Ralf W. Gothe

Developing an understanding of phenomena driven by the emergence of hadron mass (EHM) is one of the most challenging problems in the Standard Model. This discussion focuses on the impact of results on nucleon resonance ($N^{*}$) electroexcitation amplitudes (or ${\gamma }_{v}p{N}^{*}$ electrocouplings) obtained from experiments during the 6 GeV era in Hall B at Jefferson Lab on understanding EHM. Analyzed using continuum Schwinger function methods (CSMs), these results have revealed new pathways for the elucidation of EHM. A good description of the $\Delta \left(1232\right)3/2^{+}$, $N\left(1440\right)1/2^{+}$, and $\Delta \left(1600\right)3/2^{+}$ electrocouplings, achieved by CSM analyses that express a realistic dressed quark mass function, sheds light on the strong interaction dynamics underlying EHM. Extensions to $N^{*}$ studies for higher-mass states are outlined, as well as experimental results anticipated in the 12 GeV era at Jefferson Lab and those that would be enabled by a further increase in the beam energy to 22 GeV.

The electroexcitation amplitudes or ${\gamma }_{v}p{N}^{*}$ electrocouplings of the $N\left(1440\right)1/2^{+}$, $N\left(1520\right)3/2^{-}$, and $\mathrm{\Delta }\left(1600\right)3/2^{+}$ resonances were obtained for the first time from the $ep\to e^{\prime }{\pi }^{+}{\pi }^{-}{p}^{\prime }$ differential cross sections measured with the CLAS detector at Jefferson Lab within the range of invariant mass $W=1.4\text{–}1.7$ GeV of the final state hadrons, for photon virtualities $Q^2=2.0\text{–}5.0$ ${\mathrm{GeV}}^2$. A good description of the nine independent onefold differential ${\gamma }_{v}p\to {\pi }^{+}{\pi }^{-}{p}^{\prime }$ cross sections achieved within the data-driven Jefferson Lab-Moscow State University (JM) meson-baryon reaction model in each bin of ($W,Q^2$) allows for separation of the resonant and nonresonant contributions. The electrocouplings were determined in the fits of the ${\pi }^{+}{\pi }^{-}p$ cross sections within three overlapping $W$ intervals with a substantial contribution from each of the three resonances listed above. Consistent results on the electrocouplings extracted from the data in these $W$ intervals provide evidence for their reliable extraction. These studies extend information on the electrocouplings of the $N\left(1440\right)1/2^{+}$ and $N\left(1520\right)3/2^{-}$ available from this channel over a broader range of $Q^2$. The electrocouplings of the $\mathrm{\Delta }\left(1600\right)3/2^{+}$, which decays preferentially into $\pi \pi N$ final states, have been determined for the first time. The reliable extraction of the electrocouplings for these states is also supported by the description of the ${\pi }^{+}{\pi }^{-}p$ differential cross sections with $Q^2$-independent masses and total/partial hadronic decay widths into the $\pi \mathrm{\Delta }$ and $\rho p$ final states.

Understanding the strong interaction dynamics that govern the emergence of hadron mass (EHM) represents a challenging open problem in the Standard Model. In this paper we describe new opportunities for gaining insight into EHM from results on nucleon resonance ($N^{*}$) electroexcitation amplitudes (i.e., ${\gamma }_{v}p{N}^{*}$ electrocouplings) in the mass range up to 1.8 GeV for virtual photon four-momentum squared (i.e., photon virtualities $Q^2$) up to 7.5 GeV${}^2$ available from exclusive meson electroproduction data acquired during the 6-GeV era of experiments at Jefferson Laboratory (JLab). These results, combined with achievements in the use of continuum Schwinger function methods (CSMs), offer new opportunities for charting the momentum dependence of the dressed quark mass from results on the $Q^2$-evolution of the ${\gamma }_{v}p{N}^{*}$ electrocouplings. This mass function is one of the three pillars of EHM and its behavior expresses influences of the other two, viz. the running gluon mass and momentum-dependent effective charge. A successful description of the $\Delta \left(1232\right)3/2^{+}$ and $N\left(1440\right)1/2^{+}$ electrocouplings has been achieved using CSMs with, in both cases, common momentum-dependent mass functions for the dressed quarks, for the gluons, and the same momentum-dependent strong coupling. The properties of these functions have been inferred from nonperturbative studies of QCD and confirmed, e.g., in the description of nucleon and pion elastic electromagnetic form factors. Parameter-free CSM predictions for the electrocouplings of the $\Delta \left(1600\right)3/2^{+}$ became available in 2019. The experimental results obtained in the first half of 2022 have confirmed the CSM predictions. We also discuss prospects for these studies during the 12-GeV era at JLab using the CLAS12 detector, with experiments that are currently in progress, and canvass the physics motivation for continued studies in this area with a possible increase of the JLab electron beam energy up to 22 GeV. Such an upgrade would finally enable mapping of the dressed quark mass over the full range of distances (i.e., quark momenta) where the dominant part of hadron mass and $N^{*}$ structure emerge in the transition from the strongly coupled to perturbative QCD regimes.