Studies of Hadronic Structure with Electromagnetic Probes

Research Program:

1. The Central Scientific Question

The Standard Model of particle physics now lies at the center of much nuclear physics research. One of the basic elements of the Standard Model, the existence of quarks and gluons, was first inferred from the spectrum of elementary particles and from electron-scattering experiments. Susequently, Quantum Chromo-Dynamics (QCD) was developed to describe them. Just as the formulation of Maxwell's equations led to a quantitative understanding of electromagnetic phenomena in the late 19th century, so the development of QCD a century later has provided the theoretical foundation for the understanding of many strong interaction phenomena.

The nature of the strong force at long distances, where quark confinement dominates, is one of the major unsolved problems of modern physics. In fact, the Fields Institute and the Clay Institute have both listed the solution of how color 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. One of the complications 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. 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. Our program of experimental studies is intended to better our understanding of QCD in the strongly interacting, non-perturbative regime, where quark (color) confinement dominates.

Jefferson Lab (JLab) is the world's premier nuclear physics facility, with intense, high quality, polarized electron beams of energy up to 12 GeV, optimized to perform a wide variety of hadron structure measurements, as alluded to above. The newly upgraded facilities allow a new generation of very promising and very interesting experiments to study the structure of hadronic matter. These are described in further detail in Sec 2 below. In parallel, we are making preparations for the Electron-Ion Collider, a new facility that will be constructed at Brookhaven National Laboratory, in New York state this decade. This work is described in Sec 3 below.

Various News Items about our Work:

2. Jefferson Lab Measurements

I have been involved in the JLab scientific program for approximately 25 years. The table below lists the 12 GeV experiments that I am playing a leadership role in. One of the obstacles to our improved comprehension of non-perturbative QCD has been a lack of quality data, particularly for the Deep Exclusive electron scattering reactions, which provide the clearest picture of the inner workings of QCD. Jefferson Lab enables these studies with its continuous, high luminosity electron beams, and detectors with good particle identification and reproducible systematics. By making precision measurements of this nature, we hope to better make the elusive connection between the underlying quark/gluon dynamics and the observed structures of mesons and nucleons, and ultimately to understand the origin of hadronic mass.

Experiment Number	Spokespersons (contact person underlined)	Experiment Title	Scientific Priority Rating	PAC Days Awarded	Anticipated Running Time (assuming 50% data taking efficiency)
E12-06-101	D. Gaskell, G.M. Huber	Measurement of the Charged Pion Form Factor to High Q² [Superceded by E12-19-006]	A	52 days	104 days (completed)
E12-07-105	T. Horn, G.M. Huber	Scaling Study of the L-T Separated Pion Electroproduction Cross-Section at 11 GeV [Superceded by E12-19-006]	A-	36 days	72 days (completed)
E12-09-011	T. Horn, G.M. Huber, P. Markowitz	Studies of L-T Separated Kaon Electroproduction Cross-Section from 5-11 GeV	B+	40 days	80 days (partially completed)
E11-002	E.J. Brash, G.M. Huber, R. Ransome, S. Strauch	Proton Recoil Polarization in the ⁴He(e,e'p)³H, ²H(e,e'p)n, and ¹H(e,e'p) Reactions	B+	37 days	74 days
E12-10-006B	Z. Ahmed, G.M. Huber, Z. Ye	Measurement of Deep Exclusive π^- Production using a Transversely polarized ³He Target and the SoLID Spectrometer	Run Group has A priority	48 days	96 days
E12-19-006	D. Gaskell, T. Horn, G.M. Huber	Study of L--T Separated Pion Electroproduction Cross Section at 11 GeV and Measurement of the Charged Pion Form Factor to High Q² [Supercedes E12-06-101 and E12-07-105]	A	88 days	176 days (completed)
E12-20-007	G.M. Huber, W.B. Li, J. Stevens	Backward-angle Exclusive π⁰ Production above the Resonance Region	B	29 days	58 days (beam request submitted)

The first set of experiments are taking place in Hall C, and use the new SHMS spectrometer in coincidence with the HMS spectrometer in Hall C. The requirements upon this 11 GeV/c spectrometer are 5.5 degree forward angle capability, and good systematic error control in the L/T separation at high luminosity. Our responsibilities included the SHMS heavy gas (C₄F₁₀) Cerenkov detector and assistance with the spectrometer commissioning.

2a. Pion and Kaon Electric Form Factors

Central to the problem of the transition of QCD from long to short distance scales is the pion, which has a particularly important role in nature. As the lightest meson, with a single valence quark and a single valence antiquark, it is responsible for the long range character of the strong interaction that binds the atomic nucleus. The underlying rules governing the strong interaction are believed to be left-right (chirally)-symmetric. If this were completely true, the pion would have no mass. But the chiral symmetry of massless QCD is broken dynamically by quark-gluon interactions (Dynamical Chiral Symmetry Breaking, DCSB) and explicitly by inclusion of light quark masses, giving the pion mass. The pion is seen as key to confirm the mechanisms that dynamically generate >98% of the mass of the visible universe and central to the effort to understand hadron structure. With such strong theoretical motivation, it is vital to the study the pion electric form factor (F_π), which encodes our knowledge of the distribution of quarks and gluons within it.

The long-term interest in the π⁺ electric form factor is due to Farrar and Jackson [PRL 43(1979)246], who showed that F_π is rigorously calculable in perturbative QCD (pQCD). Their answer is exact and model-independent at infinite Q², dependent only on the assumption of quark asymptotic freedom. Such a reliable result is rare in QCD. However, it is not known at what region of Q² the value of F_π will reflect the onset of pQCD and this value, as well as the actual behavior of F_π as a function of Q² in the non-perturbative transition region, are important tests of our understanding of QCD in bound hadron systems. Because of the smaller number of valence quarks in the pion, the asymptotic regime will be reached at lower values of Q² than for the nucleon form factors, so the π⁺ form factor offers our best hope of directly observing QCD's transition from strong confinement at long distance scales to asymptotic freedom at short distances.

Our experiments with 6 GeV beam have confirmed that at a photon virtuality of Q²=2.45 GeV², the data are still far from the resolution region where the pion behaves like a simple q-qbar pair, i.e. far from the ''asymptotic'' limit. The measured pion form factor is a factor of about three larger than the pQCD prediction. Modern calculations show that this factor could be explained by using a pion valence quark distribution amplitude (PDA) evaluated at a scale appropriate to the experiment. An extension of this work indicates that above Q²>8 GeV², the pion form factor should exhibit Q²-dependence from hard QCD, but with normalization fixed by a pion wave function dominated by DCSB effects. Our 12 GeV JLab experimental data will allow these (and other) calculations to be tested with authority.

The kaon form factor (F_K), where the d anti-quark is replaced with an s anti-quark, provides a vital second study case. First of all, the same pQCD prediction applies to the K⁺ form factor as to the π⁺. Thus, in the hard scattering limit, pQCD predicts the two form factors will behave similarly. K⁺ structure has significant influence from DCSB, as does the π⁺, but the greater mass of the s-bar anti-quark 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. Since the K⁺ form factor is almost completely unknown above Q²=0.3 GeV², our experiment has motivated many new theoretical studies of kaon structure.

The high quality, continuous electron beam of JLab makes these measurements possible. The measurement of the pion and kaon form factors is quite challenging. Since the lifetime of the π⁺ is only 25 ns, pion targets do not exist experimentally, the pion form factor cannot be measured directly above Q²>0.3 GeV². Rather, one must deduce its value at higher Q² from a careful study of the longitudinal and transverse (L/T) cross sections of high-energy exclusive electroproduction, p(e,e'π⁺)n. Scattering from the virtual π⁺ cloud surrounding the proton dominates the longitudinal photon cross section (dσ_L/dt), at low momentum transfer. The K⁺ form factor must be accessed similarly, by scattering from the virtual kaon cloud of the proton. The high quality electron beam and well-understood magnetic spectrometers at JLab offer the possibility to measure these form factors to good precision. The objectives of our work are to: (i) establish the reliability of the extraction of the meson form factors from electroproduction data over a broad kinematic range, and (ii) obtain high quality form factor measurements to high momentum transfer. There is no other facility worldwide at which this program could be pursued.

2b. QCD Factorization Tests using Exclusive Pion and Kaon Production

Our two related 12 GeV experiments [E12-19-006, E12-09-011] will allow a direct comparison of the scaling properties of Deep Exclusive K⁺ and π⁺ electroproduction ,to better understand the onset of QCD factorization in the transition from hadronic to partonic degrees of freedom. In particular, if the QCD factorization regime has been reached in a given measurement, the longitudinal cross section will dominate over the transverse, and the separated cross sections will scale according to the 1/Qⁿ expectations of pQCD. For Deep Exclusive Meson production, quark counting rules predict σ_L proportional to 1/Q⁶, and σ_T falling at least as fast as 1/Q⁸. In 2007, we published an initial scaling study of the 1/Qⁿ dependences of charged pion electroproduction at fixed x. The study indicated only partial agreement with the factorization expectations, but the error bars on the fit were compromised by the limited kinematic range available at 6 GeV. Since the extraction of GPDs from Deep Exclusive electron scattering data relies on the factorization of the scattering amplitude into hard and soft processes, we have proposed to extend these studies to a broader kinematic range. We will also perform measurements of the longitudinal cross section at low -t to determine whether the K+ elastic form factor can be inferred from these data. If the studies are favorable, we would perform the first-ever extraction of the K⁺ form factor above Q²=0.35 GeV². The K⁺ experiment acquired data in 2018-2019, and the π⁺ experiment acquired data in 2021 and 2022.

2c. u-channel Deep Exclusive Vector Meson Electroproduction

Backward-angle (-u~ 0) meson electroproduction has been previously ignored, but is anticipated to offer complementary information to forward-angle (-t~ 0) meson electroproduction. This is particularly interesting with the development of the collinear-factorization approach of QCD, which has drawn attention to Transition Distribution Amplitidues (TDAs) as a new probe of hadronic structure. TDAs directly probe the three-quark plus sea q-qbar component in the nucleon's wave function. The kinematic domain demanded by the collinear factorization framework is unique. The meson must be emitted antiparallel to the virtual γ^*, at extreme backward angle.

This regime is now open for study, following our pioneering E01-004 work to obtain low -u data on exclusive ω electroproduction, p(e,e'p)ω, simultaneously with the p(e,e'π⁺)n data. The recoiling proton is detected at forward angle, along the axis of the momentum transfer vector, and the meson is reconstructed in missing mass. The ω is reconstructed as a sharp peak atop a broad background (primarily multi-pion phase space and ρ production). Since the missing mass reconstruction method does not require the detection of the produced ω, it allows the acquisition of data in a kinematic regime that was considered to be inaccessible through the standard direct detection method. Our studies, including a full L/T/LT/TT separation at Q²=1.6, 2.45 GeV², demonstrated that the technique is reliable. The L/T ratio demonstrated the dominance of σ_T as -u increases, particularly at the higher Q²=2.45 GeV² setting. These conclusions are broadly in line with a theoretical model based on the transition distribution amplitude (TDA) framework.

We acquired further backward-angle ω and φ data in the 12 GeV pion form factor experiment, including the Q²-dependence up to 6 GeV². Our new experiment (E12-20-007) will measure exclusive π⁰ electroproduction in u-channel kinematics. The three objectives of the 12 GeV studies are: (i) to establish the existence of a significant backward-angle cross section peak for multiple reaction channels and over a wide kinematic range; (ii) extract the dependence of the separated cross sections upon momentum transfer, to study the transition from soft to hard scattering, similar to described above for π⁺ production; and (iii) establish the applicable kinematic range of the backward angle factorization scheme. We also have an idea to use this reaction to probe the phenomenon of Color Transparency in a new experiment.

2d. Transverse Single Spin Asymmetry with SoLID

The development of the Generalized Parton Distribution (GPD) formalism is a notable advance in our understanding of the structure of the nucleon. GPDs unify the concepts of parton distributions and hadronic form factors, and are ''universal objects'' that provide a comprehensive framework for describing the quark and gluon structure of the nucleon. GPDs are probed through Deep Exclusive reactions, and their knowledge would allow a tomographic 3D understanding of the nucleon to be built up.

Beyond 2025, we intend to pursue measurements of the single-spin asymmetry in deep exclusive π^- electroproduction from the neutron in transversely polarized ³He, using the Solenoidal Large Intensity Detector (SoLID). Our primarily goal is the measurement of the A_UT^sin(φ-φS) polarization observable, which has been noted as being particularly sensitive to the most poolrly known GPD, the polarized helicity-flip E-tilde. Factorization studies have indicated that precocious scaling is likely to set in at moderate Q²~2-4 GeV², as opposed to the absolute cross section, where scaling is not expected until Q² >10 GeV². Furthermore, this observable has been noted as being important for the reliable extraction of the charged pion form factor from pion electroproduction. Our secondary goal is the measurement of the A_UT^sin(φS) asymmetry, which is sensitive to the higher twist transversity GPDs, and provides valuable information on transverse photon contributions at small -t. We are pursuing these objectives with the SoLID Collaboration at Jefferson Lab, who approved our addition to the E12-10-006 Run Group as ''a flagship experiment for the SoLID GPD program''. We have also received equipment funds from CFI and the Fedoruk Centre for HGC prototyping studies.

3. Preparations for the Electron-Ion Collider

The Electron-Ion Collider (EIC) is a major new collider facility to be built on Long Island, New York, by the US Department of Energy, with the flexibility to change the nuclear ion species as well as the beam energies. For electron-proton collisions, the Electron-Ion Collider (EIC) would be the world's first collider where both beams are polarized. The EIC luminosity is proposed to be 100-1000 times that of the former HERA accelerator at DESY. The projected completion date of the EIC is approximately 2031.

The significance of the science to be addressed by the Electron-Ion Collider, and its importance to nuclear physics in particular, and to the physical sciences in general, was highlighted in a report by the US National Academies of Sciences, Engineering, and Medicine. The report identified three core questions:

How does the mass of the nucleon arise?
How does the spin of the nucleon arise?
What are the emergent properties of dense systems of gluons?

3a. Meson form factors as probe of emergent mass generation in hadrons

Through EIC Canada, we are one of the Canadian groups involved in bringing the EIC experimental program to fruition. Our work is most closely tied to the first question. 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. 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. Thus, more than 98% of the visible mass of the universe emerges as a consequence of strong interactions within QCD, through the mechanism tied to Dynamical Chiral Symmetry Breaking (DCSB).

As shown in the figure above, the differences between the proton and the lightest mesons are also significant. Due to the strong interactions within QCD, the proton's mass is large in the absence of quark couplings to the Higgs boson (i.e. massless u, d chiral limit). Conversely, and yet still due to the same strong interactions, the kaon and pion are massless in the chiral limit (i.e. they are Goldstone bosons). The mass budgets of these crucially important particles demand interpretation. The equations of QCD stress that any explanation of the proton's mass is incomplete unless it simultaneously explains the light masses of QCD's Goldstone bosons, the pion and kaon. The generation of mass is coupled with color confinement, which is fundamental to the proton's stability. In order to finally complete the Standard Model, it is crucial to understand the emergence of mass within the strong interaction and the modulating effects of Higgs boson mass generation, both of which are fundamental to understanding the evolution of our universe. This is one of the key goals of the EIC.

At the EIC, the pion form factor measurements we are pursuing at JLab can be extended to much larger Q², by measuring ratios of positively- and negatively-charged pions in quasi-elastic electron-pion (off-shell) scattering via the p(e,e'π⁺)n and n(e,e'π^-)p reactions, accessed with proton and deuterium beams. We have written an event generator and have performed simulations demonstrating the feasibility of these measurements. The measurements would be over a range of small −t, and gauged with theoretical and phenomenological expectations, to again verify the reliability of the pion form factor extraction.

A consistent and robust EIC pion form factor data set will probe deep into the region where F_π exhibits strong sensitivity to both emergent mass generation via DCSB and the evolution of this effect with distance scale. Due to its strange quark content, roughly 1/3 of the K⁺ mass is due to the Higgs mechanism, while the π⁺ mass is barely influenced by the Higgs and is almost entirely generated by strong QCD interactions. Thus, the comparison of the charged pion and charged kaon form factors over a wide Q² range would provide unique information relevant to understanding the generation of hadronic mass. We are also extending our simulation work to the case of the charged kaon, assuming that our E12-09-011 measurements on exclusive kaon electroproduction at JLab confirm the feasibility of this technique.

3b. Study of GPDs with Deep Exclusive π Electroproduction

The polarization degrees of freedom at EIC will enable unprecedented access to GPD distributions over a wide kinematic range, offering details of the internal proton wave function that will not be available from any other source. As an extension of our planned JLab studies with SoLID, we plan to eventually perform detailed Monte Carlo simulations to investigate the feasibility of such mesurements at the EIC.