Nucleon form factors stride into the future

28 March 2006

At a three-day meeting at Frascati, physicists from around the world met to discuss the implications of striking new results on the nucleon space-like and time-like form factors.

Form factors are the most fundamental dynamical quantities for describing the inner properties of a composite particle. The nucleon form factors provide detailed information about the spatial distribution of charges and currents in the nucleon.


They are directly accessible from experiment by differential cross-section and polarization observables and from theory by all nucleon models as they enter explicitly in the expression of the hadronic current. On 12-14 October 2005 the first workshop specifically dedicated to a global view on electromagnetic hadron form factors in both space-like and time-like regions was held at the INFN-Laboratori Nazionali di Frascati (LNF). The N’05 Workshop on Nucleon Form factors attracted 85 participants from 18 countries. Forty-five talks, followed by animated discussions during breaks and dinners covered the most recent findings, ideas and suggestions for future developments in experiments and theory.

After the opening welcome from Mario Calvetti, director of the LNF, Antonino Zichichi of Bologna and CERN presented a vivid historical introduction to the topic of electromagnetic form factors. He recalled his first measurements at CERN in 1963, and underlined the role played by Frascati in the field, in particular for time-like neutron form factors, where the only existing data were collected by the FENICE collaboration at the end of 1980s. He also discussed the role that Frascati could and should play in the future.

The experimental evidence, that form factors are twice as large in the time-like region as in the space-like region and that time-like neutron form factors are much larger than time-like proton form factors, could be owing to a possible NBar resonance below threshold. Discovering and studying the properties of this resonance through dedicated and precise measurements in the threshold region would be an important step in understanding nucleon structure and nucleon spectroscopy. In Zichichi’s opinion, this is one of the 10 most compelling problems in high-energy physics, which he listed in his impressive review. Dan Olof Riska of Helsinki underlined the importance of precise data on all hadron form factors – transition, axial, and strange. He drew particular attention to the role of two-photon exchange in solving the discrepancy among electric proton form-factor data, and the importance of the pion cloud in the nucleon structure.

The first session following the overview was dedicated to the current status of the research programmes at Jefferson Lab, the Bates Linear Accelerator at the Massachusetts Institute of Technology and at the Mainz Microtron. Presentations paid special attention to the discrepancies among the recent precise measurements of the electric proton form factor at large values of momentum-transfer squared, Q2, whether measured through the recoil proton-polarization method or via the unpolarized differential cross-section in elastic electron-
proton scattering. Polarization measurements have been implemented only recently, after the advent of high-luminosity polarized-electron beams and the development of hadron polarimeters and polarized targets. The surprising feature revealed by the polarization experiments, which are far more sensitive to the small electric contribution, is that the electric and magnetic distributions inside the proton are different, contrary to what was previously assumed and suggested by results from experiments based on the unpolarized method.


The search for a solution to this problem focuses on radiative corrections, particularly on the possibility of a mechanism where momentum is not transferred by only one photon, as generally assumed, but equally shared by two photons. This would change the angular dependence of the cross-section, and, at least qualitatively, provide a better agreement between the two sets of data. The presence of such a mechanism would make life much more complicated in all electron-induced reactions, and would call for a revision of many other sets of data. Two-photon exchange induces complex amplitudes, which should be mostly imaginary. A non-zero, but small imaginary part has been found in very precise measurements on parity violating terms, as Frank Maas of Mainz described, but no experimental evidence confirms the presence of the two-photon mechanism (real part) in the present data. Therefore, theoretical and experimental efforts continue and the question remains open. Such a mechanism should be more evident in the time-like region, where form factors are complex, and could be an interesting topic for the future at Frascati, with the DAFNE storage ring upgraded in energy.

Into the time-like region

The experimental situation in the time-like region was clearly described by Diego Bettoni of Ferrara, who pointed out that until now no separation of the electric and magnetic form factors has been possible, owing to the lack of statistics. He also drew attention to the importance of a precise measurement of the neutron form factors as well as of the relative phase of form factors and the role of the possible narrow resonance below threshold. Note that the Rosenbluth separation technique in the space-like region implies measurements at fixed Q2, which requires changing both the energy of the electron beam and the scattering angle of the emitted electron, whereas, in the time-like region, it requires a precise angular distribution of the emitted nucleon (or antinucleon) while keeping the beam conditions unchanged.

Form factors have been recently accessed from initial state radiation at the BaBar experiment at SLAC. The results, presented by Vladimir Druzhinin and Evgeni Solodov of Novosibirsk, are impressive and raise new questions about the ratio of the electric and magnetic form factors, GE/GM, near threshold. Contrary to measurements at CERN’s Low Energy Antiproton Ring, the new results show that GE/GM increases quickly and also reveal unexpected evidence for a step-like behaviour of the proton time-like form factor, at threshold, around 2.2 GeV and around 2.9 GeV.

Stanislav Dubnicka of Bratislava presented model-independent properties of polarization observables in the time-like region. The extension of this formalism has recently been derived for scattering and annihilation channels in the presence of two-photon exchange and was presented for proton-antiproton annihilation into two leptons by Gennady Gakh of Kharkov.

The strange and axial nucleon form factors are strongly related to the electromagnetic form factors, and their extraction from experimental observables is largely influenced by our knowledge of these quantities, thanks to the impressive precision that experiments have achieved. The first data from the G0 experiment at Jefferson Lab were presented during a review of current experiments on parity violation by Serge Kox of Grenoble. The precision of the measurement of the asymmetry in electron-proton unpolarized scattering – around 10-6 (parts per million) – is impressive, and the combined result is surprising, as it suggests a large and positive strange-proton form factor.

Theory and outlook

The session devoted to theory covered various nucleon models. Mauro Giannini of Genova and Gottfried Holzwarth of Siegen, for example, underlined the role of relativistic corrections in the constituent quark model, and in the soliton model, respectively. A global description of the four nucleon form factors in the space-like and time-like regions can be obtained by vector-dominance models and also through dispersion relations, which can be analytically continued to the time-like region. Simone Pacetti of Frascati presented an original approach based on an extrapolation from the time-like region of dispersion-relation requirements. This showed that BaBar data would constrain a zero of GE/GM in the space-like region.

Form factors are intimately related to other quantities describing the nucleon. For example, they provide a boundary for generalized parton distributions (GPDs), which are supposed to give a global, 3D picture of the nucleon. The connections with this important subject were discussed in a dedicated session. Recent results on real, virtual and deeply virtual Compton scattering (DVCS) show in particular that single-spin observables are very promising for selecting DVCS and describing the nucleon from GPDs. Nucleon polarizabilities, interpreted in the context of dispersion relations, also show evidence for a pion cloud. Peter Kroll of Wuppertal presented a first attempt to extract the GPDs from form-factor data from Jefferson Lab. A correlation with time-odd GPDs and a test of time-reversal invariance in electromagnetic interactions would be possible with a future energy upgrade of the DAFNE linac.

Looking to the future, plans for the Facility for Antiproton and Ion Research at GSI will allow precision form-factor measurements and access their phase, in particular in the region of large momentum- transfer. The PANDA experiment will allow proton time-like form factors to be measured individually and PAX will focus on polarized measurements. At the Budker Institute for Nuclear Physics in Novosibirsk, a measurement is planned at the existing linac of the two-photon contributions in electron/positron-proton scattering. An exploration of the proton form factor very near threshold is also foreseen at the new electron-positron collider, VEPP-2000. The meeting also heard about the future programme for BESIII, together with first results in the threshold region from the Bejing Electron-Positron Collider.

The project for a complete measurement of the nucleon form factors in the time-like region at Frascati with the upgraded DAFNE storage-ring, which has already triggered a great deal of interest within the community, was presented by Marco Mirazita of Frascati. An upgrade in luminosity and energy of the machine would provide a unique tool for measuring individual nucleon form factors, in particular for the neutron. The additional possibility of measuring the polarization of the outgoing nucleon would provide the first determination of the relative phase of the form factors, in addition to their moduli.

Stan Brodsky of SLAC concluded the meeting with a talk in which he stressed the importance of the high-momentum behaviour of form factors as a fundamental test of scaling in perturbative quantum chromodynamics (QCD), helicity structure and asymptotic freedom. He also showed the potentiality of a formalism based on duality between string theory in anti-de Sitter space and conformal field theory, which should provide a direct connection between QCD and nucleon amplitudes.

• N’05 was financially supported by Istituto Nazionale di Fisica Nucleare, the Hadron Physics Integrated Infrastructure Initiative and the US Department of Energy’s Jefferson Lab. For the full programme and the complete list of speakers see

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