arXiv subjects
Publications and source records attributed to P. G. Blunden.
We show how computational symbolic packages such as FeynArts and FormCalc can be adopted for the evaluation of one-loop hadronic electroweak radiative corrections for electron-nucleon scattering and applied to calculations of the nucleon weak charge. Several numerical results are listed, and found to be in good agreement with the current experimental data.
The large energy-scale behaviour of the parity and time-reversal violating (PTV) pion-nucleon coupling constant is analyzed in a model combining renormalization-group techniques and the dressing of the PTV vertex with a pion loop. With the strong $πN N$ vertex as a mixture of the pseudovector and pseudoscalar couplings, we show that depending on the admixture parameter, two qualitatively distinct types of behaviour are obtained for the PTV coupling constant at high energy scales: an asymptotic freedom or a fixed-point. We find a critical value of the admixture parameter which delineates these two scenarios. Several examples of the high-energy scale behaviour of the PTV $πN N$ constant are considered, corresponding to realistic hadronic models of the strong pion-nucleon interaction.
One way to treat the infrared divergences of the electroweak Next-to-Leading-Order (NLO) differential cross sections to parity-violating (PV) electron-proton scattering is by adding soft-photon emission contribution. Although more physical, the results are left with a logarithmic dependence on the photon detector acceptance, which can only be eliminated by considering Hard Photon Bremsstrahlung (HPB) contribution. Here we present a treatment of HPB for PV electron-proton scattering. HPB differential cross sections for electron-proton scattering have been computed using the experimental values of nucleon form factors. The final results are expressed through kinematic parameters, making it possible to apply the computed PV HPB differential cross sections for the analysis of data of a range of current and proposed experiments.
We calculate contributions of hadron resonances to two-photon exchange effects in electron-proton scattering. In addition to the nucleon and P33 resonance, the following heavier resonances are included as intermediate states in the two-photon exchange diagrams: D13, D33, P11, S11 and S31. We show that the corrections due to the heavier resonances are smaller that the dominant nucleon and P33 contributions. We also find that there is a partial cancellation between the contributions from the spin 1/2 and spin 3/2 resonances, which results in a further suppression of their aggregate two-photon exchange effect.
The form factor of the parity and time-reversal violating (PTV) pion-nucleon interaction is calculated from one-loop vertex diagrams. The degrees of freedom included in the effective lagrangian are nucleons, pions, $η$, $ρ$ and $ω$ mesons. We show that by studying the form factor one can constrain the PTV meson-nucleon coupling constants. We evaluate the mean square radius associated with the PTV $πN N$ vertex. Using the mean square radius, we estimate the effect of the PTV $πN N$ vertex on the neutron electric dipole moment, and find a very small correction. We also extract the renormalisation group $β$ function and use it to discuss evolution of the PTV $πN N$ coupling constant beyond the hadronic mass scale.
We present an evaluation of a two-photon exchange correction to the cross section for unpolarized $Δ$ isobar production in electron-proton collisions, using a relativistic, crossing symmetric and gauge invariant approach. The calculated box and crossed-box diagrams include nucleon and $Δ$ intermediate states. We find a relation between the angular nonlinearity of the two-photon exchange contribution and the value of the $γΔΔ$ coupling constant.
We calculate the effects on the elastic electron-proton scattering cross section of the two-photon exchange contribution with an intermediate $Δ$ resonance. The $Δ$ two-photon exchange contribution is found to be smaller in magnitude than the previously evaluated nucleon contribution, with an opposite sign at backward scattering angles. The sum of the nucleon and $Δ$ two-photon exchange corrections has an angular dependence compatible with both the polarisation transfer and the Rosenbluth methods of measuring the nucleon electromagnetic form factors.
A detailed study of two-photon exchange in unpolarized and polarized elastic electron--nucleon scattering is presented, taking particular account of nucleon finite size effects. Contributions from nucleon elastic intermediate states are found to have a strong angular dependence, which leads to a partial resolution of the discrepancy between the Rosenbluth and polarization transfer measurements of the proton electric to magnetic form factor ratio, G_E/G_M. The two-photon exchange contribution to the longitudinal polarization transfer P_L is small, whereas the contribution to the transverse polarization transfer P_T is enhanced at backward angles by several percent, increasing with Q^2. This gives rise to a small, ~3% suppression of G_E/G_M obtained from the polarization transfer ratio P_T/P_L at large Q^2. We also compare the two-photon exchange effects with data on the ratio of e^+ p to e^- p cross sections, which is predicted to be enhanced at backward angles. Finally, we evaluate the corrections to the form factors of the neutron, and estimate the elastic intermediate state contribution to the ^3He form factors.
Two-photon exchange contributions to elastic electron-proton scattering cross sections are evaluated in a simple hadronic model including the finite size of the proton. The corrections are found to be small in magnitude, but with a strong angular dependence at fixed $Q^2$. This is significant for the Rosenbluth technique for determining the ratio of the electric and magnetic form factors of the proton at high $Q^2$, and partly reconciles the apparent discrepancy with the results of the polarization transfer technique.
Radiative corrections to the parity-violating asymmetry measured in elastic electron-proton scattering are analyzed in the framework of the Standard Model. We include the complete set of one-loop contributions to one quark current amplitudes. The contribution of soft photon emission to the asymmetry is also calculated, giving final results free of infrared divergences. The one quark radiative corrections, when combined with previous work on many quark effects and recent SAMPLE experimental data, are used to place some new constraints on electroweak form factors of the nucleon.
The principles behind the detailed results of a light-front mean field theory of finite nuclei are elucidated by deriving the nucleon mode equation using a simple general argument, based on the idea that a static source in equal time coordinates corresponds to a moving source in light front coordinates. This idea also allows us to solve several simple toy model examples: scalar field in a box, 1+1 dimensional bag model, three-dimensional harmonic oscillator and the Hulthén potential. The latter provide simplified versions of momentum distributions and form factors of relevance to experiments. In particular, the relativistic correction to the mean square radius of a nucleus is shown to be very small. Solving these simple examples suggests another more general approach-- the use of tilted light front coordinates. The simple examples are made even simpler.
A light-front treatment for finite nuclei is developed from a relativistic effective Lagrangian (QHD1) involving nucleons, scalar mesons and vector mesons. We show that the necessary variational principle is a constrained one which fixes the expectation value of the total momentum operator $P^+$ to be the same as that for $P^-$. This is the same as minimizing the sum of the total momentum operators: $P^-+P^+$. We obtain a new light-front version of the equation that defines the single nucleon modes. The solutions of this equation are approximately a non-trivial phase factor times certain solutions of the usual equal-time Dirac equation. The ground state wave function is treated as a meson-nucleon Fock state, and the meson fields are treated as expectation values of field operators in that ground state. The resulting equations for these expectation values are shown to be closely related to the usual meson field equations. A new numerical technique to solve the self-consistent field equations is introduced and applied to $^{16}$O and $^{40}$Ca. The computed binding energies are essentially the same as for the usual equal-time theory. The nucleon plus momentum distribution (probability for a nucleon to have a given value of $p^+$) is obtained, and peaks for values of $p^+$ about seventy percent of the nucleon mass. The mesonic component of the ground state wave function is used to determine the scalar and vector meson momentum distribution functions, with a result that the vector mesons carry about thirty percent of the nuclear plus-momentum. The vector meson momentum distribution becomes more concentrated at $p^+=0$ as $A$ increases.
A light-front treatment for spherical nuclei is developed from a relativistic effective Lagrangian and employing the mean field approximation. Minimizing the nuclear minus momentum subject to the constraint that, in the rest frame, the expectation values of the plus- and minus-momenta are the same leads to a formalism in which rotational invariance is recovered.
The equations of motion for a massive spin-3/2 Rarita-Schwinger field in a finite-range, central, Lorentz scalar potential are developed. It is shown that the resulting density may not be everywhere positive definite.