Electromagnetic Current Conservation Research Articles

General analysis and numerical estimations of polarization observables in thep¯+p→π0+e++e−reaction in an exclusive experimental setup

The dependence of the differential cross section and polarization observables in the $\overline{p}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+{e}^{+}+{e}^{\ensuremath{-}}$ reaction on the polarizations of the proton target and antiproton beam (the produced electron may be unpolarized or longitudinally polarized) have been derived in a general form using hadron electromagnetic current conservation and $P$-parity invariance of the hadron electromagnetic interaction. The analysis was done for the case of an exclusive experimental setup where the produced electron and pion are detected in coincidence. The explicit dependence of all polarization observables on two, from five, kinematic variables (the azimuthal angle $\ensuremath{\phi}$ and the virtual-photon parameter $\ensuremath{\epsilon}$) have been obtained assuming one-photon exchange. The application to the particular case of a mechanism which contains information on time-like proton form factors in the unphysical region is considered in the Born approximation.

Vector meson form factors and their quark-mass dependence

The electromagnetic form factors of vector mesons are calculated in an explicitly Poincar\'e covariant formulation, based on the Dyson-Schwinger equations of QCD, that respects electromagnetic current conservation and unambiguously incorporates effects from vector meson poles in the quark-photon vertex. This method incorporates a two-parameter effective interaction, where the parameters are constrained by the experimental values of chiral condensate and ${f}_{\ensuremath{\pi}}$. This approach has successfully described a large amount of light-quark meson experimental data, including ground-state pseudoscalar masses and their electromagnetic form factors and ground-state vector meson masses and strong and electroweak decays. Here we apply it to predict the electromagnetic properties of vector mesons. The results for the static properties of the \ensuremath{\rho} meson are as follows: charge radius $\ensuremath{\langle}{r}_{\ensuremath{\rho}}^{2}\ensuremath{\rangle}=0.54\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{2}$, magnetic moment $\ensuremath{\mu}=2.01$, and quadrupole moment $\mathcal{Q}=\ensuremath{-}0.41$. We investigate the quark-mass dependence of these static properties and find that our results at the charm quark mass are in agreement with recent lattice simulations. The charge radius decreases with increasing quark mass, but the magnetic moment is almost independent of the quark mass.

Pseudoscalar and vector mesons as qq̄ bound states

Two-body bound states such as mesons are described by solutions of the Bethe-Salpeter equation. We discuss recent results for the pseudoscalar and vector meson masses and leptonic decay constants, ranging from pions up to cc̄ bound states. Our results are in good agreement with data. Essential in these calculation is a momentum-dependent quark mass function, which evolves from a constituent-quark mass in the infrared region to a currentquark mass in the perturbative region. In addition to the mass spectrum, we review the electromagnetic form factors of the light mesons. Electromagnetic current conservation is manifest and the influence of intermediate vector mesons is incorporated self-consistently. The results for the pion form factor are in excellent agreement with experiment.

Parity-violating interaction effects in thenpsystem

We investigate parity-violating observables in the $np$ system, including the longitudinal asymmetry and neutron-spin rotation in $\stackrel{P\vec}{n}p$ elastic scattering, the photon asymmetry in $\stackrel{P\vec}{n}p$ radiative capture, and the asymmetries in deuteron photodisintegration $d(\stackrel{P\vec}{\ensuremath{\gamma}},n)p$ in the threshold region and electrodisintegration $d(\stackrel{P\vec}{e},{e}^{\ensuremath{'}})np$ in quasielastic kinematics. To have an estimate of the model dependence for the various predictions, a number of different, latest-generation strong-interaction potentials---Argonne ${v}_{18}$, Bonn 2000, and Nijmegen I---are used in combination with a weak-interaction potential consisting of $\ensuremath{\pi}$-, $\ensuremath{\rho}$-, and $\ensuremath{\omega}$-meson exchanges---the Desplanques-Donoghue-Holstein (DDH) model. The complete bound and scattering problems in the presence of parity-conserving, including electromagnetic, and parity-violating potentials are solved in both configuration and momentum space. The issue of electromagnetic current conservation is examined carefully. We find large cancellations between the asymmetries induced by the parity-violating interactions and those arising from the associated pion-exchange currents. In the $\stackrel{P\vec}{n}p$ capture, the model dependence is nevertheless quite small, because of constraints arising through the Siegert evaluation of the relevant ${E}_{1}$ matrix elements. In quasielastic electron scattering these processes are found to be insignificant compared to the asymmetry produced by $\ensuremath{\gamma}\text{\ensuremath{-}}Z$ interference on individual nucleons. These two experiments, then, provide clean probes of different aspects of weak-interaction physics associated with parity violation in the $np$ system. Finally, we find that the neutron-spin rotation in $\stackrel{P\vec}{n}p$ elastic scattering and asymmetry in deuteron disintegration by circularly polarized photons exhibit significant sensitivity both to the values used for the weak vector-meson couplings in the DDH model and to the input strong-interaction potential adopted in the calculation. This reinforces the conclusion that these short-ranged meson couplings are not in themselves physical observables; rather, the parity-violating mixings are the physically relevant parameters.

Single transverse-spin asymmetry in the Drell-Yan lepton angular distribution

We calculate a single transverse-spin asymmetry for the Drell-Yan lepton-pair's angular distribution in perturbative QCD. At leading order in the strong coupling constant, the asymmetry is expressed in terms of a twist-3 quark-gluon correlation function T_F^{(V)}(x_1,x_2). In our calculation, the same result was obtained in both light-cone and covariant gauge in QCD, while keeping explicit electromagnetic current conservation for the virtual photon that decays into the lepton pair. We also present a numerical estimate of the asymmetry and compare the result to an existing other prediction.

Nucleon properties in the covariant quark-diquark model

In the covariant quark-diquark model the effective Bethe-Salpeter (BS) equations for the nucleon and the Δ are solved including scalar and axial vector diquark correlations. Their quark substructure is effectively taken into account in both, the interaction kernel of the BS equations and the currents employed to calculate nucleon observables. Electromagnetic current conservation is maintained. The electric form factors of proton and neutron match the data. Their magnetic moments improve considerably by including axial vector diquarks and photon induced scalar-axial vector transitions. The isoscalar magnetic moment can be reproduced, the isovector contribution is about 15% too small. The ratio µG E/G M and the axial and strong couplings g A, g πNN, provide an upper bound on the relative importance of axial vector diquarks confirming that scalar diquarks nevertheless describe the dominant 2-quark correlations inside nucleons.

Current conservation in the covariant quark-diquark model of the nucleon

The description of baryons as fully relativistic bound states of quark and glue reduces to an effective Bethe-Salpeter equation with quark-exchange interaction when irreducible 3-quark interactions are neglected and separable 2-quark (diquark) correlations are assumed. This covariant quark-diquark model of baryons is studied with the inclusion of the quark substructure of the diquark correlations. In order to maintain electromagnetic current conservation it is then necessary to go beyond the impulse approximation. A conserved current is obtained by including the coupling of the photon to the exchanged quark and direct ``seagull'' couplings to the diquark structure. Adopting a simple dynamical model of constituent quarks and exploring various parametrisations of scalar diquark correlations, the nucleon Bethe-Salpeter equation is solved and the proton and neutron electromagnetic form factors are calculated numerically. The resulting magnetic moments are still about 50% too small, the improvements necessary to remedy this are discussed. The results obtained in this framework provide an excellent description of the electric form factors (and charge radii) of the proton, up to a photon momentum transfer of 3.5GeV^2, and the neutron.

Pion electroproduction at threshold.

By using the partially conserved axial-vector current hypothesis and the electromagnetic current conservation law, we calculate transverse and longitudinal multipoles for threshold pion electroproduction on the nucleon. We include off-shell form factors for the axial-vector current, the electromagnetic current, and the pion-nucleon vertex. We confirm that if the electromagnetic off-shell form factors are assumed to be finite in the chiral limit of the vanishing pion mass, the low-energy theorems are unaffected by them. However, we show that if one of these form factors has simple-pole singularity in the chiral limit, it shows up in the threshold amplitudes at next-to-leading order predicted by the low-energy theorems.

Pion electroproduction at threshold and PCAC

Threshold pion electroproduction is calculated in a model-independent way based on electromagnetic current conservation, PCAC, and crossing symmetry. The threshold s-wave multipoles E 0+ and L 0+ are expanded in terms of two dimensionless parameters, the pion-nucleon mass ratio μ = m π M , and ν 2 = k 2 M 2 , where k is the four-momentum of the virtual photon. Model-dependent terms appear in order μν 2 and μ 2 for the charged production amplitudes and in order μν 2 and μ 3 in the neutral production amplitudes. We comment on recipes to restore gauge invariance for the pseudovector electroproduction Born terms and their relationship with low-energy theorems. Finally, we discuss the possibility of determining the nucleon axial radius using threshold pion electroproduction.

Production ofWγ Paris in proton-antiproton collisions

We study the effects of an anomalous (non standard model) electric quadrupole moment λ for theW on the process\(p\bar p \to W^ - \gamma X\) and compare them to those obtained with theW anomalous (non standard model) electric dipole moment (κ). Such aW electric quadrupole moment λ is allowed by the most general γWW vertex compatible withC, P, T invariance and electromagnetic current conservation. We find that values of λ≳0.5 could produce large departures from the predictions of the standard model which may be observable at the FNALp\(\bar p\) collider.

Pion photoproduction at threshold onLi6and low-energy theorems

Low's theorem is deduced from the Born diagrams for pi /sup + / production by imposing electromagnetic current conservation (ECC), but the anomalous electric quadrupole moment contribution could be very important even at threshold. The derivation of the Kroll-Ruderman and Fubini-Furlan-Rossetti theorems is made consistent with ECC and Low's theorem in contrast to previous works where these are violated. A discussion of information obtainable from experiment shows that soft pion results cannot be used directly but an extrapolation from q/sup 2/=0 to m pi /sup 2/ is given which is compatible with ECC and Low's theorem.