QED confronts the radius of the proton

Recent results on muonic hydrogen (Pohl et al., 2010) [1] and the ones compiled by CODATA on ordinary hydrogen and ep-scattering (Mohr et al., 2008) [2] are 5σ away from each other. Two reasons justify a further look at this subject: (1) One of the approximations used in Pohl et al. (2010) [1] is not valid for muonic hydrogen. This amounts to a shift of the proton's radius by ∼3 of the standard deviations of Pohl et al. (2010) [1], in the “right” direction of data-reconciliation. In field-theory terms, the error is a mismatch of renormalization scales. Once corrected, the proton radius “runs”, much as the QCD coupling “constant” does. (2) The result of Pohl et al. (2010) [1] requires a choice of the “third Zemach moment”. Its published independent determination is based on an analysis with a p  -value – the probability of obtaining data with equal or lesser agreement with the adopted (fit form-factor) hypothesis – of 3.92×¹⁰⁻¹²$3.92\times {10}^{-12}$. In this sense, this quantity is not empirically known. Its value would regulate the level of “tension” between muonic- and ordinary-hydrogen results, currently at most  ∼4σ$\sim 4\sigma$. There is no tension between the results of Pohl et al. (2010) [1] and the proton radius determined with help of the analyticity of its form-factors.     

The RMS charge radius of the proton and Zemach moments

On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al. De Rújula's idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.     

QED is not endangered by the proton's size

Pohl et al. have reported a very precise measurement of the Lamb-shift in muonic hydrogen (Pohl et al., 2010) [1], from which they infer the radius characterizing the proton's charge distribution. The result is 5 standard deviations away from the one of the CODATA compilation of physical constants. This has been interpreted (Pohl et al., 2010) [1] as possibly requiring a 4.9 standard-deviation modification of the Rydberg constant, to a new value that would be precise to 3.3 parts in 10¹³, as well as putative evidence for physics beyond the standard model (Flowers, 2010) [2]. I demonstrate that these options are unsubstantiated.     

A covariant view on the nucleons’ quark core

Established results for the quark propagator in Landau gauge QCD, together with a detailed comparison to lattice data, are used to formulate a Poincaré-covariant Faddeev approach to the nucleon. The resultant three-quark amplitudes describe the quark core of the nucleon. The nucleon’s mass and its electromagnetic form factors are calculated as functions of the current quark mass. The corresponding results together with charge radii and magnetic moments are discussed in connection with the contributions from various ingredients in a consistent calculation of nucleon properties, as well as the role of the pion cloud in such an approach.     

Electromagnetic form factors of3He and3H

The electric and magnetic form factors of³He and³H are calculated with 3-nucleon wave functions obtained from the solution of Schrödinger equation with separable potentials of two different shapes which have already been employed in the coulomb energy calculation. The effect of important meson exchange corrections is evaluated and their dependence on the wave function studied. The form factors can depend rather sensitively on the nucleon form factors as well, and this dependence is studied by using two different parametrisations for the latter.     

The nucleon as a QCD bound state in a Faddeev approach

Established results for the quark propagator of Landau gauge QCD, together with a detailed comparison to lattice data, are implemented in a Poincaré-covariant Faddeev approach to the nucleon. The nucleon mass and its electromagnetic form factors, together with charge radii and magnetic moments, are calculated as a function of the current-quark mass. The role of the pion cloud is discussed.     

Deuteron form factors and the tensor force

Results of a non-relativistic calculation of deuteron form factors are presented for separable potentials with and without tensor force. The tensor term in triplet state is added in such a way as to keep the values of deuteron binding energy,a _t andr _0t unaltered, so that the difference in the form factors can be regarded as the effect of tensor force only. The calculation has been performed for two different shapes of separable potentials and for three differentD-state probabilities to study their comparative effect.     

Time-like proton form factor measurement with PANDA

The electromagnetic probe is an excellent tool to investigate the structure of the nucleon. The nearly 4π detector PANDA, will allow to make a precise determination of the electromagnetic form factors of the proton in the time-like region with unprecedented precision. In the one-photon exchange approximation, the center of mass unpolarized differential cross section of the reaction pp → e＋e- is a linear combination of the squared moduli of the electric GE and magnetic GM proton form factors. The precise measurement of the angular distribution over almost full angular range then directly gives these quantities. At present only two experiments have provided the ratio R=｜ GE｜/｜GM｜ but with large statistical uncertainties. It is shown that with strict PID cuts and a kinematic fit, the dominant background, pp→π＋π-, can be supressed to much less than 1% of the signal, without affecting the extraction of the ratio R. PANDA will therefore offer a unique opportunity to measure the ratio with a precision ranging from 〈1% at low q2 up to 30 % for q2 = 14 （GeV/c）2.     

Logarithmic corrections and soft photon phenomenology in the multipole model of the nucleon form factors

We analyzed the presently available experimental data on nucleon electromagnetic form factors within a multipole model based on dispersion relations. A good fit of the data is achieved by considering the coefficients of the multipole expansions as logarithmic functions of the momentum transfer squared. The superconvergence relations, applied to this coefficients, makes the model agree with unitary constraints and pQCD asymptotics for the Dirac and Pauli form factors. The soft photon emission is proposed as a mechanism responsible for the difference between the Rosenbluth, polarization and beam-target asymmetry data. It is shown that the experimentally measured cross-sections depend not only on the Dirac and Pauli form factors, but also on the average number of the photons emitted. For the proton this number is shown to be different for different types of experimental measurements and then estimated phenomenologically. For the neutron the same mechanism predicts that the data form different types of experiments must coincide with high accuracy. A joint fit of all the experimental data reproduce the Q²-dependence with the accuracy χ²/dof = 0.86 . Predictions of the model, that 1) the ratios of the proton form factors G _E/G _M are different for Rosenbluth, polarization and beam-target asymmetry experiments and 2) similar ratios are nearly the same for neutron, can be used for experimental verification of the model.     

Sensitivity of the pQCD deuteron structure to the nucleon form factors

We discuss the applicability of pQCD to the elastic scattering of electrons on protons and deuterons. We analyze the Q²-dependence of the reduced deuteron form factor, taking into account the recent data on the electric proton form factor and we find that the value of the QCD-scale parameter Λ differs essentially from the value Λ = 0.1 GeV, previously found using the dipole parametrization of the electromagnetic nucleon form factors G_E and G_M. Moreover, the predicted scaling behavior of the reduced deuteron form factor cannot be recovered in the Dirac and Pauli representations for the nucleon electromagnetic form factors. Received: 14 October 2002 / Accepted: 12 November 2002 / Published online: 11 March 2003 RID="a" ID="a"Permanent address: National Science Center KFTI, 310108 Kharkov, Ukraine. RID="b" ID="b"e-mail: etomasi@cea.fr Communicated by V.V. Anisovich     

Implications of the JLab proton polarization data for the behavior of strange nucleon form factors

A special eight-resonance unitary and analytic model of nucleon electromagnetic structure is used to analyze first the classical proton form factor data obtained by the Rosenbluth technique, and then also the contradictory JLab proton polarization data on the ratio μ_p G _Ep(Q ²)/G _Mp(Q ²) , with the aim to investigate the implications of the latter for the behavior of strange nucleon form factors.     

Probing nucleon structure on the lattice

The QCDSF/UKQCD Collaboration has an ongoing program to calculate nucleon matrix elements with two flavours of dynamical O(a) improved Wilson fermions. Here we present recent results on the electromagnetic form factors, the quark momentum fraction 〈x〉 and the first three moments of the nucleon's spin-averaged and spin-dependent generalised parton distributions, including preliminary results with pion masses as low as 320MeV.     

Strange quarks in the nucleon sea

The HAPPEX Collaboration measured parity-violating electron scattering from ⁴He$(e, e)$and H(e, e) in 2004 and 2005 for Q ²≤0.11GeV^2. Results for the strange-quark contributions to the electromagnetic form factors of the nucleon from the 2004 data will be reviewed. Preliminary results from the 2005 data, which have significantly greater statistical precision, are G _E ^s = 0.004±0.014_stat±0.013_syst for Q ² = 0.0772GeV^2 from the helium data and G _E ^s +0.088G _M ^s = 0.004±0.011_stat±0.005_syst±0.004_FF for Q ² = 0.1089GeV^2 from the hydrogen data.     

Control of the charge and energy of the proton beams from a laser-driven double-layer target

Control of the proton beam charge and energy in a laser-driven double-layer target was numerically investigated. Generally the proton beam charge is determined by the areal density σ = nl of the second layer, while the accelerating field is governed by the substrate thickness L. From a series of one-dimensional particle-in-cell simulations over a broad range of σ and L, it was confirmed that those two control parameters do not interfere significantly, indicating the beam charge and energy can be separately controlled. We suggest self-assembly monolayers technique be used for the fabrication of the areal density of the second layer.     

Time-like proton form factor measurement with P(-)ANDA

The electromagnetic probe is an excellent tool to investigate the structure of the nucleon. The nearly 4π detector PANDA, will allow to make a precise determination of the electromagnetic form factors of the proton in the time-like region with unprecedented precision. In the one-photon exchange approximation, the center of mass unpolarized differential cross section of the reaction pp → e~+e~- is a linear combination of the squared moduli of the electric G_E and magnetic G_M proton form factors. The precise measurement of the angular distribution over almost full angular range then directly gives these quantities. At present only two experiments have provided the ratio R = |G_E|/|G_M| but with large statistical uncertainties. It is shown that with strict PID cuts and a kinematic fit, the dominant background, (p)p→π~+π~-, can be supressed to much less than 1% of the signal, without affecting the extraction of the ratio R. PANDA will therefore offer a unique opportunity to measure the ratio with a precision ranging from <1% at low q~2 up to 30 % for q~2 =14 (GeV/c)~2.     

The size of the proton

The root-mean-square (rms) charge radius r _p of the proton has so far been known only with a surprisingly low precision of about 1% from both electron scattering and precision spectroscopy of hydrogen. We have recently determined r _p by means of laser spectroscopy of the Lamb shift in the exotic “muonic hydrogen” atom. Here, the muon, which is the 200 times heavier cousin of the electron, orbits the proton with a 200 times smaller Bohr radius. This enhances the sensitivity to the proton’s finite size tremendously. Our new value r _p?=?0.84184 (67) fm is ten times more precise than the generally accepted CODATA-value, but it differs by 5 standard deviations from it. A lively discussion about possible solutions to the “proton size puzzle” has started. Our measurement, together with precise measurements of the 1S–2S transition in regular hydrogen and deuterium, also yields improved values of the Rydberg constant, R _?∞??=?10,973,731.568160 (16) m^???1.