow$ pQCD transition in the running coupling. (A complete discussion of effective charges is available elsewhere Deur:2023dzc. All sources of the data in the right panel are listed in Refs. Deur:2023dzcDeur:2022msf.)
• Figure 5: CSM description of resonance electroexcitation amplitudes Barabanov:2020jvnBurkert:2017djoCloet:2013jyaSegovia:2014azaSegovia:2015hra. All diagrams describe the transition $p \to$ dressed quark plus interacting diquark correlations $\to$$N^*$. The Faddeev amplitudes for the transitions between dressed quark + diquark configurations and the ground or excited states of the nucleon correspond to the proton, $\psi_p$, or $N^*$, $\psi_{N^*}$, wavefunctions, respectively.