\section{Hadronic physics and QCD}

\subsection{Overview}

%GH: text from hadronqcd.tex
The building blocks of the atomic nucleus---the protons, neutrons, and other particles (mesons) that bind them---are collectively known as hadrons.  These consist of yet more fundamental constituents, the quarks and gluons, but because the quark-gluon interaction is very strong at long distances, the fundamental constituents are confined within hadrons. The nature of the strong force at long distances, where quark confinement dominates, is one of the \emph{major unsolved problems of modern physics}. In fact, the Fields Institute and the Clay Institute have both listed the solution of how colour confinement permits only bound states of massless gluons, forming only massive hadrons (i.e. mass gap within Yang-Mills quantum theory) as one of their Millenium Prize problems. 

On the theoretical side, Quantum Chromo-Dynamics (QCD) is a framework that accurately describes quark-gluon interactions at extremely high energies (when quarks are close together), but what is poorly understood is how QCD gives rise to properties such as the mass and spin of hadrons.  A taxing complication is that in the confinement regime, the quark-gluon interaction is too strong for perturbative methods to be reliably applied, and so far QCD can only be used as a basis for either model development or numerical solutions such as Lattice QCD, both of which must be guided by experimental data.

Key hadron properties and their spectrum are best studied via electron scattering and photoproduction experiments, such as at Jefferson Lab (JLab, USA) and the Mainz Microtron (MAMI, Germany) that employ continuous wave electron beams. Experimental studies using inclusive electron scattering at high momentum and energy transfer have provided important information on the elementary interactions of quarks and gluons; however, our understanding is fragmented and further experimental work is needed.   Canadian research has advanced and continues to advance the understanding of the structure and properties of hadrons.

\subsection{The Canadian Program}

\subsubsection{Hadronic physics theory program}

Combining a range of approaches, such as Lattice QCD, Light Front Holographic (LFHQCD), studies of exotic hadrons using QCD sum rules, and Chiral Perturbation Theory (ChPT), the Canadian theory community is working on both advancing the field and supporting experimental efforts in Canada and off-shore (Section \ref{sec:Theory}). 

\subsubsection{Thomas Jefferson National Accelerator Facility (Jefferson Lab, JLab)}
%GH: text from jlab_hadrons_brief

The bulk of the Canadian involvement in experiments on hadronic physics and QCD
is currently carried out at Jefferson Lab, in Newport News, Virginia,
USA.  The Canadian-led experiments at JLab have acquired and continue to acquire high quality data intended to better our understanding of QCD in the strongly interacting, non-perturbative
regime, where quark (colour) confinement dominates.

The JLab 12-GeV Upgrade, enabling a doubling of the available electron beam
energy and the construction of a suite of new detectors, was completed in
2017.  Canadians are now in the ``exploitation phase'' of the new facility.
The experiments are in data-taking and/or analysis phases, with detector R\&D
having been completed and detectors developed by the team installed and
operating in both Hall~C and Hall~D.  
\begin{itemize}
\item In the medium-term (2022--26), Canadians will be significantly
involved in data-taking and leading experimental efforts in the analysis and
publication of data, resulting in the publication of Canadian-led publications.
The JLab Eta Factory (JEF) experiment is planned with an upgraded GlueX Experiment in Hall~D, and simulations, R\&D and detector construction will take place at JLab with Regina participation. 
\item  In the longer-term (2027--36), the
SoLID experiment will come online.  SoLID will use the latest detector and
readout technology to enable an increase in luminosity by a factor of 10
compared to existing detectors.  SoLID is in an advanced stage of project
planning, with Canadians contributing to Cherenkov detector R\&D and
construction.  SoLID will see continuing activity through the end of the new
LRP (2036), in parallel with the MOLLER experiment (covered elsewhere in this
document).
\end{itemize}

\paragraph{\underline{Current Program}}

\paragraph{Gluonic Excitations Experiment, GlueX}
\noindent{(JLab) Regina; {\intl{Armenia, Chile, China, Germany, Greece, Russia, UK, USA}}}

Quantum Chromodynamics permits a ``zoo'' of particles.  Traditionally, the
manifestation of hadrons in nature has their spectrum dominated by colourless
``quark model'' states---such as quark-antiquark pairs (mesons) and quark
triplets (baryons)---while gluonic degrees of freedom are difficult to
observe or suppressed. The key question is to understand how the quark and
gluonic degrees of freedom that are present in the fundamental QCD Lagrangian
manifest themselves in the spectrum of hadrons.

\begin{figure}[htbp]\centering
\includegraphics[width=3.0in]{Figs/EtaComparison.pdf}
\includegraphics[width=3.0in]{Figs/b1-PWA.png}
\caption{\label{fig:physicsresults}
  a) The photon beam asymmetry $\Sigma_{\eta}$ shown as a function of Mandelstam $-t$ for $\gamma p \rightarrow p \eta$. Previous GlueX (2017) results {H. Al Ghoul et al. (GlueX), Phys.\ Rev.\ C 95, 042201(R) (2017)} are shown along with predictions from several Regge theory calculations: {J. M. Laget, Phys.\ Rev.\ C 72, 022202(R) (2005), Phys.\ Lett.\ B 695, 199 (2011); J. Nys et al. (JPAC), Phys.\ Rev.\ D 95, 034014 (2017); EtaMAID: V. L. Kashevarov, M. Ostrick, and L. Tiator, Phys.\ Rev.\ C 96, 035207 (2017); G. R. Goldstein and J. F. Owens, Phys.\ Rev.\ D 7, 865 (1973)}.  b) Initial PWA showing the $\omega \pi^0$ and $3\pi$ invariant masses and four angles in the helicity frame of the $\omega \pi^0$, using a JPAC amplitude analysis model {A. Szczepaniak et al. (JPAC Collaboration), private communication}, and indicating the dominance of $J^P = 1^+$ $b_1$(1235).
  }
\end{figure}

Mesons are grouped in {\em multiplets}, each characterized by a given $J^{PC}$
combination. Hybrid mesons result from the addition of angular momentum quantum
numbers from a gluonic component to those of the two quarks and are visualized
as $q\bar{q}g$ states. Among the hybrids, a subset is predicted to have exotic
$J^{PC}$ combinations that are not allowed in the simple quark model. Our
understanding is maturing thanks to results from Lattice QCD
calculations that predict a clear and detailed spectrum of hybrid mesons. On
the experimental side, hadron spectroscopy has become more exciting since evidence
for new types of groupings in heavy-quark systems has been found: tetraquark
and pentaquark,  candidates in the charmonium sector, and hybrids in the
light-quark sector probed in pion production.

GlueX's place in the global spectroscopy program is pivotal; the statistics
from the GlueX experiment significantly exceed past data sets and provide data
in unexplored domains of meson and baryon spectroscopy. More generally, the
study of the light-quark hadron spectrum is the centrepiece of experimental hadron
spectroscopy effort in the U.S, as articulated in the 2015 NSAC Long Range
Plan: ``GlueX at JLab, one of the flagship experiments of the 12-GeV Upgrade,
is designed to search for exotic particles where the {\em glue} is in an
energetically excited state.''  Hadron spectroscopy ties in with the 2017--2021
Canadian Subatomic Physics LRP under section 5, ``How do Quarks and Gluons Give
Rise to the Hadronic Properties and the Phases of Hadronic Matter?''

The GlueX-I program commenced in 2016 and has been completed, while GlueX-II
(higher luminosity) is under way and will continue over the next few years. The
Regina-GlueX is charged with gain calibrations of the silicon photomultipliers
(SiPMs) for the Barrel Calorimeter (BCAL), a 30-ton detector designed and built at
Regina with a combination of NSERC and US-DOE funds,
as well as online and offline monitoring of the SiPM stability and
saturation using an LED system.  Since 2019, they have started machine learning efforts to improve the understanding of the BCAL's electromagnetic and
hadronic response.  The group led efforts to extract the photon-beam asymmetry
for $\eta$ and $\eta^{\prime}$, resulting in a 2019 Ph.D. Thesis
(T. Beattie, 2019, UofR President's Distinguished Medal) 
and a publication \footnote{\href{https://doi.org/10.1103/PhysRevC.100.052201}{The GlueX Collaboration, S. Adhikari et al.,
Phys.\ Rev.\ C 100, 052201(R) (2019)}}. The extracted beam asymmetry afforded
comparisons to theoretical models, and indicated the dominance of natural
parity exchange in the reaction mechanism.
An analysis of beam asymmetry in the $\eta \Delta^+$ channel is being carried
out in a similar fashion to the recently completed analysis in the $\pi^-
\Delta^{++}$ channel.
In addition, work is ongoing in the extraction of cross section, moments and
first pass at a Partial Wave Analysis (PWA) of the $b_1$(1235) meson in its
dominant $\omega \pi$ decay, on the road to looking at hybrid decays into $b_1
\pi$; the initial foray shows the need to include both S- and D-waves at a
ratio close to what is predicted by theory \footnote{
\href{https://doi.org/10.1103/PhysRevD.100.054506}{Hadron
Spectrum Collaboration A. J. Woss et al., Phys.\ Rev. D 100, 054506 (2019)}}.  Three Regina Ph.D.
students and a postdoc are working on these analyses.

In addition, Hornidge has recently initiated the process of joining the GlueX Collaboration in order to participate in measurements of the neutral and charged pion polarizabilities, which dovetails nicely with the MAMI polarizability program.

\paragraph{Pion and Kaon Form Factors as probe of emergent mass generation in hadrons}
\noindent (JLab) Regina; {\intl{Armenia, USA}}

The elastic electromagnetic form factors of the charged pion and kaon,
$F_{\pi}(Q^2)$ and $F_K(Q^2)$, are a rich source of insights into basic
features of hadron structure, such as the roles played by confinement and
Dynamical Chiral Symmetry Breaking (DCSB) in fixing the hadron’s size,
determining its mass, and defining the transition from the strong- to
perturbative-QCD domains.  The pion's properties in particular are intimately
connected with DCSB, which explains the origin of more than 98\% of the mass of
the visible matter in the universe.  Furthermore, owning to the intimate
connection between DCSB and the pion, the properties of nature's lightest
hadron provide the most direct access to QCD's momentum-dependent effective
quark mass.  The measurement of the pion electric form factor
($F_{\pi}$), which encodes our knowledge of the distribution of quarks and gluons
within it, presents an extraordinary opportunity to observe QCD's transition
from confinement-dominated physics at large length-scales to short-distance
scales where the aspects of perturbative QCD become apparent.

\begin{figure}[htbp]
\begin{center}
%\vspace{-0.5cm}
\includegraphics[width=2.95in]{Figs/fpi12GeV_err2020.png}
\includegraphics[width=2.95in]{Figs/fK_err11.png}
\vspace{-0.2cm}
\caption{\label{fig:fpiK}
Existing data (green, black, red, blue, yellow) and projected uncertainties for
data expected by 2026 from JLab Hall~C for the charged pion form
factor (left) and charged kaon form factor (right), in comparison to model calculations.  In both cases, the planned data will be a dramatic improvement in the world database of these fundamental hadron structure observables.}
\end{center}
\end{figure}

The Regina group also leads the pion form factor program at Jefferson Lab.
Their to date work has had significant impact, gathering over 1000
citations, and appearing in various review articles.  The work has confirmed
that at a photon virtuality of $Q^2=2.45$~GeV$^2$, one is still far from the
resolution region where the pion behaves like a simple $q\bar{q}$ pair,
i.e. far from the ``asymptotic'' limit.  The measured pion form factor is a
factor of about three larger than the hard (perturbative) QCD prediction.
Modern calculations show that this factor could be explained by using a pion
valence quark distribution amplitude evaluated at a scale appropriate to
the experiment.  An extended calculation indicates that above $Q^2>8$~GeV$^2$,
the pion form factor should exhibit $Q^2$-dependence from hard QCD, but with
normalization fixed by a pion wave function dominated by DCSB effects.  The
JLab experimental data allow these (and other) calculations to be tested with
authority.  The extension of these studies to shorter distance scales is underway.
Data taking is scheduled for 2021--24, followed by 3--5 years of analysis.  This
work is expected to yield high quality $F_{\pi}$ data up to $Q^2=6.0$ GeV$^2$,
and lower quality data up to $Q^2=8.5$ GeV$^2$, and will provide the world's
best data set on this fundamental quantity until these studies can be extended
at the EIC.

The $K^+$ form factor, where the $d$ anti-quark is replaced with the $s$
anti-quark, provides a vital second study case.  The $K^+$ structure has
significant influence from DCSB, as does the $\pi^+$, but the greater mass of
the $\bar{s}$ also has influence from the Higgs mechanism.  The understanding
of the structure of both mesons, within a unified theoretical framework, will
greatly assist with our understanding of the origin of hadronic mass.  The data
taking for the first $F_K$ experiment was completed in spring 2019, and results
are anticipated to be published over the period 2022--25.  If the data confirm
that the scattering from the virtual $K^+$ in the nucleon dominates at low
four-momentum transfer to the target $|t|\ll m_p^2$, similar to as was done for
the pion, the experiment will yield the world's first quality data for $F_K$
above $Q^2>0.2$~GeV$^2$.

\paragraph{\underline{New Projects}}

\paragraph{JLab Eta Factory, JEF
\label{sec:qcd_jef}}
\noindent{(JLab) Regina; {\intl{Armenia, Chile, China, Germany, Greece, Russia, UK, USA}}}

JEF involves a significant upgrade of the GlueX base instrumentation, by
replacing the inner section of the GlueX forward calorimeter (FCAL), and is
planned to come online in 2024.  
This will allow experiments to explore both fundamental topics with
experimental sensitivities not previously achievable. This device will provide
enhanced performance over the base FCAL (a factor of two improvement in energy
and position resolution, a factor of four enlargement in granularity, and one
order of magnitude enhancement in radiation resistance).  These features will
enhance the GlueX exotic hybrid meson search with better particle
identification and up to 60\% improvement in the sensitivity of PWA and will
also allow precision measurements of rare meson decays that will: (1) enable
the JEF experiment to measure various $\eta/\eta^{\prime}$ decays with emphasis
on rare neutral modes; (2) provide the radiation resistance needed by GlueX to
run at high luminosity for exotic hybrid meson search with better particle
identification and up to 60\% improvement in the sensitivity of PWA.

\begin{figure}[htbp]\centering
\includegraphics[width=3.18in]{Figs/JEF-exclusion.png}
\includegraphics[width=2.82in]{Figs/FCAL-II.png}
\caption{\label{fig:jef}
  a) Current exclusion regions for a leptophobic gauge boson $B^{\prime}$ {S. Tulin, Phys.\ Rev.\ D 89, 114008 (2014)}, with the proposed search region via $\eta \rightarrow  B^{\prime} (\rightarrow \gamma \pi^0)$ labelled ``JEF'' for the coupling versus mass plane. Dashed gray contours denote the upper bound on the mass scale $\Lambda$ for new electroweak fermions needed for anomaly cancellation. b) The FCAL-II insert/upgrade, showing the new, finer-granularity $\rm PbWO_4$ crystals in the centre in brown, with the original, re-stacked FCAL lead glass blocks in green.}
\end{figure}

JEF will probe the role of scalar meson dynamics in chiral perturbation theory
for the first time, tighten the uncertainty in the light quark mass ratio
extracted from $\eta \rightarrow 3\pi$, search for sub-GeV dark gauge bosons (a
leptophobic vector $B^{\prime}$ and an electrophobic scalar $\varphi^{\prime}$)
by improving the existing bounds more than two orders of magnitude that is
complementary to the ongoing worldwide efforts on invisible decays or decays
involving leptons;
and provide direct probes for $C$-violating, $P$-conserving new forces.  
Work is underway on event generators and full Geant4
simulations. R\&D and construction of the FCAL-II insert is at an advanced
stage: detector assembly and testing has commenced at a new clean room at JLab
with the Regina postdoc and Ph.D. students contributing to the efforts.

The GlueX plans for the next five years have been recently optimized to start
with three publications in 2019 on beam asymmetries and the first on cross
sections, which will pave the path to PWA publications planned from 2021 and
beyond.  The experiment will continue to run until $\sim$2023,
when a shutdown is planned to start to install the FCAL-II insert for the JEF
progam.  During the 2021--26 period, the JEF program will ramp up and continue
into the next five years.

\paragraph{Solenoidal Large Intensity Detector, SoLID
\label{sec:qcd_solid}}
\noindent{(JLab) Regina; {\intl{Australia, China, France, Israel,
Italy, Korea, Mexico, Russia, Slovenia, Ukraine, UK, USA}}}

The development of the Generalized Parton Distribution (GPD) formalism in the
last 20 years is a notable advance in our understanding of the structure of the
nucleon.  Unifying the concepts of parton distributions and hadronic form
factors, GPDs are ``universal objects'' which provide a comprehensive framework
for describing the quark and gluon structure of the nucleon.  Knowledge of GPDs
would allow a tomographic 3D understanding of the nucleon to be built up.  They
are probed experimentally through a variety of Deep Exclusive reactions, where
the system responds coherently to the incoming probe.  The Solenoidal Large
Intensity Detector (SoLID), planned to be constructed in Hall A of Jefferson
Lab in the next five years, has an open geometry and high luminosity capability
which makes it optimally suited to the study of GPDs.

\begin{figure}[htbp]
\begin{center}
%\vspace{-0.5cm}
\includegraphics[width=4.5in]{Figs/SoLID_SIDIS_3He-coil_s.png}
\vspace{-0.2cm}
\caption{\label{fig:solid}
The Solenoidal Large Intensity Device (SoLID), planned for Jefferson Lab.  The
polarized $^3$He target is at far left, and
the Heavy Gas Cherenkov detector is second from right.}
\end{center}
\end{figure}

The Regina-led experiment will use SoLID, in conjunction with a polarized
$^3$He target, to probe the poorest-known GPD, $\tilde{E}$.  The four
lowest-order GPDs are parameterized in terms of quark chirality, with
$\tilde{E}$ involving the difference between left and right handed quarks, and
corresponds to a process where the proton helicity is flipped.  $\tilde{E}$ is
believed to contain an important pion pole contribution, and hence is optimally
studied in Deep Exclusive Meson Production (DEMP).  $\tilde{E}$ cannot be
related to already known parton distributions, and so experimental information
about $\tilde{E}$ via DEMP can provide new information on nucleon structure
which is unlikely to be available from any other source.  The experimental
access to $\tilde{E}$ is through the azimuthal variation of the emitted pions
from a transversely polarized nucleon target.  Since polarized $^3$He is an
excellent proxy for a polarized neutron, the reaction of interest is
essentially $\vec{n}(e,e'\pi^-)p$.  Due to their higher $Q^2$, the SoLID
measurements should be more readily interpretable than earlier results from
HERMES, providing the first clear experimental signature of $\tilde{E}$.

The essential idea of SoLID is to use the latest technology detector and
readout to enable an increase in luminosity by a factor of ten compared to
existing detectors (such as CLAS-12).  The construction of the SoLID detector,
an international project estimated at ~US\$70M, has received very favorable
feedback in scientific reviews conducted by the U.S. Department of Energy
(US-DOE).  The SoLID Collaboration has 300 members from 72 institutions in 13
countries, and is in an advanced stage of project planning, in anticipation of
project approval in 2021.  Construction and
installation would extend through 2026, with the physics program to last at
least 10 years.  The Regina group, in partnership with Duke University, is
responsible for the Heavy Gas Cherenkov detector, which will be used for
forward angle pion identification.  They have received funds from CFI and
provincial sources for HGC prototyping.  The full HGC detector is projected to
cost $\sim$US\$4M, which is planned to be funded through a combination of CFI-IF and
US-DOE funds.

\subsubsection{Mainz Microtron}

\paragraph{A2 Collaboration} (MAMI) Mount Allison, Regina, Saint Mary's;
{\intl{Croatia, Germany, Italy, Russia, Switzerland,  UK, USA}}

As already mentioned above, a portion of the Canadian experimental research
program on QCD is carried out at facilities other than than JLab. One of those
is MAMI, the Mainz Microtron (Mainz, Germany), where Canadians are members of
the A2 Collaboration. The Mainz laboratory provides a high-quality,
high-flux continuous-wave 1.5 GeV electron beam providing a beam of polarized
photons, a refurbished near-$4\pi$ CB-TAPS detector system, and a frozen-spin
polarized proton target.  These have allowed unique access to high-precision
measurements of nucleon structure.  Obtaining these new, precise
nucleon-structure data is the aim of each of the experiments that have
significant Canadian contributions.

\underline{Proton Spin and Scalar Polarizabilities}
We have conducted a program of measurements to extract the spin polarizabilities of the proton in the 250--320 MeV energy range, and scalar polarizabilities of the proton below pion threshold.  Such polarizabilities are fundamental observables of hadron structure, and are amenable to calculation with various QCD-inspired models and effective theories.  To extract the heretofore unknown spin polarizabilities we took data on three polarization observables in the $\Delta$ region: the asymmetries $\Sigma_{2x}$, $\Sigma_3$, and $\Sigma_{2z}$, and to determine the scalar polarizabilities with unprecented precision and reduced model dependence we measured the polarziation observable $\Sigma_3$ at low energy for the very first time.

The results for $\Sigma_{2x}$ have been published---along with a first independent determination of the individual proton spin polarizabilities---in Physical Review Letters \footnote{\href{https://doi.org/10.1103/PhysRevLett.114.112501}
{P.~Martel et al., PRL 114, 112501 (2015)}}.  The paper for the $\Sigma_{2z}$ asymmetry was recently published in PRC 
\footnote{\href{https://doi.org/10.1103/PhysRevC.102.035205}
{D. Paudyal et al., PRC 102, 035205 (2020)}}.  
The manuscript for the $\Sigma_3$ asymmetry in the $\Delta$ region with new fits for the spin polarizabilities is in preparation.  The combination of all three asymmetries allows for an independent extraction of all four spin polarizabilities with small statistical and model-dependent systematic errors, and our results should be completely finalized in the fall of 2020.  In order to get the statistics necessary to appreciably reduce the errors on the scalar polarizabilities, the tagging spectrometer and data-acquisition electronics were upgraded, allowing for a significant increase in the photon flux and trigger rate.  Mainz Ph.D. student E.~Mornacchi is in the final stages of the data analysis and we expect to publish the results by the end of 2020.  It is possible that we will take more data on the $\Sigma_{2x}$ observable in 2021, but this would be the final measurement on the proton part of the Mainz polarizability program.

\underline{Neutron Polarizabilities}
Information on the neutron polarizabilities remains extremely fragmentary, largely due to the lack of a free-neutron target. The scalar polarizabilities are poorly known compared to the proton and the spin polarizabilities are almost entirely unknown.  With the help of colleagues in Glasgow and Mainz we are developing an active, high-pressure helium target for use at the centre of the CB-TAPS detector system.  As our third set of polarizability experiments, we will measure elastic Compton scattering on both $^3$He and $^4$He, and with the help of theoretical work in the Chiral Perturbation Theory framework we will be able to extract the neutron scalar polarizabilities accurately for the first time.  The proposal for this measurement has been given an ``A'' rating by the MAMI Program Advisory Committee and we expect to conduct this measurement in 2021 or 2022.

The neutron spin polarizabilities are of equal importance to the proton spin polarizabilities, but most neutron observables are at best poorly measured due to the nuclear effects present when attempting to extract the neutron quantities.  The neutron spin polarizabilities are no exception.  Although there are some predictions, and due to isospin invariance the neutron should behave in much the same manner as the proton, there are no experimental measurements on the neutron spin polarizabilities.  The only result is a ``recommended experimental value'' of the linear combination $\gamma_\pi^{n} = (58.6\pm4.0)\times10^{-4}\,\text{fm}^2$.  There are, however, recent theory results in the framework of ChPT and more are on the way. Measuring the neutron spin polarizabilities would provide another important tool for testing models of QCD in the low- and intermediate-energy region.  Similar to what was done for the proton spin polarizabilities, the plan for the fourth set of measurements is to use deuterated butanol in the frozen-spin target and polarized photons in the $\Delta$ region, along with theory support to attempt an extraction of the neutron quantities.  The experiments should run in the middle of the decade, 2023--26, with the corresponding analysis completed and papers published by the decade's end.

\subsection{The longer term: The Electron-Ion Collider (EIC)
\label{sec:eic3}}

%GH: text from EIC_Canada_Brief

\subsubsection{Physics Program}

The EIC will uniquely address three profound questions about nucleons (neutrons and protons) and how they are assembled to form the nuclei of atoms. In addition, the EIC presents significant opportunities that connect to neutrino, high energy, particle physics and astrophysics.

\begin{figure}[htbp]
\begin{center}
%\vspace{-0.5cm}
\includegraphics[width=4.5in]{Figs/luminosity-landscape.png}
\vspace{-0.2cm}
\caption{\label{fig:com-lumi-overview}
The opportunity to use a variety of electron-ion center of mass energies enables rich physics potential at the EIC, from studying the internal structure of the nucleons and nuclei, to the tomographic visualization of the correlated three-dimensional structure of the nucleon at the femtoscale. The ongoing Yellow Report process will provide input to the detailed accelerator design to identify at which center of mass energy the luminosity should be optimized.}
\end{center}
\end{figure}

\paragraph{How does the mass of the nucleon arise?}

The problem is that while gluons have no mass, and $u$, $d$ quarks are nearly
massless, the nucleons that contain them are heavy; the total mass of a nucleon
is some 100 times greater than the mass of the valence quarks it contains (see Figure~\ref{fig:nucleon-mass}).
The largest contribution to the mass of the proton originates from the gluon
field energy. In this sense, the source of visible mass in the universe is not
the Higgs field, but the gluon field.
By selecting the energy and resolution of the virtual photon, an EIC can
address different regions of Bjorken $x$ going from the regime of moderate $x$
dominated by valence quarks to the small $x$ regime controlled by sea quarks
and gluons. These types of experiments have been carried out before, but the
EIC will add several new dimensions by studying the distribution of partons in
the plane transverse to the motion of the nucleon, and by determining their
transverse motion. These measurements will provide tomographic images of
nucleons and nuclei, to determine: the relative spatial size of the valence
quark, sea quark, and gluon distributions; the spatial structure of the
different contributions to the energy density and pressure forces in the
nucleon; and the spatial distribution of gluons in a large nucleus.

\begin{figure}[htbp]
\begin{center}
%\vspace{-0.5cm}
\includegraphics[width=4.5in]{Figs/img-38-1.jpg}
\vspace{-0.2cm}
\caption{\label{fig:nucleon-mass}
The mass of the nucleon originates not only in the mass of its constituent quarks, but overwhelmingly from the energy in its quark and gluon fields.}
\end{center}
\end{figure}

\paragraph{How does the spin of the nucleon arise?}

How the angular momentum, both intrinsic as well as orbital, of the internal
quarks and gluons gives rise to the known nucleon spin is not understood.  The
quark polarization contribution to the nucleon spin is only about 30
percent. The remainder of the spin must reside in orbital angular momenta of
quarks and gluons or gluon polarization.  Polarized proton--proton collisions
at the Relativistic Heavy Ion Collider (RHIC) have provided the first evidence
for a nonvanishing gluon spin polarization in the proton. A central goal of the
EIC program is to provide a determination of the gluon spin contribution and
its orbital angular momentum. These measurements would be based on the
resolution dependence of polarized Deep Inelastic Scattering (DIS). This
dependence arises from quark and gluon partons radiating additional
partons. When a polarized gluon radiates a quark-antiquark pair, the spin
orientation of the gluon is transferred to the quark and the antiquark. This
effect can be measured using polarized electron scattering with a polarized
proton beam.  The orbital angular momentum of gluons can be probed via the
exclusive measurements described. Precise knowledge of the spin of gluons
combined with sum rules of the generalized parton distributions (GPDs) determined in these measurements offer the possibility of isolating the contribution
to the nucleon spin of the orbital angular momentum of gluons.

\paragraph{What are the emergent properties of dense systems of gluons?}

The nature of gluons in matter, i.e. their arrangements or states, and the
details of how they hold matter together, is not well known. Gluons in matter
are somewhat like dark matter in the universe, unseen but playing a crucial
role.  The EIC would be able to study the gluons that bind quarks and
antiquarks into nucleons and nuclei with unprecedented precision. A central
goal of such studies is to explore the limit of low Bjorken $x$, where the
number of gluons in the target is very large. Here, the description of the
nucleus in terms of colored degrees of freedom is expected to simplify
dramatically, and discovery of a new type of state composed of dense gluon
matter is also expected. The EIC would also be able to explore modifications of
the quark distributions in nuclei.  These issues are fundamental to an
understanding of the matter in the universe.

\paragraph{Connections with other fields}

Nuclear physics also includes high-priority programs in neutrino physics and
fundamental symmetries. Neutrinos are messengers from hot and dense
environments like the solar interior, type II supernova explosions, and cooling
neutron stars. Neutrinos also provide an important window into fundamental
symmetries and possible extensions of the Standard Model of particle
physics. One central question is whether the neutrino is its own antiparticle,
which would imply that neutrinos would violate lepton number
conservation. Evidence for lepton number violation is being sought in
neutrinoless double beta decay experiments, and nuclear physicists are
actively working toward a ton-scale detector of such processes. Electron
accelerators have also made important contributions to the study of fundamental
symmetries. JLab studies parity-violating electron scattering, and a series
of past and planned experiments, QWeak, Measurement Of Lepton Lepton
Elastic Reactions (MOLLER), and Solenoidal Large Intensity Device (SoLID), study the
evolution of the fundamental electroweak coupling, and search for physics
beyond the Standard Model.  An EIC would naturally extend this program,
studying fundamental symmetries at higher energies.

\subsubsection{Current Canadian effort}

Multiple groups are already active in the EIC program. Below are the current and projected Canadian subatomic physics efforts at U.~Manitoba, U.~Regina, and Mount Allison U.

\paragraph{Pion form factors as probe of emergent mass generation in hadrons}

The elastic electromagnetic form factors of the charged pion and kaon,
$F_{\pi}(Q^2)$ and $F_K(Q^2)$, are a rich source of insights into basic
features of hadron structure, such as the roles played by confinement and
Dynamical Chiral Symmetry Breaking (DCSB) in fixing the hadron’s size,
determining its mass, and defining the transition from the strong- to
perturbative-QCD domains.  Studies during the last decade, based on JLab 6-GeV
measurements, have generated confidence in the reliability of pion
electroproduction as a tool for pion form factor extractions. Forthcoming
measurements at the 12-GeV JLab will deliver pion form factor data that are
anticipated to bridge the region where QCD transitions from the strong (color
confinement, long-distance) to perturbative (asymptotic freedom,
short-distance) domains.

At EIC, pion form factor measurements can be extended to still larger $Q^2$, by
measuring ratios of positively- and negatively-charged pions in quasi-elastic
electron-pion (off-shell) scattering via the $p(e,e'\pi^+)n$ and
$n(e,e'\pi^-)p$ reactions, accessed with proton and deuterium beams. Huber's
group at U.~Regina has written an event generator and have performed
simulations demonstrating the feasibility of these measurements.  The
measurements would be over a range of small $-t=-(p_{p}-p_{n})^2$, and gauged with theoretical
and phenomenological expectations, to again verify the reliability of the pion
form factor extraction.

\begin{figure}[htbp]
\begin{center}
\vspace{-0.5cm}
\includegraphics[width=3.5in]{Figs/fpi_EIC_18.png}
\vspace{-0.2cm}
\caption{\label{fig:eic_fpi}
Existing data (blue, black, yellow, green) and projected uncertainties for 
future data on the pion form factor from JLab (cyan, red) and EIC (black), in
comparison to a variety of hadronic structure models.  The EIC projections 
clearly cover a much larger $Q^2$ range than the JLab
measurements, providing access to the mass 
These results have been
published in {A.C. Aguilar {\em et al.}, Eur.Phys.J.A 55 190 (2019).}}
\end{center}
\end{figure}

A consistent and robust EIC pion form factor data set will probe deep into the
region where $F_{\pi}(Q^2)$ exhibits strong sensitivity to both emergent mass
generation via DCSB and the evolution of this effect with distance
scale. Figure~\ref{fig:eic_fpi} shows the EIC projections for possible pion form
factor measurements. The pion form factor projections assume an integrated
luminosity of 20~fb$^{-1}$ with a 5 GeV electron beam colliding with a 100 GeV
proton beam.  Simulation work to refine the eRHIC detector requirements is ongoing, 
as part of EIC Yellow Report efforts.

Due to its strange quark content, roughly 1/3 of the $K^+$ mass is due to the
Higgs mechanism, while the $\pi^+$ mass is barely influenced by the Higgs and
is almost entirely generated by DCSB.  Thus, the comparison of the charged pion
and charged kaon form factors over a wide $Q^2$ range would provide unique information
relevant to understanding the generation of hadronic mass.  Planned simulation work for
2021-23 include extensions to the case of the charged kaon, assuming that
measurements by Huber's group at the 12-GeV JLab on exclusive kaon
electroproduction beyond the resonance region at $-t\leq 0.9$ GeV$^2$ and $Q^2$
up to $\sim 5$ GeV$^2$ confirm the feasibility of this technique.

%%%%% Precision electroweak measurements
\paragraph{Electroweak mixing angle measurements and tests of the Standard Model}

Precision measurements of fundamental observables in the electroweak sector of the Standard Model have allowed us to impose strict limits on the existence of potential new physics beyond the Standard Model. Canadian subatomic physicists were instrumental in such experiments at Jefferson Lab in the PV-DIS experiment \footnote{
\href{https://doi.org/10.1038/nature12964}
{Jefferson Lab PVDIS Collaboration, Nature 506, 67–70 (2014)}} and QWeak experiment \footnote{
\href{https://doi.org/10.1038/s41586-018-0096-0}{Jefferson Lab Qweak Collaboration,
Nature 557, 207–211 (2018)}}.

The EIC presents opportunities for isoscalar hadrons, \textit{i.e.} electron--deuteron collisions, which have never been available. Measurements of interference structure functions $F^{\gamma Z}_1$ and $F^{\gamma Z}_3$ in polarized electron--unpolarized deuteron scattering will allow for clean separation of the weak vector and weak axial-vector quark couplings, and determination of the electroweak mixing angle $\sin^2\theta_W$ in the poorly explored region between 10 and 70~GeV (see Figure~\ref{fig:sin_world}). Additionally, the measurements of $F^{\gamma Z}_3$ will improve our knowledge of the $V_{ud}$ term in the $u$-quark unitarity relation for the CKM matrix, another avenue for Standard Model tests.

The EIC presents opportunities outside hadronic physics as well, for example in the area of fundamental symmetries.
New channels for Standard Model tests of lepton flavor violation present themselves through $e^- \to \tau^-$ decays. At the anticipated integrated luminosities of 100~fb$^{-1}$, this channel holds discovery potential for leptoquarks, $R$-parity violating supersymmetry, leptophobic $Z^{\prime}$ bosons, and other charged lepton flavor violation theories.

In Spring 2020, the U.~Manitoba members of the EIC-Canada Collaboration organized a (virtual) workshop on Electroweak and Beyond the Standard Model physics at the EIC that attracted over 80 theoretical and experimental subatomic physicists. The outcomes of this workshop are directly impacting the Yellow Report process.

\begin{figure}[htbp]
\begin{center}
%\vspace{-0.5cm}
\includegraphics[width=4.25in]{Figs/WeakMixingAngleAll2-gg.pdf}
\vspace{-0.2cm}
\caption{\label{fig:sin_world}
Available and anticipated (Moller, SOLID, Belle-II) measurements of the electroweak mixing angle at facilities worldwide are compared with projected measurements and their uncertainties at the EIC for a variety of kinematic conditions. The EIC projections cover an energy scale $\mu$ between the low-energy regime and the $Z$-pole where little data is currently available. These projections have been published in {Eur.Phys.J.A 53, 55 (2017)}}
\end{center}
\end{figure}

Accurate knowledge of the electron beam polarization is important for the electroweak mixing angle program. The U.~Manitoba group plans to apply its expertise in Compton polarimetry at HERA, Jefferson Lab, and the EIC. The development of Compton polarimetry for the EIC has significant synergies with the upgrade of the Belle II facility to use polarized electrons in their high energy ring.

\paragraph{Light and heavy quark spectroscopy}

Interactions and structures are convolved with each other in nuclear matter. The observed properties of nucleons and nuclei emerge out of this complex system. Achieving an understanding of this dynamical system promises to be transformational.

Strong QCD dynamics results in many-body correlations between quarks and gluons and, as a result,  hadron structure emerges. Traditionally, the manifestation of hadrons in nature has their spectrum dominated by colorless ``quark model'' states --- such as quark-antiquark pairs (mesons) and quark triplets (baryons) --- while gluonic degrees of freedom are difficult to observe or suppressed. 
A question arises: 
how do the quark and gluonic degrees of freedom that are present in the fundamental QCD Lagrangian manifest themselves in the spectrum of hadrons?

In hadron spectroscopy there are standard quarkonium states but also a host of unexpected resonances have appeared that are not well reconciled with the usual charmonium interpretation.  Specifically, one of the challenges in the charmonium sector at the moment is that if all the bumps that are seen are true resonances, it's not clear what the underlying degrees of freedom are (multiquark states, molecules, etc.).  One great advantage of electro-/photo-production is that most of these states have been seen in $e^+e^-$ annihilation or decays, and  electro-/photo-production allows access to different kinematics which can help confirm their resonant nature and exclude them being kinematical effects; this is particular important for Z-states.  In addition, not only are these states created 
in larger numbers than $e^+e^-$ annihilation experiments, but one has a well-controlled initial state (e-p) which makes determining the $J^{PC}$ of these states 
a lot easier than, say, at the LHC. In addition, the bottomonium exotic sector needs to be explored with sufficient detail, in order to achieve a comprehensive and consistent understanding of both sectors. 

New states need to be confirmed such as $\tilde{X}(3872) \rightarrow J/\psi \pi \pi$, 
the observed charged charmonium structure observed by BESIII and Belle (Figure~\ref{fig:charmonium}), and CLEO \footnote{
\href{https://doi.org/10.1016/j.physletb.2013.10.041}
{T. Xiao et al, PLB 727, 366 (2013)}} in decay of Y(4260) to $Z_c^+(3900) \rightarrow J/\psi \pi$ needs to be studied, as do 
pentaquarks \footnote{\href{https://doi.org/10.1103/PhysRevD.94.034002}
{A.N. Hiller Blin et al. (JPAC), PRD 94, 034002 (2016)}} whose confirmation in photo- and electro-production will be the first step towards elucidating their nature. 
These studies are statistically limited at the B-factories and difficult/impossible at LHCb.  
Experimentally, the EIC will offer centre of mass variability with minimal loss of luminosity, which is a critical feature in the study of the onset of interesting QCD phenomena.  
The EIC is the perfect lab to carry out thorough studies of hadron spectroscopy and to address the remaining open questions in that field.  

\begin{figure}[htbp]\centering
\includegraphics[width=3.0in]{Figs/BESIII-Charmonium.png}
\includegraphics[width=3.0in]{Figs/Belle-Charmonium.png}
\caption{\label{fig:charmonium}
  Charged charmonium structure observed by BESIII (left) {Phys. Rev. Lett. 110, 252001 (2013)}, and Belle (right) {Phys. Rev. Lett. 110, 252002 (2013)} in the decay of $\Upsilon$(4260).}
\end{figure}

An EIC Physics Working Group has been formed focusing on light and heavy spectroscopy at EIC.  This group plans to demonstrate a strong physics case for a hadron spectroscopy program at EIC, which will be included in the next EIC Physics Book. Studies have commenced using event generators and simulating the kinematics %(Figure~\ref{fig:emometa} left two panels) and signal-to-noise (Figure~\ref{fig:emometa} right two panels), 
which will help define the detector design.
The Regina-GlueX group that has joined the EIC Spectroscopy effort, which has a strong contingent of GlueX collaborators from the USA.  Likewise, the group has joined the EIC Calorimetry group (with BNL and JLab participants) where the group's experience in building the 30~ton sampling fraction, electromagnetic barrel calorimeter (BCAL) for GlueX will be leveraged, as will the expertise in testing and deploying silicon photomultipliers.

In the 2021--2026 period, the group will be active in using/developing event generators and simulating and smearing generated events in the EIC detector framework, to study kinematical regions and see how observables depend on acceptance, achievable resolutions, etc., towards achieving the spectroscopy physics goals and in ensuring that the developed detector(s) can meet those goals.  
In parallel, the effort of the Calorimetry Working group is focused on collecting information about different calorimetry technologies and simulations studies, as well as examine physics-driven requirements to ECAL and HCAL calorimetry.  

During the 2026-2031 period, final design, construction and commissioning of the EIC detector(s) is planned.  The group will be active in calorimetry R\&D and testing, together with American colleagues from JLab and BNL.  The group's FTE and HQPs will increase during this period, as the GlueX and JEF projects in Hall~D wind down.

\subsubsection{Long Range Planning Visions}

\paragraph{5 year outlook (2022--26)}
Over the next 5 years, the EIC community plans to achieve the next three critical decisions, CD-1 (alternative selection and cost range, by March 2021), CD-2 (final design, by September 2022), and CD-3 (start  construction, by the 4th quarter of 2023). This aggressive schedule is only possible because of the strong international user community of over 1000 subatomic physicists working in concert with the joint accelerator design teams at Brookhaven National Laboratory and Jefferson Lab.

The EIC-Canada Collaboration anticipates that the next 5 years will be a period of growth. Opportunities exist for subatomic physics groups with detector technology expertise to join the EIC-Canada Collaboration. The current members are in leadership positions in the detector development and physics working groups, as well as the software working groups. The Canadian theorists are also interested in joining EIC working groups and committees and complementing the experiment efforts, with broad range of contributions such as e+A gluon saturation, GPDs and TMDs, radiative corrections and Lattice QCD.

By 2026, the number of Canadian PIs are anticipated to increase to 2.5 FTE and the number of HQP to 9, following the acceptance of the Canadian Expression of Interest in international detector development efforts (to be submitted in late 2020). At that point, the construction phase of a major Canadian detector component (funded through a substantial CFI investment of at least \$1.5M) will begin.

\paragraph{Long-term vision (2027--36)}
In the longer term, the Canadian detector construction and commissioning efforts will result in an increase to 15 HQP by 2029, and the start of physics data taking will result in an increase to 21 HQP supervised by 5.6 FTE. The start of the first North American collider of this century will be associated with significant scientific interest. In the first years of the 2030s, significant new results will be published by the two detector collider collaborations.

\paragraph{Interface with the Jefferson Lab program}

There is significant synergy in the physics programs of the Electron-Ion Collider and the Jefferson Lab 12 GeV facility. As the Electron-Ion Collider program is ramping up, the Jefferson Lab 12 GeV program continues to take advantage of the energy upgrade completed in 2017. As of summer 2020, there are another 11 years of physics experiments approved for running at Jefferson Lab, with additional experiment proposals evaluated annually. The Jefferson Lab leadership is currently engaging in a 1-year idea gathering effort to define how their mission will be reshaped or expanded in the 2030s. However, this is unlikely to include a hardware project of similar scope as the Jefferson Lab 12 GeV upgrade or the Electron-Ion Collider construction. With the completion of the upgraded detector construction and commissioning (including the new Hall D GlueX experiment that is in its third year of data taking), this bandwidth has become available to Electron-Ion Collider detector design and construction efforts. While we anticipate an increasing focus on the Electron-Ion Collider program, this will not come at a cost to the Jefferson Lab 12 GeV program. In particular, the Canadian proponents remain committed to the success of the Jefferson Lab parity program, a unique program world-wide.

\subsection{Summary}

The research community involved in hadronic/QCD physics pursue a program that is rich and diverse. The many projects in the program aim to study QCD under all of its facets, from understanding the nature of the many-body problem at zero and finite temperatures, to mapping out the transition between hadronic and partonic degrees of freedom. Canadians have undertaken key responsibilities in their respective experimental collaborations, and have continued to make fundamental contributions to theory. In the years ahead, a specific example of the potential to access new physics is the successful 12 GeV upgrade of the Jefferson Laboratory, which has transformed that facility into a site that will provide unique opportunities to understand the nature of the strong interaction, the nucleon, and the nucleus. In addition, as new facilities like the proposed EIC enter an advanced stage of planning, the Canadian hadronic/QCD community is already at work, preparing its
participation in detector design and development, as well as in experiment preparation.
In order to realize the strong scientific potential of the new generation of experiments in which the Canadian hadronic/QCD community is involved and to enable a vigorous theoretical effort (see Section \ref{sec:Theory}), a continued strong support of researchers and a strategic investment in HQP is necessary.