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11institutetext: Victor I. Mokeev 22institutetext: Jefferson Laboratory, 12000
Jefferson Ave., Newport News, VA 23602, USA 22email<EMAIL_ADDRESS>33institutetext: Daniel S. Carman 44institutetext: Jefferson Laboratory, 12000
Jefferson Ave., Newport News, VA 23602, USA 44email<EMAIL_ADDRESS>
# Photo- and Electrocouplings of Nucleon Resonances

Victor I. Mokeev  Daniel S. Carman
(for the CLAS Collaboration)

(Received: date / Accepted: date)

###### Abstract

Advances in the exploration of the spectrum and structure of the excited
states of the nucleon from experiments with electromagnetic probes on proton
targets are presented. Impressive progress has been achieved in the studies of
exclusive meson photoproduction in experiments with continuous electron beams
and with detectors of almost $4\pi$ acceptance. The high-quality data, coupled
with the advances in the amplitude analyses of exclusive photo- and
hadroproduction data, allow for the observation of several long-awaited new
baryon states known previously as the “missing” resonances. Studies of
exclusive meson electroproduction in the resonance region with the CLAS
detector at JLab have provided the dominant part of the available world
information on exclusive meson electroproduction observables. These data offer
unique information on the structure of most well-established excited nucleon
states in the mass region up to 1.8 GeV in terms of the evolution of their
electroexcitation amplitudes with momentum transfer of the virtual photon. We
discuss the impact of these results on the insight into the strong interaction
dynamics that underlie the generation of the full spectrum of nucleon
resonances of distinctively different structure. These results shed light on
the emergence of hadron mass, which is one of the most important and still
open problems in the Standard Model. The extension of the nucleon resonance
studies in the experiments of the 12-GeV era at JLab with the CLAS12 detector
are outlined.

##  1 Introduction

Studies of the spectrum and structure of the excited states of the nucleon
(generically referred to here as $N^{*}$s) represent an important part of the
effort to explore the strong interaction dynamics of quantum chromodynamics
(QCD) in the regime of large (comparable with unity) running coupling. This
regime of what is termed strong QCD underlies the generation of hadrons
(mesons and baryons) as bound systems of quarks and gluons Brodsky:2020vco ;
Burkert:2019bhp . The experimental results on the $N^{*}$ spectrum shed light
on the approximate symmetries of strong QCD that are relevant for the
generation of these states. The full $N^{*}$ spectrum, including those states
already observed and those that are still to be discovered, defines the rate
for the transition from the primordial deconfined mixture of quarks and gluons
into the hadron gas phase that took place within the first microseconds after
the Big Bang baz2014a ; bur2020 . In this phase transition, quark-gluon
confinement emerged and the masses of hadrons were generated in close
connection with the dynamical breaking of the approximate chiral symmetry of
QCD. These features define the essence of the strong QCD regime that makes the
studies of the $N^{*}$ spectrum a compelling experimental program to explore
the emergence of hadron matter in the early Universe and the evolution towards
its contemporary status.

Studies of $N^{*}$ structure from the data on the nucleon resonance
electroexcitation amplitudes, the $\gamma_{v}pN^{*}$ electrocouplings, as a
function of the $Q^{2}$, the squared four-momentum transfer of the virtual
photon to the target proton, offer a unique opportunity to explore the many
facets of strong QCD involved in the generation of $N^{*}$s of different
quantum numbers and structural features Burkert:2019bhp ; fbs-carman ; azbu12
; barab20212 . This information has provided critically needed input for the
understanding of strong QCD dynamics and its emergence from the QCD
Lagrangian. Any theoretical approach for the description of hadron structure
with a connection to QCD is required to describe the structure of both the
ground and excited states of the nucleon within a common framework. Studies of
the $\gamma_{v}pN^{*}$ electrocouplings address key open problems of the
Standard Model on the emergence of hadron mass (EHM) and on the nature of
quark-gluon confinement in connection with dynamical chiral symmetry breaking
cdrob20 ; cui20 .

In this lecture the advances of the past decade in the exploration of the
spectrum and structure of the $N^{*}$ states are reviewed. The impact of these
studies on understanding strong QCD dynamics is discussed.

##  2 Manifestation of Nucleon Resonances in Inclusive Hadro-, Photo-, and
Electroproduction Data

The global analyses of the data on inclusive and semi-inclusive electron
scattering off nucleons, Drell-Yan lepton-pair production, $W$/$Z$-boson
asymmetries, and $\gamma$+jet cross sections revealed the structure of the
ground state nucleon as a bound system of a large number of current quarks and
gluons (partons) in relativistic motion moff2021 ; accard2016 . These
constituents are always confined inside the nucleon interior and have never
been observed as free particles. Such a complex composite system should
possess a rich spectrum of excited states.

Figure 1: (Left) Inclusive $\pi N$ cross section as a function of the
invariant mass $W$ of the final state hadrons fully integrated over the final
state kinematic variables crede2013 . (Right) Fully integrated $\gamma_{v}p\to
X$ inclusive cross sections as a function of $W$ and $Q^{2}$ foster1983 . The
nucleon resonances contributing into the first, second, and the third
resonance regions are shown in both figures.

The contributions from nucleon resonances have been observed in total pion-
nucleon cross sections and in inclusive photo- and electroproduction off
proton targets pdg ; foster1983 . In Figs. 1 and 2 these cross sections are
shown as a function of the invariant mass $W$ of the final hadron system or
the incident photon energy $E_{\gamma}$ for photoproduction. The inclusive
$(e,e^{\prime}X)$ electroproduction cross sections were measured over a broad
range of $Q^{2}$. In the $W$-dependence of the measured cross sections,
resonance-like peaks are clearly seen. Their maxima in both the hadro- and
electroproduction data are located at nearly the same $W$-values: 1.23 GeV
(the first resonance region), 1.52 GeV (the second resonance region), and 1.70
GeV (the third resonance region). These features suggest contributions from
$s$-channel resonances in $\pi N$ and $\gamma_{v}p$ collisions. The $\pi N$
channels are sensitive to those resonances with substantial decays to the $\pi
N$ final states. Instead, the photo- and electroproduction channels are
sensitive to the contributions from those $N^{*}$ states with sizable decays
not only to $\pi N$ but also to other final hadron states such as $\eta p$,
$K\Lambda$, $K\Sigma$, $\pi^{+}\pi^{-}p$, etc. The $N^{*}$ studies in both
photo- and electroproduction offer complementary information on the resonance
spectrum and structure in comparison with the hadroproduction studies.

Figure 2: (Left) Fully integrated exclusive meson photoproduction cross
sections in the resonance region as a function of the incident photon energy
beck2017 . (Right) Schematic representation of the meson-baryon
photoproduction amplitudes: the sum of the resonant and non-resonant
contributions is shown in the top row and the hadronic initial/final state
interactions with the open meson-baryon $M^{\prime}B^{\prime}$ and
$M^{\prime}M^{\prime\prime}B$ channels are shown in the bottom row.

Studies of the electroproduction process allow us to explore the structure of
nucleon resonances. The $N^{*}$ electroexcitation amplitudes extracted from
these data as a function of $Q^{2}$ are directly related to the structure of
the $N^{*}$ states. The electroexcitation of nucleon resonances can be fully
described by two transverse electrocouplings, $A_{1/2}(Q^{2})$,
$A_{3/2}(Q^{2})$, and by the longitudinal electrocoupling $S_{1/2}(Q^{2})$.
These electrocouplings are proportional to the helicity amplitudes that
describe the transition between the initial state virtual photon-target proton
and the final $N^{*}$ states for different helicities of the photon and proton
in their center-of-mass (CM) frame. These quantities are unambiguously
determined through the connection of the $N^{*}$ electromagnetic decay widths
to the final states with transversely ($\Gamma_{\gamma}^{T}$) and
longitudinally ($\Gamma_{\gamma}^{L}$) polarized photons at the resonant point
($W=M_{r}$) via:

$\Gamma_{\gamma}^{T}(W=M_{r},Q^{2})=\frac{q^{2}_{\gamma,r}(Q^{2})}{\pi}\frac{2M_{N}}{(2J_{r}+1)M_{r}}\left(|A_{1/2}(Q^{2})|^{2}+|A_{3/2}(Q^{2})|^{2}\right),$
(1)
$\Gamma_{\gamma}^{L}(W=M_{r},Q^{2})=2\frac{q^{2}_{\gamma,r}(Q^{2})}{\pi}\frac{2M_{N}}{(2J_{r}+1)M_{r}}|S_{1/2}(Q^{2})|^{2},$
(2)

with $q_{\gamma,r}=\left.q_{\gamma}\right|_{W=M_{r}}$. Here $M_{r}$ and
$M_{N}$ represent the masses of the $N^{*}$ and ground state nucleon,
respectively, and $J_{r}$ is the $N^{*}$ spin. In these expressions, the
electrocouplings should have dimension [GeV-1/2]. The transverse $A_{1/2}$ and
$A_{3/2}$ couplings at the photon point ($Q^{2}$=0) fully describe nucleon
resonance photoexcitation. The longitudinal $S_{1/2}$ coupling becomes
irrelevant in photoproduction processes for which the flux of longitudinally
polarized photons is zero, owing to gauge invariance of quantum
electrodynamics (QED). Frequently, the absolute values of the $A_{1/2}$,
$A_{3/2}$, and $S_{1/2}$ photo-/electrocouplings are presented after
multiplication by 1000. More details on the nucleon resonance photo- and
electrocouplings can be found in Ref. azbu12 .

Figure 3: (Left) Resonant contributions to the inclusive $F_{2}$ structure
function evaluated from the CLAS results on the $\gamma_{v}pN^{*}$
electrocouplings blin2019 ; blin2021 . The resonant contributions shown are
obtained as the coherent sum of the Breit-Wigner amplitudes (thick, solid
curves) and the incoherent sum of the cross sections from the individual
resonances (thin, solid curves). (Right) The ratio of the $F_{2}$ resonant
contributions to the full inclusive $F_{2}$ as a function of $Q^{2}$ at
$W$-values corresponding to the peak locations in the first, second, and third
resonance regions.

Studies of meson electroproduction in the nucleon resonance region with the
CLAS detector provided the first and only available results on the
electrocouplings of most nucleon resonances in the mass range up to 1.8 GeV
bur2020 ; fbs-carman ; mok2020 . These results allow for the evaluation of the
resonant contributions into inclusive electron scattering from the
experimental data on the electrocouplings blin2019 ; blin2021 ; blin2021a .
The evaluated resonant contributions into the inclusive $F_{2}$ structure
function are shown in Fig. 3. The peak in the first resonance region is mainly
due to the contribution of the well-isolated $\Delta(1232)3/2^{+}$ resonance.
The structures in the second and third resonance regions are generated by
multiple overlapping resonances. The differences in the structure of the
contributing resonances in the three resonance regions result in pronounced
differences in the $Q^{2}$-evolution of the resonant contributions into the
inclusive cross section and structure functions seen in the three resonance
regions. Therefore, studies of the electrocouplings of all prominent nucleon
resonances are critical for gaining insight into the many facets of the
dynamics of strong QCD responsible for the generation of the structure of the
nucleon ground and excited states.

##  3 Facilities for $N^{*}$ Studies in Exclusive Meson Photo- and
Electroproduction

The results shown in Fig. 3 demonstrate that the resonance peaks seen in the
second and third resonance regions are due to several overlapping states. In
order to disentangle their individual contributions, it is important to
explore the different exclusive meson photo- and electroproduction channels
that have selective sensitivity to the different $N^{*}$s. For this purpose,
the differences in the angular distributions of the decay products from the
resonances of different spins and parities can be helpful. This consideration
makes the measurements from detectors of nearly $4\pi$ acceptance of
particular importance. These studies rely upon the exploration of all
prominent exclusive photo- and electroproduction channels with electron beams
of nearly 100% duty factor. The beam duty factor $D$ is defined as the product
of the pulse length and the repetition frequency. The counting rate for
exclusive events $R_{exc}$ and the rate of accidental events $R_{acc}$ are
related to the beam current $i_{b}$ as $R_{exc}\sim i_{b}$,
$R_{acc}\sim(i_{b}/D)^{n_{c}}$, where $n_{c}$ is the number of measured final
state particles in coincidence. Continuous beams of $\sim$100% duty factor are
essential in order to minimize the rate of accidental events, especially in
the exploration of multi-meson exclusive channels. The facilities for $N^{*}$
studies with continuous electron beams and detectors of $\sim$4$\pi$
acceptance for studies of exclusive photo- and electroproduction are listed in
Table 1 ireland2020  and Table 2 azbu12 , respectively.

Facility |  $W$ coverage, | Beam type/Flux | Country
---|---|---|---
| GeV |  |
CLAS/JLab | 1.1-3.0 | Tagged bremsstrahlung | USA
|  | 108 $\gamma$/s | decommissioned
CLAS12/JLab | 1.1-4.0 | Quasi-real photons | USA
|  |  $L$=1035 cm-2s-1 | operational
Graal | 1.1-1.9 | Compton scattering | France
|  | 106 $\gamma$/s | decommissioned
MAMI | 1.1-1.9 | Tagged bremsstrahlung | Germany
|  | 107 $\gamma$/s | operational
ELSA | 1.1-2.7 | Tagged bremsstrahlung | Germany
|  | 107 $\gamma$/s | operational
SPring-8 | 1.1-2.5 | Compton scattering | Japan
|  | 106 $\gamma$/s | operational
Table 1: Facilities for nucleon resonance studies in exclusive photoproduction experiments ireland2020 . For the CLAS12 experiments with quasi-real photons, the luminosity ${\cal L}$ for reactions induced by the electron beam on the liquid-hydrogen target clas12-nim  is presented. Facility |  $Q^{2}$ coverage, |  $W$ coverage, | Luminosity, | Country
---|---|---|---|---
| GeV2 | GeV | cm-2 s-1 |
CLAS/JLab | 0.2-5.0 | 1.1-2.5 | 1034 | USA
|  |  |  | decommissioned
CLAS12/JLab | 0.05-10.0 | 1.1-4.0 | 1035 | USA
|  |  |  | operational
Hall C/JLab |  $<$ 7.0 | 1.1-2.8 | 1037 | USA
|  |  |  | operational
MAMI |  $<$ 0.2 | 1.1-1.3 | 1036 | Germany
|  |  |  | operational
MIT/Bates |  $<$ 0.15 | 1.1-1.3 | 1036 | USA
|  |  |  | decommissioned
Table 2: Facilities for nucleon resonance studies in exclusive
electroproduction experiments azbu12 ; clas12-nim .

The unique combination of multi-GeV continuous electron beams and a detector
of $\sim$4$\pi$ acceptance made the CLAS facility in Hall B at JLab
mecking2003  the best for studies of the spectrum and structure of $N^{*}$
states from exclusive meson photo- and electroproduction data. CLAS allowed
for the study of exclusive electroproduction reactions in the range of $Q^{2}$
up to 5 GeV2 and $W$ up to 3 GeV. These data have provided the dominant part
of the available world information on the $\pi N$, $\eta p$, $K\Lambda$,
$K\Sigma$, and $\pi^{+}\pi^{-}p$ electroproduction channels in the resonance
region ($W<2.5$ GeV) with almost complete coverage of the final state CM phase
space. The majority of the experiments were carried out with an unpolarized
liquid-hydrogen target and a longitudinally polarized electron beam.
Approximately 200k data points for differential cross sections, separated
structure functions, and single- and double-polarization observables have
become available based on analyses of these experimental data, which are
stored in the CLAS Physics Database clasdb . $N^{*}$ studies in exclusive
meson electroproduction at $Q^{2}<7.5$ GeV2 were carried out with the
spectrometers of small millisteradian acceptance in Hall C at JLab, but with
luminosity two orders of magnitude larger than that achieved with CLAS.
Nucleon resonance electroexcitation at small $Q^{2}$ was explored at MAMI and
MIT/Bates with spectrometers of small acceptance (see Table 2).

In the period from 2012 to 2017, CLAS was replaced with the new large
acceptance CLAS12 spectrometer clas12-nim  as part of the JLab 12-GeV upgrade
project. The extended program includes a number of experiments as part of the
continuing $N^{*}$ program in Hall B, which will collect data over an
unprecedented kinematic range for the study of nucleon excited states in the
range of $Q^{2}$ from 0.05 GeV2 up to at least 10 GeV2, spanning the full CM
angular range of the decay final states.

The CLAS detector was also optimized for the studies of exclusive
photoproduction with charged mesons in the final states. Unpolarized and
circularly polarized photons produced by passage of the electron beam through
a thin gold radiator were used in photoproduction experiments, along with
linearly polarized photons from coherent bremsstrahlung on a diamond radiator.
The energy of the bremsstrahlung photons was tagged by measuring the recoil
electron in the Hall B tagging spectrometer sober2000  located upstream of
CLAS. Two different frozen-spin polarized targets were used in photoproduction
experiments, allowing both longitudinal and transverse proton polarizations
keith2012  and longitudinal proton and deuteron polarizations lowry2016 .

Studies of exclusive meson photoproduction were also carried out at European
and Asian facilities that combine continuous electron beams and detectors of
nearly $4\pi$ acceptance as listed in Table 1. These facilities are optimized
for the measurements of final states with neutral mesons and provide
complementary information on nucleon resonances to that available from the
JLab experiments.

##  4 Nucleon Resonance Parameters from Exclusive Meson Photoproduction

The studies of exclusive meson photoproduction in experiments with continuous
electron beams and large-acceptance detectors allow us to determine the types
of all final state particles and their four-momenta in each reaction. Most
exclusive photoproduction channels in the resonance region were studied
ireland2020 ; crede2013 ; klempt2010 ; krusche2003  and include results on
differential cross sections and polarization asymmetries for different
combinations/orientations of the photon beam, target nucleon, and the final
state hadron polarization vectors.

Representative examples of the fully integrated cross sections for the major
exclusive meson photoproduction channels in the resonance region are shown in
Fig. 2, together with the inclusive $(\gamma,X)$ cross section beck2017 . The
different exclusive channels clearly demonstrate selective sensitivities to
different resonance contributions. The exclusive $\pi^{0}p$ channel shows
sensitivity to the resonances located in the first, second, and third
resonance regions. The pronounced structure at $W\sim 1.53$ GeV seen in the
$\eta p$ cross section is related to the contribution from the
$N(1535)1/2^{-}$ resonance. The $\pi\pi N$ channels are suitable for the
exploration of high-lying resonances in the mass range of $W>1.6$ GeV,
together with the $K\Lambda$ and $K\Sigma$ channels. The exclusive
photoproduction channel amplitudes can be described by the sum of the resonant
contributions and the complex set of non-resonant mechanisms (see Fig. 2 top
right panel). There are substantial differences in the non-resonant amplitudes
in different channels. Instead, the $N^{*}$ photocouplings seen in all
channels should be the same since the nucleon resonance photoexcitation and
hadronic decay amplitudes are independent. Therefore, consistent results on
the nucleon resonance photocouplings available from independent studies of
different meson photoproduction channels validate the credible extraction of
these quantities.

The nucleon resonance parameters such as the masses, the total and partial
hadronic decay widths, and the photocouplings, can be determined either within
the framework of reaction models drechsel2007 ; tiator2018 ; tiator2018a ;
aznauryan2003 ; aznauryan2003a ; gol2019  or from the amplitudes directly
determined from the measured observables of meson photoproduction data within
so-called “complete” measurements svarc2018 ; workman2017 ; workman2012 . In
reaction models, the resonant amplitudes are frequently parameterized within
the framework of the Breit-Wigner ansatz. The non-resonant contributions are
described by partial waves and/or by effective meson-baryon mechanisms
described by the tree-level diagrams. In the different analyses, additional
constraints from dispersion relations were employed for the photoproduction
amplitudes drechsel2007 ; tiator2018 ; tiator2018a ; aznauryan2003 ;
aznauryan2003a . The $N^{*}$ parameters were determined from fits to all
available measured observables of the exclusive reaction channels under study.

The impressive progress achieved in the last decade with the measurements of
the photoproduction differential cross sections and polarization asymmetries
bur2020 ; ireland2020 ; crede2013  has provided a dataset for “complete”
measurements. Combined analyses of these observables makes it possible to
determine the pseudoscalar meson-baryon photoproduction amplitudes for the
$\pi N$, $K\Lambda$, and $K\Sigma$ channels directly from the experimental
data. These reactions can be described by eight independent amplitudes as a
function of the Mandelstam variables $s$ and $t$ (or alternatively, $W$ and
the polar angle $\theta_{m}$ of the final state meson in the CM frame) and the
azimuthal angle $\phi_{m}$ between the reaction plane and the plane composed
by the target polarization vector and the beam photon momentum. The number of
independent amplitudes can be obtained by counting the number of helicity
states for the initial and final state particles. Both the beam photon and the
target proton have two possible helicity quantum numbers. The final state
baryon of spin 1/2 also has two helicity quantum numbers, while the
pseudoscalar meson exists in a single helicity 0 state. Overall, $2\times
2\times 2=8$ helicity amplitudes describe pseudoscalar meson-baryon
photoproduction. Parity conservation reduces this number down to four. The
amplitudes are complex numbers that have real and imaginary parts, hence,
eight real numbers fully describe these photoproduction amplitudes. Therefore,
a minimum of eight well chosen independent observables are needed in order to
determine these amplitudes from the data.

Figure 4: (Left) The initial and final state particle polarizations in the
measurements of polarization observables in pseudoscalar meson-baryon
photoproduction. (Right) Polarization observables accessible from pseudoscalar
meson-baryon photoproduction in experiments with a polarized photon beam,
proton target, and measurements of the recoil hyperon polarization
sandorfi2011 .

The observables of pseudoscalar meson-baryon photoproduction available from
experiments with polarized photon beam, proton target, and from measurements
of the recoil hyperon polarization are detailed in Fig. 4. They can be
inferred from the angular distributions of the final state meson over the
azimuthal angle $\phi_{m}$ from the measurements with different orientations
of the photon and proton polarization vectors, or with circularly polarized
photons. In addition, in the $K\Lambda$ and $K\Sigma$ channels, the hyperon
polarization can be obtained from the angular distributions of the hyperon
decay products, providing access to double and triple polarization
observables.

The angular distribution of the final state meson in the CM frame over the
azimuthal angle $\phi_{m}$ is given by Eqs.(1a-p) in Ref. ireland2020  in
terms of the polarization observables listed in Fig. 4, while the connection
between these observables and the well-known Chew-Goldberger-Low-Nambu (CGLN)
amplitudes is given by Eqs.(58a-p) in Ref. sandorfi2011 . The relations
between the amplitudes in different representations can be found in Ref.
knochlein1995 . As of now, eight of the observables listed in Fig. 4 from $\pi
N$ photoproduction data and sixteen observables from $K\Lambda$
photoproduction data have become available ireland2020 . They allow for the
extraction of the pseudoscalar meson-baryon amplitudes directly from the
experimental data, avoiding reaction model bias by fitting the amplitudes to
all the observables. The results for the extracted $\pi N$ photoproduction
amplitudes are shown in Fig. 5 after decomposition over the partial waves.
Each partial wave corresponds to the production amplitudes for the final state
of isospin $I$, orbital angular momentum $L$ shown by the subscript index of
the multipole, and the total angular momentum $J$, which is equal to either
$L+1/2$ or $L-1/2$ for plus or minus signs in the multipole subscript index,
respectively.

Figure 5: $\pi N$ photoproduction amplitudes extracted directly from the
complete measurements of the unpolarized cross sections and polarization
observables after decomposition over the partial waves workman2017 . The
results for the final states of isospin 1/2 and 3/2 are shown in the top and
bottom panels, respectively. The real and imaginary parts of the multipoles
are shown in the top and bottom rows of each panel of plots, respectively.

For the extraction of the $N^{*}$ parameters from the amplitudes determined
directly from the data, they should be analytically continued into the complex
energy plane. The real and imaginary parts for the pole position in the second
Riemann sheet can be related to the $N^{*}$ mass and total decay width,
respectively. The residues at the pole position can be related to the product
of the amplitudes for the resonance photoexcitation and decay to the final
state under study kamano2016 . The data from a complete measurement paves the
way to a nearly model-independent extraction of the $N^{*}$ spectrum and
photocouplings from exclusive photoproduction data.

In the extraction of the $N^{*}$ parameters from the exclusive meson photo-
and electroproduction data, it is important to account for final state
interactions (FSIs) as schematically depicted in Fig. 2 (bottom right). In
these processes many intermediate $M^{\prime}B^{\prime}$ and
$M^{\prime}M^{\prime\prime}B^{\prime}$ states can be populated in the
kinematically allowed channels, and through a sequence of hadron re-
scattering, they can populate the $MB$ final state under study. Also, the
amplitude for the production of the $MB$ final state under study can be
reduced owing to its hadronic interaction with other meson-baryon channels.
Several coupled-channel approaches have been developed allowing for the
combined extraction of $N^{*}$ parameters from global multi-channel analyses
of all available meson hadro- and photoproduction data. They include the
approaches by the Bonn-Gatchina anisovich2012 ; anisovich2017 , Argonne-Osaka
kamano2016 ; kamano2013 , and Jülich-Bonn-Washington roenchen2014 ;
roenchen2019  groups. These approaches have provided information on the
$N^{*}$ photocouplings and their hadronic decay widths, allowing for a
rigorous accounting of the constraints imposed on the production amplitudes by
the general unitarity condition. The red lines in Fig. 5 represent the $\pi N$
photoproduction amplitudes evaluated from a global multi-channel analysis
roenchen2014 . They are in good agreement with the amplitudes extracted
directly from the complete $\pi N$ photoproduction data workman2012 .

##  5 The Search for “Missing” Resonances

Constituent quark models, based on approximate symmetries of the strong
interaction Hamiltonian established from the experimental results on the
$N^{*}$ spectrum known before 2012 klempt2010 ; capstick2000 ; capstick1986 ;
giannini2015 , predict many more excited states of the nucleon than have been
established from experiment. The expectation from quark models that employ
SU(6)$\times$O(3) (spin-flavor$\times$space-rotational) symmetry is depicted
in Fig. 6. The predicted and observed nucleon resonances are shown by the
filled boxes. The states that are predicted but still not observed are shown
by the open boxes. These expectations gain support from the $N^{*}$ spectrum
studies starting from the QCD Lagrangian both within lattice QCD edwards2011
and the continuum Schwinger method approach (CSM) chen2019a ; qin2019 . The
search for states in the mass range above 1.7 GeV that have eluded detection
has become the focus of extensive studies to address the so-called “missing”
resonance problem.

Figure 6: Spectrum of nucleon resonances expected in quark models employing
${\rm SU(6)}_{\rm spin-flavor}\times{\rm O(3)}_{\rm space}$ symmetry. $L_{3q}$
is the orbital angular momentum of the three constituent quarks and the
quantum number $N$ corresponds to the radial excitation of the three-quark
system. The predicted and observed states are shown by the filled boxes, while
the predicted and still not observed states are shown by the open boxes.

Figure 7: Representative examples for the description of the CLAS results on
the $K\Lambda$ differential cross sections (left column) and induced
polarization (right column) mcc2009  achieved within the Argonne-Osaka
coupled-channel approach (red lines) kamano2013  with the well-established
resonances before 2012 (top row) and the Bonn-Gatchina coupled-channel
approach (red lines) anisovich2012  after implementation of nine new nucleon
resonances (bottom row). The $W$ value in MeV is given in the top corner of
each plot.

Recently, several long-awaited new nucleon resonances were discovered in
global multi-channel analyses of exclusive meson photo- and hadroproduction
data anis2017 ; ron2014  with a decisive impact of the CLAS results on
$K\Lambda$ and $K\Sigma$ photoproduction brad2007 ; mcc2009 ; dey2010 . The
CLAS results on the differential cross sections and induced polarization $P$
for $K\Lambda$ photoproduction, along with their description within coupled-
channel approaches developed by the Argonne-Osaka kamano2013  and Bonn-
Gatchina anisovich2012  groups, are shown in Fig. 7. Both approaches
incorporate most exclusive $\pi N$ and photoproduction channels relevant in
the resonance region. There are substantial differences in accounting for the
resonant contributions in these two approaches. The Argonne-Osaka group
includes all resonances known before 2012 with three- or four-star PDG status
and, in general, the measured observables included are well reproduced in the
kinematic ranges covered by the data, except for the interval 1.8 GeV $<W<2.0$
GeV. Here, the data on the $K\Lambda$ differential cross sections and induced
polarization $P$ are not well reproduced, as can be seen in Fig. 7 (top). The
observed discrepancies emphasize the importance of the polarization data and
demonstrate that accounting for the contributions from only the conventional
resonances does not allow for the description of the data. The Bonn-Gatchina
coupled-channel approach accounts for the contributions from all well-
established resonances and from nine new resonances with masses, hadronic
decay widths, and photocouplings fit to data from the meson hadro- and
photoproduction channels. After implementation of the new baryon states, a
good description of the CLAS data is achieved over the entire kinematic range
as shown in Fig. 7 (bottom). Furthermore, the Bonn-Gatchina approach provides
a good description of the observables for most relevant exclusive meson hadro-
and photoproduction channels in the nucleon resonance region after
implementation of the new states. This provides strong evidence for the
existence of these new nucleon resonances.

Figure 8: (Left) Spectrum of the excited states of the nucleon established in
2020 bur2020 . (Right) The nucleon resonance PDG status before 2012 and in
2020 pdg .

The spectrum of nucleon resonances, as it is now known, is shown in Fig. 8
(left) with the new states highlighted by the brown boxes. Figure 8 (right)
shows a comparison between the PDG status of nucleon resonances in the mass
range $W>1.6$ GeV in 2012 and 2020. Two of the nine recently discovered
resonances get the highest four-star status of firmly established states. The
status of the other new states was elevated to three stars as likely existing.
Discovery of the long-awaited new nucleon resonances with decisive impact from
the CLAS $K\Lambda$ and $K\Sigma$ photoproduction data, represents an
important achievement in hadron physics in the past decade.

Figure 9: Photo- and electroexcitation amplitudes of the new
$N^{\prime}(1720)3/2^{+}$ resonance (blue points connected by blue solid
lines) and the conventional $N(1720)3/2^{+}$ (black points connected by black
dotted lines) obtained in Ref. mokeev2020a  from the combined analysis of
$\pi^{+}\pi^{-}p$ photo- and electroproduction data.

Combined studies of exclusive meson photo- and electroproduction data
represent the next step in the search for new excited states of the nucleon.
New resonances seen in photoproduction can be observed in electroproduction
data with $Q^{2}$-independent values of their masses and hadronic decay
widths. These studies, therefore, will validate the existence of these new
states in a nearly model-independent way.

The new $N^{\prime}(1720)3/2^{+}$ state has recently been discovered in the
combined studies of $\pi^{+}\pi^{-}p$ photo- and electroproduction data
measured with CLAS mokeev2020a , in addition to the nine new resonances
already discussed. Implementation of the $N^{\prime}(1720)3/2^{+}$ is required
in order to describe the $\pi^{+}\pi^{-}p$ reaction in the third resonance
region in the range 0.5 GeV${}^{2}<Q^{2}<1.5$ GeV2 with $Q^{2}$-independent
masses and hadronic decay widths of the resonances relevant in this kinematic
area. As of now, the $N^{\prime}(1720)3/2^{+}$ is the only new resonance for
which the $Q^{2}$-evolution of the electroexcitation amplitudes has been
determined, as shown in Fig. 9 in comparison with the conventional
$N(1720)3/2^{+}$ state. These results offer an opportunity to gain insight
into the structural features of the states that have made their observation so
elusive. The structure of the new $N^{\prime}(1720)3/2^{+}$ resonance has
already been studied in analysis of its electroexcitation amplitudes within
the light-front holography approach lub2020 .

##  6 Nucleon Resonance Electroexcitation Amplitudes from Exclusive Meson
Electroproduction

The available and foreseen data from CLAS and CLAS12 on exclusive meson
electroproduction in the resonance region open up a unique opportunity for the
systematic exploration of the structure of all prominent nucleon resonances.
The continuous, multi-GeV electron beam from the CEBAF accelerator, combined
with a detector of nearly $4\pi$ acceptance, provides the best opportunity for
the exploration of nucleon resonance structure from the results on the
evolution of the nucleon resonance electroexcitation amplitudes
($\gamma_{v}pN^{*}$ electrocouplings) as a function of $Q^{2}$. The extensive
research efforts in progress in Hall B at JLab are focused on the extraction
of the amplitudes of all prominent nucleon resonances in the mass range
$W<2.5$ GeV and 0.05 GeV${}^{2}<Q^{2}<10$ GeV2 from both the independent and
combined studies of the different meson electroproduction channels
Brodsky:2020vco ; Burkert:2019bhp ; bur2020 ; fbs-carman ; azbu12 . Currently,
the new CLAS12 detector, installed in Hall B as the part of the JLab 12-GeV
upgrade, is the only available and foreseen facility in the world capable of
providing information on the electrocouplings of all prominent resonances in
the almost unexplored range $Q^{2}>5$ GeV2 Brodsky:2020vco ; burkert2018 .

The three $\gamma_{v}pN^{*}$ electrocouplings, $A_{1/2}(Q^{2})$,
$A_{3/2}(Q^{2})$, and $S_{1/2}(Q^{2})$, defined in Eqs. (1) and (2) of Section
2, describe the resonance electroexcitation. The longitudinal electrocouplings
are relevant for electroproduction only, since in photoproduction, owing to
gauge invariance of QED, the virtual photon flux of longitudinally polarized
photons is equal to zero. On the other hand, the behavior of $S_{1/2}$ at
$Q^{2}<0.2$ GeV2 is largely unknown and represents an interesting open problem
to be addressed in electroproduction experiments. The non-resonant
contributions to the amplitudes of different exclusive electroproduction
channels are substantially different, while the electrocouplings extracted
from different exclusive channels should be the same, since the resonance
electroexcitation and hadronic decay amplitudes are independent. Therefore,
consistent results in the extraction of the $\gamma_{v}pN^{*}$
electrocouplings from independent studies of different exclusive channels
validate reliable extraction of these quantities in a nearly model-independent
way.

Studies of $N^{*}$ electroexcitations in different exclusive meson
electroproduction channels became feasible with the experimental results from
the CLAS detector, which has provided the dominant part of the available world
information on differential cross sections, as well as beam $A_{b}$, target
$A_{t}$, and beam-target $A_{bt}$ asymmetries for most exclusive meson
electroproduction channels in the resonance region. These measurements are
summarized in Table 3.

Hadron Final |  $W$ Coverage, |  $Q^{2}$ Coverage, | Measured
---|---|---|---
State | GeV | GeV2 | Observables
$\pi^{+}n$ | 1.1-1.38 | 0.16-0.36 | $\frac{d\sigma}{d\Omega}$
| 1.1-1.55 | 0.3-0.6 | $\frac{d\sigma}{d\Omega}$
| 1.1-1.70 | 1.7-4.5 |  $\frac{d\sigma}{d\Omega}$, $A_{b}$
| 1.6-2.00 | 1.8-4.5 | $\frac{d\sigma}{d\Omega}$
$\pi^{0}p$ | 1.1-1.38 | 0.16-0.36 | $\frac{d\sigma}{d\Omega}$
| 1.1-1.68 | 0.4-1.8 |  $\frac{d\sigma}{d\Omega}$, $A_{b}$, $A_{t}$, $A_{bt}$
| 1.1-1.39 | 3.0-6.0 | $\frac{d\sigma}{d\Omega}$
| 1.1-1.80 | 0.4-1.0 |  $\frac{d\sigma}{d\Omega}$, $A_{b}$
$\eta p$ | 1.5-2.30 | 0.2-3.1 | $\frac{d\sigma}{d\Omega}$
$K^{+}\Lambda$ | 1.61-2.60 | 1.40-3.90 | $\frac{d\sigma}{d\Omega}$
|  | 0.70-5.40 |  $P^{0}$, $P^{\prime}$
$K^{+}\Sigma^{0}$ | 1.68-2.60 | 1.40-3.90 | $\frac{d\sigma}{d\Omega}$
|  | 0.70-5.40 | $P^{\prime}$
$\pi^{+}\pi^{-}p$ | 1.3-1.6 | 0.20-0.60 | Nine 1-fold
| 1.4-2.10 | 0.5-1.5 | differential cross
| 1.4-2.00 | 2.0-5.0 | sections
Table 3: Summary of the exclusive meson electroproduction data obtained with
the CLAS detector in the resonance region fbs-carman ; azbu12 ; mok2019 ,
including differential cross sections $\frac{d\sigma}{d\Omega}$, beam $A_{b}$,
target $A_{t}$, and beam-target $A_{bt}$ asymmetries, as well as recoil
$P^{0}$ and transferred $P^{\prime}$ polarizations of $\Lambda$ and
$\Sigma^{0}$ hyperons.

A large body of around 150k data points, on differential cross sections,
polarization asymmetries, and hyperon recoil/transferred polarization has
become available spanning almost the entire range of the final state meson
emission angles in the CM frame. These data provide sufficient information for
the extraction of the electrocouplings for most excited nucleon states in the
mass range up to 2 GeV for 0.2 GeV${}^{2}<Q^{2}<5$ GeV2. Tables of the
numerical results on the observables listed in Table 3 can be found in the
CLAS Physics Database clasdb  and in the SAID database saiddb .

Figure 10: The transverse $\gamma_{v}pN^{*}$ photo-/electrocouplings of the
$N(1440)1/2^{+}$ (left) and $N(1520)3/2^{-}$ (right) determined from
independent studies of $\pi N$ aznauryan2009  and $\pi^{+}\pi^{-}p$ mok2020 ;
mokeev2012 ; mokeev2015  electroproduction off protons.

Several approaches were developed for the extraction of the electrocouplings
from these data. They include analyses from independent studies of individual
meson electroproduction channels: $\pi^{+}n$ and $\pi^{0}p$ tiator2018 ;
aznauryan2003 ; aznauryan2009 ; aznauryan2015 ; tiator2011 , $\eta p$
aznauryan2003a ; knochlein1995 ; denizli2007 , and $\pi^{+}\pi^{-}p$
mokeev2009 ; mokeev2012 ; mokeev2015 . The results on the electrocouplings of
the $\Delta(1232)3/2^{+}$ and $N(1440)1/2^{+}$ resonances have become
available from global multi-channel analysis of hadro-, photo-, and
electroproduction data for the first time within the coupled-channel approach
developed by the Argonne-Osaka group kamano2018 . Recently, the multipoles for
$\pi N$ mai2021  and $\eta p$ mai2021a  electroproduction were extracted from
the CLAS data at $W<1.6$ GeV and $Q^{2}<5$ GeV2 within the coupled-channel
approach developed by the Jülich-Bonn-Washington group. The multipoles
inferred from the data pave allow for the extraction of the electrocouplings.

Most of the electrocoupling results obtained so far have become available from
independent studies of the CLAS data on $\pi N$ and $\pi^{+}\pi^{-}p$
electroproduction fbs-carman . The unitary isobar model and dispersion
relation approaches developed by the CLAS Collaboration to study $\pi N$
electroproduction have provided a good description of the observables in the
$W$ range up to 1.7 GeV for $Q^{2}<5$ GeV2 aznauryan2003 ; aznauryan2009 ;
aznauryan2015 . The data-driven JLab-Moscow (JM) meson-baryon reaction model
for the study of $\pi^{+}\pi^{-}p$ electroproduction offers a good description
of the data for $W<2$ GeV and $Q^{2}<5$ GeV2 mok2019 ; mokeev2012 ; mokeev2015
. The reaction models for $\pi N$ and $\pi^{+}\pi^{-}p$ electroproduction
provide for a reliable isolation of the resonant contributions to the
observables needed for a reliable extraction of the electrocouplings. A
summary of the results from the exclusive meson electroproduction data is
presented in Table 4. Currently, the electrocouplings of most proton excited
states in the mass range $W<1.8$ GeV and $Q^{2}<5$ GeV2 have become available
from the studies of exclusive meson electroproduction with CLAS. The most
recent results on their values can be found in Ref. blin2019 .

Channel | Excited Nucleon |  $Q^{2}$ Range (GeV2) of
---|---|---
| States | Electrocouplings
$\pi^{+}n$, |  $\Delta(1232)3/2^{+}$, | 0.16-6.0
$\pi^{0}p$ |  $N(1440)1/2^{+}$, $N(1520)3/2^{-}$, $N(1535)1/2^{-}$ | 0.3-4.16
$\pi^{+}n$ |  $N(1675)5/2^{-}$, $N(1680)5/2^{+}$, $N(1710)1/2^{+}$ | 1.6-4.5
$\eta p$ | $N(1535)1/2^{-}$ | 0.2-2.6
$\pi^{+}\pi^{-}p$ |  $N(1440)1/2^{+}$, $N(1520)3/2^{-}$ | 0.25-1.50, 2.0-5.0 (prelim)
|  $\Delta(1620)1/2^{-}$, $N(1650)1/2^{-}$, |
|  $N(1680)5/2^{+}$, $\Delta(1700)3/2^{-}$ | 0.5-1.5
|  $N(1720)3/2^{+}$, $N^{\prime}(1720)3/2^{+}$, $N(1535)1/2^{-}$ |
Table 4: The $\gamma_{v}pN^{*}$ electrocouplings determined from CLAS data on
exclusive meson electroproduction off protons.

The electrocouplings of the $N(1440)1/2^{+}$ and $N(1520)3/2^{-}$ obtained
from independent studies of $\pi N$ and $\pi^{+}\pi^{-}p$ electroproduction
are shown in Fig. 10. For both resonances, the electrocouplings determined
from these two channels agree within the error bars. This agreement validates
the extraction of these quantities in a nearly model-independent way. This
success has also validated the reaction models aznauryan2003 ; aznauryan2009 ;
aznauryan2015 ; mokeev2009 ; mokeev2012 ; mokeev2015  used to extract these
quantities. The CLAS measurements isupov2017 ; trivedi2018  have extended the
kinematic coverage of the $\pi^{+}\pi^{-}p$ electroproduction data for 1.4 GeV
$<W<2.0$ GeV and 2.0 GeV${}^{2}<Q^{2}<5.0$ GeV2. Extraction of the
electrocouplings of most excited states of the proton in this kinematic range
from these data is in progress. The expected results will provide valuable
information on the evolution of the resonance structure in the transition from
the interplay between the inner quark core and the external meson-baryon cloud
to the regime where the quark core dominates fbs-carman . Recently, new data
from CLAS on the $\pi^{0}p$ differential cross sections markov2020  and beam
asymmetries isupov2021  have become available. The sensitivity of these
observables to the contributions of the nucleon resonances in the third
resonance region was demonstrated. The upcoming results on the
electrocouplings of the nucleon resonances in the third resonance region from
these $\pi N$ data, as well as from the $\pi^{+}\pi^{-}p$ electroproduction
data available within the same kinematic range fedotov2018 , will shed further
light on the interplay between the quark core and the meson-baryon cloud in
the structure of excited nucleon states Burkert:2019bhp ; azbu12 ; mokeev2015
.

In the mass range $W>1.6$ GeV, several nucleon resonances decay preferentially
to $\pi\pi N$ with a small branching fraction to $\pi N$. This makes
$\pi^{+}\pi^{-}p$ electroproduction the major source of information on the
electrocouplings of these states mok2020 ; mokeev2020a ; mok2019 . These
quantities can also be determined independently from exclusive $K\Lambda$ and
$K\Sigma$ ($KY$) electroproduction. The quality of the CLAS data on $KY$
electroproduction 5st ; carman13 ; carman03 ; rauecarman ; sltp ; carman09 ;
ipol  certainly provides an opportunity to extract the electrocouplings from
these exclusive channels when a suitable reaction model becomes available. The
development of such a reaction model for the extraction of the
electrocouplings from the available $KY$ electroproduction data represents an
urgent need for advancing the exploration of the spectrum and structure of the
higher-lying nucleon resonances. The exclusive $\pi^{+}\pi^{-}p$ and $KY$
channels look very promising in the search for new baryon states in the
combined studies of meson photo- and electroproduction data bur2020 ; fbs-
carman .

##  7 Nucleon Resonance Electrocouplings and Emergence of Hadron Mass

The emergence of hadron mass represents a challenging open problem in the
Standard Model that arises from the comparison between the measured masses of
protons and neutrons and the sum of the masses of their current-quark
constituents. Nucleons consist of the lightest $u$ and $d$ quarks. By adding
the masses of the current quarks in the proton and neutron, which enter into
the QCD Lagrangian and are generated through the Higgs mechanism, we get the
current quark mass contribution to the proton of $8.99^{+1.45}_{-0.65}$ MeV
and to the neutron of $11.50^{+1.45}_{-1.60}$ MeV pdg . The sum of the current
quark masses accounts for $<$1.1% and $<$1.4% of the measured proton and
neutron masses, respectively. Important questions arise, namely, which
mechanism underlies the generation of the dominant part of $>$98% of hadron
mass and how it is related to the generation of the non-zero trace of the
nucleon energy-momentum tensor, the so-called trace anomaly?

The impressive progress achieved using CSMs during the past decade has
conclusively demonstrated that the dominant part of hadron mass is generated
by the strong interaction in the regime of large QCD running coupling through
the dressing of the bare QCD quarks and gluons driven by the QCD Lagrangian
roberts2021 ; roberts2020b . Currently, CSMs present the only available
approach capable of making predictions on the EHM manifestation in the $Q^{2}$
evolution of the pion and nucleon elastic form factors, the pion parton
distribution function (PDF), and the $\gamma_{v}pN^{*}$ electrocouplings
within a common framework for both mesons and baryons. The studies of
electrocouplings play an important role in validating the EHM concept
developed within CSMs from the experimental data Brodsky:2020vco ;
Burkert:2019bhp ; fbs-carman .

Figure 11: (Left) Graphical representation of the QCD equations of motion for
the quark and gluon fields that underlie the generation of the dressed quark
and gluon masses through dynamical chiral symmetry breaking. (Right) QCD
running coupling evaluated using CSMs starting from the QCD Lagrangian cui20 ;
binosi2017 ; roberts2020c .

Figure 12: (Left) Momentum dependence of the $u$ and $d$ dressed quark masses
computed with CSMs starting from the QCD Lagrangian roberts2020c . (Right)
Momentum dependence of the $u$ and $d$ dressed quark masses evaluated within
LQCD for different lattice spacings $a$ and current quark masses $m$
oliviera2019 .

The QCD Lagrangian implies that the current quarks should be dressed in the
processes shown in the top left part of Fig. 11. Similarly, the gauge QCD
gluons should be dressed in the processes shown in the bottom left part of
Fig. 11 cui20 ; binosi2017 ; roberts2020c . In the regime of large QCD running
coupling (see Fig. 11 (right)), the QCD-driven dressing processes shown in
Fig. 11 (left) generate dressed quarks and gluons with dynamical
distance/momentum-dependent masses. The dressed quark and gluon masses
evaluated using CSMs from the QCD Lagrangian are shown in Fig. 12 (left)
roberts2020c . The dressed quark mass function shows how almost massless,
perturbative QCD quarks in the ultraviolet at momenta $k>2$ GeV, eventually in
the infrared at momenta $k<0.5$ GeV, become fully dressed quarks of
$\approx$400 MeV mass that are employed in the constituent quark models. In
the infrared regime, the dressed quark and gluon running masses converge,
setting up the strong interaction mass scale of $\approx$400 MeV, which is
consistent with the measured nucleon mass. The Higgs boson discovered at CERN
accounts for the generation of only the current quark mass, with a
contribution into the fully dressed quark mass of $<$2%. The Higgs mechanism
is almost irrelevant for the generation of mass of the nucleon and its excited
states. The dominant part of the $N/N^{*}$ masses is generated through the
quark and gluon dressing processes shown in Fig. 11 (left) that are
responsible for dynamical chiral symmetry breaking (DCSB). In the strong QCD
regime, the energy stored in the gluon field is transferred into the running
mass of the dressed quarks. The interaction between the three dressed quarks
with dynamically generated masses eventually produces the experimentally
observed masses of the ground and excited states of the nucleon. Notably, the
CSM results on the momentum dependence of the dressed quark mass are fully
consistent with the independent evaluation of this quantity within lattice QCD
(LQCD) simulations oliviera2019 . The LQCD results are shown in Fig. 12
(right) and confirm the CSM predictions. The dressed quark mass function is
computed with the CSM as the solution of the QCD equations of motion for the
quark and gluon fields in the strong QCD regime. So far, these equations can
be solved under approximations mostly related to the description of the
dressed quark-gluon vertex. It is a challenging task for contemporary
experimental hadron physics to check the CSM concept on EHM. A large body of
predictions on both meson and baryon structure observables was made within the
CSM, offering an excellent opportunity to check the CSM concept for EHM
against different sets of hadron structure observables Brodsky:2020vco ; fbs-
carman ; roberts2020c .

Studies of the $\gamma_{v}pN^{*}$ electrocouplings, in combination with the
nucleon elastic form factors, play a particular role in this effort, allowing
for the exploration of EHM in conditions when the dominant part of the ground
and excited nucleon state mass comes dynamically from the generated dressed
quark masses. Consistent results on the dressed quark mass function from
independent studies of nucleon elastic form factors and the electrocouplings
of nucleon resonances of different structure provides insight into EHM in a
nearly model-independent way.

Figure 13: (Left) $N\to\Delta(1232)3/2^{+}$ magnetic transition form factor in
the Jones-Scadron convention in comparison with CSM predictions segovia2014 .
The CSM prediction for the contact $qq$-interaction with a frozen quark mass
is shown by the red dashed line, while the CSM prediction with a realistic
$qq$-interaction that results in a running quark mass is shown by the blue
solid line. (Right) $A_{1/2}$ electrocoupling of the $N(1440)1/2^{+}$
resonance from the CLAS measurements in comparison with the CSM prediction
segovia2015  shown by the black solid line.

The CLAS results on the electrocouplings of low-lying nucleon resonances in
the mass range $W<1.65$ GeV have already demonstrated a profound impact on the
understanding of EHM. CSMs have, for the first time, provided a good
description of the CLAS results on the electrocouplings of the
$\Delta(1232)3/2^{+}$ and $N(1440)1/2^{+}$ starting from the QCD Lagrangian
(see Fig. 13) chen2019 ; segovia2016 ; segovia2016a ; segovia2016b ;
segovia2015 ; segovia2014 . The CSM predictions for the dominant
$N\to\Delta(1232)3/2^{+}$ magnetic transition form factor were obtained under
two assumptions for the $qq$-interaction. The exploratory computation of this
form factor employed a simplified contact $qq$-interaction segovia2014 . Such
an interaction allows for the description of the dressed quark mass of 360
MeV, but results in a momentum-independent “frozen” dressed quark mass
function (see the dashed red line in Fig. 13 (left)). This CSM prediction
overestimates the experimental results at $Q^{2}>1$ GeV2. The discrepancy
between the data and the CSM prediction increases with $Q^{2}$, approaching an
order magnitude at $Q^{2}\approx 6$ GeV2. Instead, use of a realistic
$qq$-interaction roberts2020c , which predicts a momentum-dependent dressed
quark mass (see Fig. 12), offers a good description of the CLAS results in the
entire range of $Q^{2}>0.8$ GeV2, where the contribution from the quark core
into the structure of the $\Delta(1232)3/2^{+}$ becomes the largest. Analysis
of the CLAS results on the $N\to\Delta(1232)3/2^{+}$ magnetic transition form
factor using CSMs has conclusively demonstrated for the first time that the
dressed quark mass is, in fact, running.

Significantly, a good description of both the $\Delta(1232)3/2^{+}$ and
$N(1440)1/2^{+}$ electrocouplings (see Fig. 13) was achieved with exactly the
same dressed quark mass function as was used previously for the successful
description of the pion and nucleon elastic form factors and the pion PDF
roberts2021 ; roberts2020c ; segovia2014 . Consistent results on the momentum
dependence of the dressed quark mass obtained from independent experimental
studies of the structure of the ground state pion and nucleon, as well as from
the results on the $Q^{2}$ evolution of the resonance electrocouplings of
different excited nucleon states of different structure, the first spin-
isospin flip for the $\Delta(1232)3/2^{+}$, and the first radial excitation of
the $N(1440)1/2^{+}$, strongly suggest that dressed quarks with a dynamically
generated mass represent an active component in the structure of the ground
state pion and nucleon, as well as the $\Delta(1232)3/2^{+}$ and
$N(1440)1/2^{+}$ resonances. This success offers strong support for the CSM
concept of EHM from the experimental data and demonstrates the capability to
gain insight into EHM from the experimental data on the pion and the
ground/excited states of the nucleon, analyzed within the common CSM
theoretical framework. This is a very impressive achievement in hadron physics
in the past decade resulting from synergistic efforts between experiment,
phenomenology, and QCD-rooted hadron structure theory.

Figure 14: (Left) Expected results on the $N(1440)1/2^{+}$ electrocouplings
from CLAS12 data in comparison with those available from CLAS fbs-carman .
(Right) Kinematic coverage for insight into the dressed quark mass function
from the electrocoupling data with CLAS fbs-carman  (left yellow shaded area),
CLAS12 Brodsky:2020vco , and from the foreseen JLab measurements with
increased energy up to 24 GeV and luminosity above $10^{36}$ cm-2s-1 as a part
of the future JLab research program (area between the vertical lines).

The predictions of the electrocouplings of the $\Delta(1600)3/2^{+}$ have
recently become available from CSMs lu2019 . The extraction of the
electrocouplings for this state from the CLAS $\pi^{+}\pi^{-}p$
electroproduction data isupov2017 ; trivedi2018  at 2.0 GeV${}^{2}<Q^{2}<5.0$
GeV2 is in progress. A successful description of these quantities will
solidify insight into the momentum dependence of the dressed quark mass in a
nearly model-independent way. CSMs continue to extend the exploration of
$N^{*}$ structure with the first results on the electrocouplings of the
$N(1535)1/2^{-}$ resonance raya2021 . In leading order, the structure of this
state can be described as an $L=1$ orbital excitation of three dressed quarks.
Systematic studies of the resonances that belong to the [$70,1^{-}$] SU(6)
spin-flavor supermultiplet will shed light on either the universality or the
environmental sensitivity of the dressed quark mass function.

Currently, the CLAS12 detector in Hall B at JLab is the only available and
foreseen facility in the world capable of exploring exclusive meson
electroproduction in the resonance region at the highest $Q^{2}>5$ GeV2 ever
achieved in the studies of exclusive electroproduction. The electrocouplings
of all prominent nucleon resonances will be determined from the data of
experiments with CLAS12 within the $Q^{2}$ range from 5 GeV2 to 10 GeV2 from
independent and combined studies of the $\pi N$, $K\Lambda$, $K\Sigma$, and
$\pi^{+}\pi^{-}p$ channels Brodsky:2020vco ; fbs-carman . As a representative
example, the quality of the expected results on the electrocouplings of the
$N(1440)1/2^{+}$ in comparison with the available results is shown in Fig. 14
(left). The $Q^{2}$ coverage of CLAS12 will allow for the mapping out of the
dressed quark mass function in the range of quark momenta up to 1.3 GeV. This
is an essential extension in comparison to the range of quark momentum $<$0.5
GeV accessible from the CLAS results (see Fig. 14 (right)). Consistent results
on the momentum dependence of the dressed quark mass function from the studies
of the electrocouplings over the full spectrum of the excited nucleon states
of distinctively different structure, different spin-isospin flips, and
different radial and orbital excitations will validate credible insight into
this fundamental quantity in a nearly model-independent way. The expected
CLAS12 results on the electrocouplings of most excited nucleon states will
allow the key open problems in the Standard Model on the emergence of hadron
mass and quark gluon confinement to be addressed.

In order to overlap the full range of dressed quark momenta where the dominant
part of hadron mass is generated (see Fig. 14 (right)), the electrocouplings
should be determined within the range of $Q^{2}$ up to 36 GeV2, assuming
roughly equal sharing of the momentum transferred by virtual photons among the
three dressed quarks. Such experiments require a further increase of the JLab
electron beam energy up to 24 GeV and the construction of a new large-
acceptance detector capable of measuring exclusive meson electroproduction at
luminosities above 1036 cm-2s-1. The exploration of EHM at $Q^{2}>10$ GeV2
motivates the future experimental studies of resonance structure after the
completion of the 12-GeV program.

##  8 Conclusion and Outlook

Studies of exclusive meson photoproduction in the resonance region have
provided precise results on the differential cross sections and polarization
observables for most exclusive photoproduction channels. Progress in the
amplitude analyses has allowed for the establishment of the masses,
total/partial hadronic decay widths, and photocouplings for all prominent
resonances in the mass range $<$2.5 GeV. Further efforts are needed to improve
agreement between the $N^{*}$ parameters available from different analysis
approaches. Several long-awaited new baryon states (referred to as “missing”
resonances) have been discovered in global multi-channel analyses of exclusive
meson photo- and hadroproduction data with a major impact from the CLAS
$K\Lambda$ and $K\Sigma$ photoproduction data. The new
$N^{\prime}(1720)3/2^{+}$ resonance has been observed in the combined studies
of $\pi^{+}\pi^{-}p$ photo- and electroproduction data measured with CLAS.
Currently, this is the only new resonance for which the results on the
$Q^{2}$-evolution of the electrocouplings have become available, allowing us
to gain insight into the structure of new baryon states. The experiments of
the 12-GeV era at JLab, as well as at facilities in Asia and Europe, will
complete studies of the spectrum of the excited nucleon states, including the
search for hybrid baryons with glue as an active structural component. These
studies will address approximate symmetries for the strong QCD regime that
underlie the generation of the $N^{*}$ spectrum, the emergence of hadrons from
a deconfined mixture of quarks and gluons in the early Universe, and the dual
role of gluons as the strong force carrier and as hadron matter constituents.
Experiments of the 12-GeV era at JLab will also considerably extend our
knowledge on the spectra of excited baryons with strange quarks burkert2018 ;
klong2020 .

The CLAS detector has provided the dominant part of the world data on most
exclusive meson electroproduction channels in the resonance region. These data
have allowed for the determination of the electrocouplings of most resonances
in the mass range up to 1.8 GeV with consistent results from analyses of the
$\pi^{+}n$, $\pi^{0}p$, $\eta p$, and $\pi^{+}\pi^{-}p$ channels. The
resonance electrocouplings will become available for most nucleon resonances
in the mass range $<$2 GeV and at $Q^{2}<5$ GeV2 from CLAS and at $Q^{2}<10$
GeV2 from CLAS12. The EHM paradigm makes a broad array of predictions for the
structure of $N/N^{*}$ states that are worth testing to gain insight and
understanding of hadron mass generation by mapping out the momentum dependence
of the dressed quark running masses. A good description of the CLAS results on
the $\Delta(1232)3/2^{+}$ and $N(1440)1/2^{+}$ electroexcitation amplitudes
achieved with the same dressed quark mass function as used previously in the
successful evaluations of the nucleon elastic and pion form factors and the
pion PDF, validate insight into the dynamics that underlie the emergence of
hadron mass. Studies of the $\Delta(1600)3/2^{+}$ electrocouplings are in
progress and, when complete, may be compared with CSM predictions made using
the same dressed quark mass function employed in all other calculations.
CLAS12 is the only facility in the world capable of obtaining the
electrocouplings of all prominent $N^{*}$ states at the still unexplored
ranges at the highest $Q^{2}$ for exclusive reactions from 5 GeV2 to 10 GeV2
from measurements of $\pi N$, $KY$, and $\pi^{+}\pi^{-}p$, allowing us to map
out the dressed quark mass function at quark momenta up to 1.3 GeV. Extension
of the results on the electrocouplings into the $Q^{2}$ range from 10 GeV2 to
36 GeV2 from measurements at future facilities with luminosity $>$1036 cm-2s-1
will allow for the completion of the exploration of the dressed quark mass
function within the full range of distances where the bulk of hadron mass is
generated in the transition from quark-gluon confinement to the regime of
perturbative QCD. Studies over this full range are essential in order to
address the most challenging problems of the Standard Model on the nature of
$>$98% of the mass of hadrons.

## Acknowledgments

This work was supported in part by the U.S. Department of Energy and the
Skobeltsyn Nuclear Physics Institute and Physics Department at Lomonosov
Moscow State University. The Southeastern Universities Research Association
(SURA) operates the Thomas Jefferson National Accelerator Facility for the
U.S. Department of Energy under Contract No. DE-AC05-06OR23177.

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