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Nuclear Physics


The Electric and Magnetic Elastic Proton Form Factor Ratio GEp/GMp

ratio GEp/GMp obtained

Figure 1: The ratio GEp/GMp obtained by the recoil polarization technique (Punjabi et al. (2005) (filled blue circle), Puckett et al. (2012)  (filled red squares) and Puckett et al. (2010) (filled black triangles)) compared to ratio obtained by the Rosenbluth technique (green open points). Theoretical curves from Lomon (2002), Guidal et al. (2005), de Melo et al. (2009), Gross et al. (2008), and Roberts et al. (2009), shown as solid (red), short-dashed (blue), dash-dot (orange), dash (green), and short dash-dot (magenta), respectively.

Interaction of electron

Figure 2:  Interaction of electron with one of the quark in a proton through exchange of a virtual photon.

One of the fundamental goals of nuclear physics is to understand the structure and behavior of strongly interacting matter in terms of its basic constituents, quarks and gluons. An important step towards this goal is the characterization of the internal structure of the nucleon; the elastic electric and magnetic form factors of the proton and neutron are key ingredients of this characterization. The elastic electromagnetic form factors are directly related to the charge and current distributions inside the nucleon; these form factors are among the most basic observables of the nucleon.

The challenge of understanding the nucleon's structure and dynamics has occupied a central place in nuclear physics; many experimental and theoretical physicists have spent a considerable amount of effort in the last five decades to understand it. A break-through was made towards this goal in the last decade and a half, when two JLab Hall A experiments extracted the elastic electromagnetic form factor ratio of the proton, GEp/GMp , from the measured recoil proton polarization components, using the polarization transfer method. A third experiment in Hall C at JLab has pushed the highest Q2 limit to 8.5 GeV2 using the same method.

The form factor ratio data from all three JLab recoil polarization experiments are shown in Figure 1, which display a strikingly different Q2 dependence than the Rosenbluth results. The most important feature of the data from JLab is the decrease of the ratio to Q2= 8.5 GeV2, which indicates that GEp falls faster with increasing Q2 than GMp and demonstrates that the spatial extension of charge is larger than that of magnetization. This is the first definitive experimental indication that the Q2 dependence of GEp and GMp is different. In the third experiment in Hall C, the ratio is decreasing, however with a strong indication that the linear behavior has softened toward a possible constancy of the ratio at Q2 values beyond the range covered so far.

1. M. K. Jones et al., Phys. Rev. Lett. 84 (2000) 1398; V. Punjabi et al., Phys. Rev. C 71 (2005) 055202
2. O. Gayou et al., Phys. Rev. Lett. 88 (2002) 092301; A.J.R. Puckett et al., Phys. Rev. C 85 (2012) 045203
3. A.J.R. Puckett et al., Phys. Rev. Lett. 104 (2010) 242301
4. C.F. Perdrisat, V. Punjabi and M. Vanderhaeghen, Prog. Nucl. Part. Phys. 59 (2007) 694

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Nuclear Dependence of the EMC Effect

Nuclear Dependence of the EMC Effect

Visualization of the  dominant 4He and 9Be configurations.

Nuclear Dependence of the EMC Effect

Slope of the isoscalar EMC ratios for 0.35 < x < 0.7 as a function of scaled nuclear density as calculated using  GFMC of spatial distributions as described in Ref [1] . A clear breakdown of the simple density dependence model for the EMC effect for 9Be is observed.

Protons and neutrons are complex bound states of quarks and gluons, held together by the strong interactions of quantum chromo dynamics (QCD). Their structure may be modified inside of the dense environment of a nucleus, and such modification of hadron properties in the nuclear environment is of fundamental importance in understanding QCD. Measurements of deep inelastic scattering in nuclei show that the quark distributions in heavy nuclei are not simply the sum of the quark distributions of the constituent protons and neutron, as one might expect for a weakly bound system.

Despite much theoretical work, no unique and universally accepted explanation of this difference, known as the “EMC effect”, has emerged. The nuclear effects come in part from binding and Fermi motion mechanisms with possible internal modifications of the nucleon. Many models of the EMC effect predict that it depends on the mass or density of the parent nucleus, but previous data, focusing mainly on heavier nuclei, could not determine if the EMC effect scales with mass or density. A detailed experimental study [1, 2] was performed in Hall C to test these predictions on a variety of light nuclei. 

Figure 1 shows the magnitude of the EMC effect  as a function of average nuclear density. The difference between 3He and 4He is much larger than predicted by an A-dependent fit from a previous experiment at SLAC, while the large EMC effect in 9Be is at odds with a density-dependent parameterization. A likely explanation is the unusual structure of 9Be, with two orbiting alpha-like clusters with an additional neutron as shown in Figure 2. The orbiting clusters yield a large radius but most of the protons and neutrons are contained within the high local densities of the clusters. Thus, the observed nuclear dependence suggests that the local environment of the nucleons may be driving the nuclear modification. Plans are being made to test this hypothesis with the 12 GeV upgrade of Jefferson Lab by including a more complete set of light nuclei.

J. Seely, et al., Phys. Rev. Lett. 103 (2009) 202301

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Precision Test of the Standard Model

Figure 1

Figure 2 shows the model independent mass limit (Λ/g) in TeV of new physics as a function of the up and down quark flavor mixing angle, theta. The dashed red curve is the Particle Data Group limit, while the solid blue curve is the improvement from including recent PVES measurements.

Figure 1

Figure 1 shows the knowledge of the weak charges associated with an axial coupling to the electron and a vector coupling to the up and down quarks. All experimental limits and contours are shown at 1 standard deviation. The dashed contour displays the previous experimental limits reported by the Particle Data Group, together with the prediction of the Standard Model (the black star). The filled ellipse denotes the new constraint provided by recent high precision PVES measurements on p, D and He, while the smaller contour indicates the full constraint obtained by combining all current results. The width of the solid blue line is the anticipated uncertainty of the upcoming Qweak experiment - assuming the SM.

The Electroweak Standard Model (SM) has to date been enormously successful. The search for a fundamental description of nature which goes beyond the SM is driven by two complementary experimental strategies. The first is to build increasingly energetic colliders, such as the Large Hadron Collider (LHC) at CERN, to excite matter into a new form. The second approach is to perform high precision measurements where an observed discrepancy with the SM would reveal the signature of new forms of matter. As shown in Figure 1, state-of-the-art measurements of parity-violating electron scattering (PVES) at Jefferson Lab have led to the most precise determination of the weak charges of the quarks hitherto possible. Shown in Figure 2, these measurements also constrain the possibility of new physics to an energy scale of order one TeV or higher — a factor of two above previous limits, which were dominated by atomic parity violation (APV) data. While limiting the early discovery potential for new Z' bosons, this result provides guidance as to the best windows of opportunity for discovery, both at the LHC and in the Qweak experiment now in preparation at Jefferson Lab.

R. D. Young, R. D. Carlini, A. W. Thomas and J. Roche, Phys. Rev. Lett. 99 (2007) 122003
R.D. Young et al. Phys. Rev. Lett. 97 (2006) 102002
D. S. Armstrong et al. (G0 Collaboration), Phys. Rev. Lett. 95 (2005) 092001
A. Acha et al. (HAPPEX Collaboration), Phys. Rev. Lett. 98 (2007) 032301

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Strange Quarks in the Proton

Strange quark proton

The worldwide program of parity violating electron scattering data that constrain the contributions of strange quarks to the proton’s charge and magnetism at large spatial distances (low Q2). The solid ellipse represents a fit to the data shown, incorporating a theoretical prediction for the proton’s axial form factor (GA), which is not yet well-constrained experimentally. The dashed ellipse incorporates more data at shorter spatial distances and removes the theoretical constraint on the axial term.

While the proton is most simply described as a bound state of three quarks (2 up and 1 down), a more complete description includes a sea of gluons and virtual quark/anti-quark pairs arising from interactions between the three quarks. For instance, strange quark/anti-quark pairs are present in this quark sea even though the proton has, on average, no overall strangeness. The effect of this intrinsic strangeness on the charge and magnetism of the proton can be precisely studied by using the weak interaction (Z-boson exchange) as a probe. While the weak force is normally too slight to be detected alongside the dominant electromagnetic force, the weak interaction is required in any process which violates parity symmetry.

Researchers at Jefferson Lab and elsewhere have therefore turned to high precision measurements of the parity-violating electron scattering (PVES) asymmetry in order to study the effects of strange quarks in the proton. PVES has become an essential tool in mapping out the flavor composition of the electromagnetic form factors. Exposing the role of the strange quark with such measurements provides direct information on the underlying dynamics of non-perturbative QCD – a considerable achievement both experimentally and theoretically.

World data at the lowest momentum transfer Q2, which most directly relates to the “static” strange magnetic moment and charge radius, is shown in figure 1 as constraints on the fractional strange quark contributions to the proton form factors. Superimposed are results from global fits of the low Q2 data , which differ in treatment of the theoretically challenging correction term from the anapole moment of the proton. The ellipses represent allowed regions at 95% statistical confidence level. As is evident from these fits, the strange charge radius is very small, while the strange quark contribution to the proton magnetic moment contribution is less than 10%.

(See also Strange Magnetic Moment entry in the Theory section)

A. Acha et al. (HAPPEX Collaboration), Phys. Rev. Lett. 98 (2007) 032301
D. S. Armstrong et al. (G0 Collaboration), Phys. Rev. Lett. 95 (2005) 092001
R.D. Young et al., Phys. Rev. Lett. 97 (2006) 102002
Jianglai Liu et al., Phys. Rev. C 76 (2007) 025202

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Generalized Parton Distributions (GPDs)


DVCS cross section results for one of twelve kinematics bins measured in Hall A E00-110. See C. Munoz Camacho et al. for a full description.


A model-dependent extraction of up- and down-quark contributions (orbital angular momentum plus spin) to the spin of the proton (Hall A E03-106).

Example of DVCS asymmetry data obtained in the e1-DVCS experiment.  Left: kinematic coverage and binning in the (xB, Q2) space

An important goal of Jefferson Lab is to provide a detailed, three-dimensional picture of the nucleon in terms of its quark and gluon constituents, and to understand how this complex structure leads to its well known properties such as mass, spin and magnetic moment. A promising theoretical framework for this task is provided by generalized parton distributions (GPDs), which are hybrids of the usual form factors and parton distributions, but in addition include correlations between states of different longitudinal and transverse momenta.

The simplest processes that allow extraction of GPDs from data and provide the cornerstone of their exploration are deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP).  In these processes, the scattering takes place from a single quark in the nucleon, producing a highly energetic photon or meson in the final state.

The first comprehensive study of DVCS was performed in the e1-DVCS experiment in Hall B, the first part of which ran in 2005.  In this experiment the electron beam was alternately polarized parallel and anti-parallel to the beam direction, enabling measurements of beam spin asymmetries (BSA) in more than 600 kinematic intervals.

In Hall A, accurate measurements of the helicity-dependent DVCS cross sections e pe p γ and e ne n γ have been obtained in two dedicated experiments (E00-110: DVCS on the proton and E03-106: DVCS on the deuteron). The Q2 dependence of the proton cross section indicates scattering on individual quarks, which allows the DVCS data to be interpreted in terms of GPDs. The feasibility of accessing experimentally the quark orbital angular momentum, which may constitute the missing link in the nucleon spin puzzle, was also demonstrated in E03-106.

R. DeMasi et al., Phys. Rev. C 77 (2008) 042201
F-X. Girod et al, Phys. Rev. Lett. 100 (2008) 162002
C. Munoz Camacho et al., Phys. Rev. Lett. 97 (2006) 262002
M. Mazouz et al., Phys. Rev. Lett. 99 (2007) 242501
M. Guidal, M.V. Polyakov, A.V. Radyushkin, and M. Vanderhaeghen, Phys. Rev. D 72 (2005) 054013

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Electric and Magnetic Elastic Proton Form Factors (GEp/GMp)

The ratios μpGEp/GMp from two JLab recoil polarization experiments, compared to the Rosenbluth separation data (left) and with several theoretical calculations (right).

Data from experiments measuring the ratio of the electric and magnetic elastic form factors of the proton, GEp/GMp, have shown an unexpected and significantly different dependence on the four-momentum transfer squared, Q2, for GEp than for GMp. This has been interpreted as indicating a difference between the spatial distributions of charge and magnetization at short distances. The results from two JLab experiments using the new polariztion transfer method were surprising, as they disagree with the ratios μpGEp/GMp, where μp is the proton magnetic moment, obtained by measuring cross sections (Rosenbluth method). The latter appear to be near unity up to about 6 GeV2, whereas the polarization results show a ratio value around 0.3 at Q2 of 5.6 GeV2.

The large discrepancy between the ratios obtained with the Rosenbluth and the recoil polarization method was confirmed by recent precision measurements of GEp/GMp in Hall A using the traditional Rosenbluth method. These demonstrated that the discrepancy is due to missing physics in the extraction of GEp/GMp from the data, rather than systematic problems in either data set. A likely explanation is the two-photon exchange process, which affects both cross section and polarization transfer components at the level of a few percent. However, because the Rosenbluth method is very sensitive to small variations in the angular dependence of the cross section, the two-photon effects have a much more dramatic impact on the results from Rosenbluth separation, while modifying the ratios obtained with the polarization method by a few percent only.

(See also Two-Photon Exchange entry in the Theory section

M. K. Jones et al., Phys. Rev. Lett. 84 (2000) 1398
V. Punjabi et al., Phys. Rev. C 71 (2005) 055202
O. Gayou et al., Phys. Rev. Lett. 88 (2002) 092301
I.A. Qattan et al., Phys. Rev. Lett. 94 (2005) 142301

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Neutron Charge Distribution (GEn)

charge distribution

The world data set on GEn, including data from two Jefferson Lab experiments, E93-026 (using a polarized deuteron target) and E93-038 (using an unpolarized deuteron target and a recoil polarimeter), and other experiments that have used polarized targets and recoil polarimeters.

The Q2 dependence of the charge form factor of the neutron, GEn, can provide vital information on the origin of charge distribution in the neutron. A precise determination of GEn has challenged physicists for more than 40 years, primarily from the lack of a free neutron target and the fact that the charge form factor is so small.

The application of new techniques and technologies at Jefferson Lab has allowed decisive steps to be made toward rectifying the situation, with two experiments providing a precise measurement of the charge form factor out to large Q2. These unique experiments have put the neutron charge form factor on nearly equal footing with the other nucleon form factors. For the first time, data are available which constrain any modern theory which attempts to describe all four nucleon form factors: the proton electric and magnetic form factors and the neutron electric and magnetic form factors.

H. Zhu et al., Phys. Rev. Lett. 87 (2001) 081801
R. Madey et al., Phys. Rev. Lett. 91 (2003) 122002
G. Warren et al., Phys. Rev. Lett. 92 (2004) 042301
B. Plaster et al., Phys. Rev. C 73 (2006) 025205

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Nucleon-Delta Transition

Pion Cloud

a) The pion cloud probed at long wavelengths. b) The nucleon core probed at high Q2 (high resolution).


The ratio E2/M1 as a function of Q2.

One of the many success stories of JLab's resonance physics program has been what we have learned about the Delta resonance, which is the lowest energy quantum excitation of the nucleon. There are several ways the nucleon can be electromagnetically excited to the Delta. One, denoted M1, or magnetic dipole moment, gives us information about the distribution of the quarks' electric current within the nucleon and Delta. Another, denoted E2, or electric quadrupole moment, describes the deviation from sphericity of the quarks' electric charge distribution.

In the simplest quark picture, both the nucleon and Delta are spherical objects, so that E1=0, and the excitation proceeds completely by M1. Experiments at JLab have shown, however, that the E2/M1 ratio is small but non-zero, suggesting that the nucleon and Delta are not perfectly spherical. The physical picture which this reveals is that the nucleon is a "core" of three quarks enveloped by a non-spherical "cloud" of pions, and photons often interact with this cloud rather than the core. The expectation is that at very high Q2, or short wavelengths, one penetrates the cloud and observes the core, which looks very different, so that E2/M1 should significantly change, even approaching unity at very high Q2.

The E2/M1 ratio has been measured at JLab up to the very highest Q2 ever recorded, corresponding to a resolution of less than 0.05 femtometers. Remarkably, E2/M1 doesn't change very much, but remains approximately constant at a small negative value. At this time, we do not yet understand what properties of the nucleon or Delta give rise to this behavior. There is evidence that further development of the theoretical tool called Lattice QCD may supply the answer.

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Pion Form Factor


Pion form factor results from the two JLab Hall C experiments. Also shown are e-pi elastic data from CERN and earlier pion electroproduction data from DESY. The curves are from a Dyson-Schwinger equation (Maris and Tandy, 2000), QCD sum rule (Nesterenko, 1982), constituent quark model (Hwang, 2001), and a pQCD calculation (Bakulev, 2004).


The pion form factor in leading order pQCD.

In research carried out in Jefferson Lab's Hall C, the Fπ collaboration is studying how the strong force combines nature's fundamental building blocks into the lightest particle built of quarks: the pion – which is arguably the most important of the mesons due to its Goldstone nature (it has an unusually small mass). We can naively picture the pion as consisting of one each of the lightest quarks and anti-quarks. As with all quark-based particles, however, a more realistic description of the pion also includes the quark-gluon sea: a strong-force driven bevy of quarks, anti-quarks and gluons popping into and out of existence and providing the foundation of the pion's structure.

This structure is mapped out by a single form factor (Fπ), which provides information about the distribution of charge inside the pion. By measuring Fπ at ever shorter distances, it is possible to study its transition from a particle where the quark-gluon sea plays a significant role in its structure to what looks like a simple quark-antiquark system.

In 2001, Jefferson Lab provided the first high precision pion electroproduction data for Fπ between Q2 values of 0.6 and 1.6 (GeV/c)2. The new result, at Q2=2.45 (GeV/c)2, is still far from the transition to the Q2 region where the pion looks like a simple quark-antiquark pair and is providing a stringent test for models that attempt to incorporate the important "softer" quark sea contributions. Plans are now being made to access the transition region with the higher-energy electron beam proposed for the 12 GeV Upgrade at Jefferson Lab. The Upgrade will allow an extension of the Fπ measurement up to a value of Q2 of about 6 (GeV/c)2, which will probe the pion at double the resolution.

T. Horn et. al., Phys. Rev. Lett. 97 (2006) 192001
V. Tadevosyan et al., Phys. Rev. C 75 (2007) 055205
J. Volmer et al., Phys. Rev. Lett. 86 (2001) 1713

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Nucleon-Nucleon Short-Range Correlations


Illustration of the 12C(e,e'pN) reaction. The incident electron couples to a nucleon-nucleon pair via a virtual photon. In the final state, the scattered electron is detected along with the knocked-out proton, as well as the correlated partner.

The nucleus can often be approximated as an independent collection of protons and neutrons confined in a volume, but for short periods of time, the nucleons in the nucleus can strongly overlap. This quantum mechanical overlapping, known as a nucleon-nucleon short-range correlation, is a manifestation of the nuclear strong force, which produces not only the long-range attraction that holds matter together, but also the short-range repulsion that keeps it from collapsing.

Direct observation of short-range correlations has been a challenge for nuclear physics, as other phenomena often mask the signal. Cross section ratios of inclusive scattering of heavy nuclei to 3He at Q2>1.4 [GeV/c]2 and as function of Brokjen x have shown scaling regions that have been interpreted as corresponding to two- and three-nucleon correlations [1]. To directly observe high momentum pairs emerging from the nucleus, a triple coincident 12C(e,e'pN) experiment was designed to probe high Q2>1.5 [GeV/c]2, Brokjen x>1 and missing momenta greater than 300 [MeV/c]2.

The experiment found, for these special conditions, that every single knocked-out proton had a correlated partner [2]. As predicted by theorists [3], the correlated nucleon pairs were predominately proton-neutron pairs with only a small fraction of proton-proton pairs. Since the nuclear density of a correlated pair is approximately five times larger than average nuclear matter, these results may give scientists new insight into dense nuclear systems such as neutron stars.

[1] K. S. Egiyan et al., Phys. Rev. C 68 (2003) 014313 and Phys. Rev. Lett. 96 (2006) 082501.
[2] R. Subedi et al., Science 320 (2008) 1476 and R. Shneor et al., Phys. Rev. Lett. 99 (2007) 072501.
[3] M. M. Sargsian et al., Phys. Rev. C 71 (2005) 044615. and R. Schiavilla et al., Phys. Rev. Lett. 98 (2007) 132501

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Quark-Hadron Duality in Structure Functions



One of the principal challenges of QCD is to bridge the small- and large-scale behavior of the strong nuclear interactions. At short distances, perturbative QCD is very successful in describing nucleon structure in terms of quarks and gluons. At large distances, the effects of confinement impose a more efficient description in terms of collective hadron degrees of freedom. Despite this apparent dichotomy, an intriguing connection has been observed between the low- and high-energy data on nucleon structure functions, which is referred to as "quark-hadron duality."

A detailed experimental study performed in Hall C on unpolarized structure functions found that quark-hadron duality occurs at much lower momentum transfers, in more observables, and in far less limited regions of energy than expected.

More recently, the spin dependence of duality has been studied in Hall B for the proton and deuteron g1 structure functions and in Hall A for the neutron using 3He targets. The results of the E01-012 Hall A experiment suggest the appearance of duality in the neutron and 3He polarized g1 structure functions down to Q2 as low as 1.8 (GeV/c)2.

These results allow the first studies to be made of the spin and flavor dependence of quark-hadron duality and provide vital clues to the long-standing challenge of QCD to describe nuclear forces at large distances.

P. Solvignon et al., Phys.  Rev. Lett. 101 (2008) 182502
P. E. Bosted et al., Phys. Rev. C 75 (2007) 035203
W. Melnitchouk, R. Ent and C.E. Keppel, Phys. Rept. 406 (2005) 127

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The Spin Structure of the Nucleon


Figure 1: Improvement on the gluon polarization ∆. Solid (dashed) lines: uncertainty on ∆ before (after) the JLab data.


Figure 2: Large-x JLab data on quark polarizations. The solid lines include quark orbital anglar momentum while the dashed lines do not.

Nucleon spin is being extensively studied at JLab [1-4], addressing fundamental questions unanswered by earlier generations of experiments. While previous experiments made important contributions to our understanding of the nucleon spin (for example that quark spins alone cannot explain it), crucial questions such as the role of gluon polarization and quark orbital angular momentum remained unresolved. With its unique capabilities, JLab has investigated these questions with high-precision measurements. Our knowledge of the gluon polarization ∆ significantly improved after the JLab polarized structure function data were included in the world data set and reanalyzed recently in Ref. [5], see Fig. 1. Furthermore, the effect of the quark orbital momentum ∆, which has been difficult to measure in experiments, can be seen in the large-x data in Fig. 2, where the predictions based on perturbative QCD (dashed curves) disagree with JLab large-x measurements if quark orbital momenta are neglected. The perturbative QCD results and data are reconciled only after quark orbital momentum components are added to the nucleon wave function [6], (solid line in Fig. 2).

[1] For a review of older JLab data, see e.g. J.P. Chen, A. Deur et Z.-E. Meziani, Mod. Phys. Lett. A20 (2005) 2745
[2] Hall A results : K. Slifer et al. Phys. Rev. Lett. 101 (2008) 022303; P. Solvignon et al., arXiv: 0803.3845 (2008)
[3] Hall B results : K. V. Dharmawardane et al., Phys. Lett. B 641 (2006) 11 ; P. E. Bosted et al., Phys Rev C 75 (2007) 
035203 ; A. Deur et al., Phys. Rev. D 78 (2008) 032001; Y. Prok et al., arXiv: 0802.2232 (2008)
[4] Hall C results : F. R. Wesselmann et al., Phys. Rev. Lett. 98 (2007) 132003
[5] E. Leader, A. Sidorov, D. Stamenov, Phys. Rev. D 75 (2007) 074027
[6] H. Avakian, S. Brodsky, A. Deur, F. Yuan, Phys. Rev. Lett. 99 (2007) 082001

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A Precision Measurement of the π0 Lifetime

An effect of color confinement in quantum chromodynamics (QCD) is that traditional perturbation theory breaks down at large distances and low energies. A quantitative understanding of the strong interaction in this region remains one of the greatest intellectual challenges in physics. The symmetries of QCD in the chiral limit (in which the quark mass vanishes) are an important element in resolving this problem.

As the lightest particle in the hadron spectrum, the neutral pion represents the most sensitive platform to study fundamental symmetry issues in QCD at low energy. Spontaneous chiral symmetry breaking gives birth to the π0 as one of the Goldstone particles, and the chiral axial anomaly primarily determines the π0 lifetime. As such, a precision measurement of the lifetime of the π0 will provide a fundamental test of QCD at the confinement scale. The present experimental uncertainty of the π0 decay width is about an order of magnitude greater than the theoretical uncertainties, so a measurement of the π0 lifetime with a precision comparable to these calculations will provide an important test of the fundamental QCD predictions.

The PrimEx collaboration at Jefferson Lab developed an experimental program to measure the π0 lifetime with high precision using the small angle coherent photoproduction of pions in the Coulomb field of a nucleus (the Primakoff effect). It uses the high intensity and high resolution photon tagging facility in Hall B and a newly developed and novel high-resolution electromagnetic hybrid calorimeter (HYCAL). The first experiment on 12C and 208Pb targets was performed in 2004. A preliminary result on the π0 decay width gives Γ(π0→ γγ) =7.93 eV± 0.18 eV (stat) ± 0.13 eV (sys), with a total error of 2.8%, which is about a two and half times improvement over the Particle Data Book average value. The experimental systematic errors on the cross section measurement are controlled at the 1.3% level and verified by Compton scattering and pair-production cross section measurements. Further results are forthcoming.


J. L. Goity, A.M. Bernstein, B.R. Holstein, Phys. Rev. D 66 (2002) 076014
B. Ananthanarayan and B. Moussallam, JHEP 0205 (2002) 052
B. L. Ioffe and A. G. Oganesian, Phys. Lett. B 647 (2007) 389

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Nucleon Generalized Parton Distributions from Full Lattice QCD

Calculated quark spin and orbital angular momentum contributions to the spin of the nucleon for up- and down-quarks versus the pion mass squared. The stars at the physical pion mass denote the experimental values of the quark spin contributions, ΔΣu and ΔΣd

Understanding how the structure of hadrons emerges from QCD is one of the central challenges of contemporary nuclear physics. Recent advances in lattice field theory, developments in computer technology and investment in computer resources for fundamental QCD research have now made lattice QCD a powerful quantitative tool that provides an unprecedented opportunity to understand the phenomena arising from QCD from first principles, and to make precision calculations of the predictions of QCD.

A revealing example is exhibited in an investigation of the source of the spin of the nucleon. The contribution of the quark spin to nucleon spin is known relatively well from polarized deep-inelastic scattering experiments. More recently, it has been shown how to determine the contribution of the total angular momentum of the quarks to nucleon spin, and hence the orbital angular momentum carried by the quarks, from generalized parton distributions (GPDs) using Ji's sum rule [1]. The figure shows the calculation [2] of the contribution from up and down quarks to the angular momentum of the nucleon (neglecting the disconnected diagrams in the lattice simulations).  While the contributions of the orbital angular momentum of the u and d quarks separately are not small, only a negligible fraction of the nucleon's spin is found to arise from the total quark angular momentum.

[1] X. Ji, Phys. Rev. Lett. 78 (1997) 610
[2] P. Haegler et al., Phys. Rev. D 77 (2008) 094502

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Two-Photon Exchange in Elastic Electron-Proton Scattering

Ratio μp GEp/GMp extracted from polarization transfer (blue filled diamonds) and Rosenbluth separations (red open circles) including two-photon exchange corrections

The ratio of the electric to magnetic proton form factors has traditionally been determined using the "Rosenbluth" or longitudinal-transverse (LT) separation method, in which the ratio is extracted from the angular dependence of the cross section at fixed momentum transfer, Q2. Recent measurements at JLab using the alternative, polarization transfer (PT) technique have found a dramatically different behavior of the ratio compared with the Rosenbluth results, leading to much discussion about the possible origin of the discrepancy.

In a series of recent papers, JLab Theory Center staff and users have analyzed in detail the effects of two-photon exchange (TPE) in elastic ep scattering. In particular, contributions from elastic and excited nucleon intermediate states have been found to have a strong angular dependence when the finite size of the nucleon is taken into account, largely reconciling the LT and PT measurements. A complementary approach, in which the TPE contributions have been calculated at the partonic level in terms of generalized parton distributions, was also found to reduce the Rosenbluth cross sections, bringing them closer to the PT results.

The TPE calculations have subsequently been used in a global reanalysis of all elastic ep data, with corrected values of the proton's electric and magnetic form factors extracted over the full Q2 range of the existing data. The analysis combined the corrected Rosenbluth cross section and PT data and was the first extraction of GEp and GMp including explicit TPE corrections and their associated uncertainties.

P. G. Blunden, W. Melnitchouk, and J. A. Tjon, Phys. Rev. C 72  (2005) 034612 
A.V. Afanasev, S.J. Brodsky, C.E. Carlson, Y.C. Chen and M. Vanderhaeghen, Phys. Rev. D 72 (2005) 013008
J. Arrington, W. Melnitchouk and J.A. Tjon, Phys. Rev. C 76 (2007) 035205 

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Charmonium Spectrum and Quark Confinement


Electric dipole transition matrix element between χc0 and J/ψ charmonium systems as a function of photon virtuality Q2. Lattice data (green and blue) is fitted with a phenomenological form consistent with the quark model.The fitted curve agrees with experimental data (purple) at the real photon point Q2=0.

Hall D of the 12 GeV upgraded CEBAF will house the GlueX experiment, which intends to map the spectrum of mesons, the hybrid mesons in particular, through photoproduction off protons. Knowledge of the spectrum of hybrid mesons will aid us in understanding the nature of the confinement of quarks within hadrons, since within hybrids the gluonic field binding the meson is excited. Just as the excited states of hydrogen taught us about QED, we hope the excited states of glue in mesons will teach us about the non-trivial aspects of QCD.

An essential unknown in the GlueX proposal is the coupling strength of hybrid mesons to photons interacting with the meson cloud surrounding the proton target. Such quantities have been calculated within models such as the flux-tube model, in which the gluonic field between quarks forms itself into a tube, but no attempt has yet been made to make the computation directly from QCD. The first stage of a program to do this is underway in the Jefferson Lab Theory Center, where we are applying the powerful technique of lattice QCD to the problem.

Simulations within lattice QCD of hadrons made of realistically light quarks currently require either excessive computing time or a well-controlled theory with which to extrapolate data computed at un-physically heavy quark masses. Since neither of these are available for the problem at hand, the closely related problem of charmonium radiative transitions was addressed. Charmonia are mesons composed of a charm quark and an anti-charm quark, where the charm quark is a heavier cousin of the up quark, having the same color and electric charge, but a much larger mass. Charmonia are a subject of much interest at experimental facilities such as CLEO, BES, Belle, Babar and Fermilab, where despite thirty years of intense study, they continue to spring surprises. They provide a set of states analogous to the light mesons, but over which we have much tighter theoretical control, in lattice QCD and in models.

We have computed, for the first time within a lattice QCD simulation, the radiative transition rates between many of the lightest charmonium states, observing good agreement with experimental measurements. In addition, we are able to compute in regions inaccessible to experiment — and it is here that we have the power to test phenomenological models, which have the advantage of allowing computation "with paper and pencil" but the disadvantage of not being as closely related to the full theory of QCD.

J. J. Dudek, R. G. Edwards and D. G. Richards, Phys. Rev. D73 (2006) 074507
F. E. Close and J. J. Dudek, Phys. Rev. Lett. 91 (2003) 142001

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The JLab Frozen Spin Target


Nuclear-spin polarized targets play a key role in experimental nuclear and particle physics. They are essential for understanding how the proton and neutron get their spins from their constituent quarks and gluons and for measuring the electromagnetic structure of these nucleons in both their ground and excited states. While the Jefferson Lab Frozen Spin Target (FROST) is the fourth and latest polarized target to be used at JLab, it is the first to be entirely designed and built here. FROST is designed to be used inside the CEBAF Large Acceptance Spectrometer (CLAS) with beams of real photons.

Scientists in the JLab Target Group use a microwave-based technique called dynamic nuclear polarization, or DNP, to polarize free protons (hydrogen nuclei) within a sample of frozen butanol.  However, to polarize the free protons, DNP also requires a powerful superconducting magnet, which obscures a large fraction of particles scattering from the target.

To overcome this problem, the Target Group constructed one of the world's most powerful 3He-4He dilution refrigerators to cool the target to less than three hundredths of a degree above absolute zero.  At such low temperatures, the polarization of the protons decays very slowly (in other words, the spins are "frozen"), and both the microwave source and the polarizing magnet can be switched off.

The sample is then removed from the polarizing magnet, and a smaller, 0.56 tesla magnet is used to "hold" the polarization during the scattering experiment. This holding magnet, integrated into the FROST cryostat, is thin enough for scattered particles to pass through and be detected by the CLAS spectrometer. Under these field and temperature conditions, the polarization decay is only about 1% per day.

FROST has already been used in Hall B for experiments with the target polarized along the direction of the photon beam. In its next use (2010), the polarization must be perpendicular to the beam. To accomplish this, the Target Group has also built a 0.54 tesla dipole magnet to rotate the spins 90º after polarization and hold them in the perpendicular direction.

St. Goertz, W. Meyer, and G. Reicherz, Progr Part Nucl Phys 49 (2002) 403-489
C.D. Keith, FROST webpage

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