Field theory of nucleon to higher-spin baryon transitions

Physical Review C, 2000

We develop a relativistic covariant and unitary description of the pion-nucleon interaction in a hadron-exchange model. The model is based on the solution of a dimensionally reduced (quasipotential) Bethe-Salpeter equation for the partial-wave off-shell πN scattering amplitudes with the potential consisting of the field-theoretical s-and u-channel nucleon, Roper, Delta, D 13 , S 11 exchanges, and the t-channel ρ and σ meson exchanges. The contributions of the spin-3/2 Delta and D 13 resonances are treated within the Rarita-Schwinger formalism and different forms of the πN ∆ vertex are investigated. The free parameters of the model are fitted to the πN phase-shift data of the KH80 and SM95 partial-wave analyses in the region up to 600 MeV pion kinetic energy. The resulting on-shell solution provides a good description of the πN scattering lengths, as well as the energy behavior of the S, P, and D partial waves. The sensitivity of the phase shifts on various model-dependent effects is examined.

Physical Review C, 2008

We present an optimization scheme that employs a Genetic Algorithm (GA) to determine the properties of low-lying nucleon excitations within a realistic photo-pion production model based upon an effective Lagrangian. We show that with this modern optimization technique it is possible to reliably assess the parameters of the resonances and the associated error bars as well as to identify weaknesses in the models. To illustrate the problems the optimization process may encounter, we provide results obtained for the nucleon resonances ∆(1230) and ∆(1700). The former can be easily isolated and thus has been studied in depth, while the latter is not as well known experimentally.

2006

We employ the two independent Casimir operators of the Poincaré group, the squared four-momentum, p2, and the squared Pauli-Lubanski vector, W2, in the construction of a covariant mass m, and spin- \( {\frac{{3}}{{2}}}\) projector in the four-vector spinor, ψμ. This projector provides the basis for the construction of an interacting Lagrangian that describes a causally propagating spin- \( {\frac{{3}}{{2}}}\) particle coupled to the electromagnetic field by a gyromagnetic ratio of \(g_{\ensuremath \frac{3}{2}}=2\) .

Physical Review C, 2009

We present a fully relativistic formalism for describing neutrino-induced ∆-mediated single-pion production from nuclei. We assess the ambiguities stemming from the ∆ interactions. Variations in the cross sections of over 10% are observed, depending on whether or not magnetic-dipole dominance is assumed to extract the vector form factors. These uncertainties have a direct impact on the accuracy with which the axial-vector form factors can be extracted. Different predictions for C A 5 (Q 2 ) induce up to 40-50% effects on the ∆-production cross sections. To describe the nucleus, we turn to a relativistic plane-wave impulse approximation (RPWIA) using realistic bound-state wave functions derived in the Hartree approximation to the σ-ω Walecka model. For neutrino energies larger than 1 GeV, we show that a relativistic Fermi-gas model with appropriate binding-energy correction produces comparable results as the RPWIA which naturally includes Fermi motion, nuclear-binding effects and the Pauli exclusion principle. Including ∆ medium modifications yields a 20 to 25% reduction of the RPWIA cross section. The model presented in this work can be naturally extended to include the effect of final-state interactions in a relativistic and quantummechanical way. Guided by recent neutrino-oscillation experiments, such as MiniBooNE and K2K, and future efforts like MINERνA, we present Q 2 , W , and various semi-inclusive distributions, both for a free nucleon and carbon, oxygen and iron targets.

Physical Review C, 2009

The contribution of the low-lying nucleon resonances P 33 (1232), P 11 (1440) D 13 (1520) and S 11 (1535) to the invariant mass spectra of di-electrons stemming from the exclusive processes pp → pp e + e − and pn → pn e + e − is investigated within a fully covariant and gauge invariant diagrammatical approach. We employ, within the one-boson exchange approximation, effective nucleon-meson interactions including the exchange mesons π, η, σ, ω and ρ as well as excitations and radiative decays of the above low-lying nucleon resonances. The total contribution of these resonances is dominant, however, bremsstrahlung processes in pp and, in particular, pn collisions at beam energies of 1 -2 GeV are still significant in certain phase space regions.

Physical Review D

{"data":{"abstract":{"value":"<p>A physical model is presented for the nonperturbative parton distributions in the nucleon. This is based on quantum fluctuations of the nucleon into baryon-meson pairs convoluted with Gaussian momentum distributions of partons in hadrons. The hadronic fluctuations, here developed in terms of hadronic chiral perturbation theory, occur with high probability and generate sea quarks as well as dynamical effects also for valence quarks and gluons. The resulting parton momentum distributions <math xmlns=\"at low momentum transfers are evolved with conventional Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equations from perturbative QCD to larger scales. This provides parton density functions <math xmlns=\"for the gluon and all quark flavors with only five physics-motivated parameters. By tuning these parameters, experimental data on deep-inelastic structure functions can be reproduced and interpreted. The contribution to sea quarks from hadronic fluctuations explains the observed asymmetry between <math xmlns=\"

Physical Review C, 2010

The details of the calculation of the two-boson exchange effects in the parityviolating elastic ep scattering within a simple hadronic model, including both the nucleon and ∆(1232)-resonance intermediate states, are presented. We examine the sensitivity of our results with respect to choice of form factors. We emphasize the importance to use correct relations relating N → ∆ and ∆ → N transition vertex functions. The N ∆ Coulomb quadrupole transition is found to play important role at higher Q 2 ≥ 3.0 GeV 2. We also elucidate the relation between our results and the well-known result on the γZE effect given by Marciano and Sirlin (MS). The effect of the nucleon contribution δ N to parity-asymmetry A P V , is found to be in general, larger than the corresponding ∆ contribution δ ∆ except at extreme forward angles. The corrections to the extracted values of the strange form factors G s E + βG s M from the HAPPEX, A4, and G0 data are also presented. The total TBE corrections to the extracted values of G s E + βG s M in recent experiments of HAPPEX G0, and A4 are, depending on kinematics, found to be small except in a few cases where they range from −20.6% to 48.3%.

Physical Review C, 2009

We study the leading electroweak corrections in the precision measurement of the strange form factors. Specifically, we calculate the two-boson-exchange (TBE), two-photon-exchange (TPE) plus γZ-exchange (γZE), corrections with ∆(1232) excitation to the parity-violating asymmetry of the elastic electron-proton scattering. The interplay between nucleon and ∆ contributions is found to depend strongly on the kinematics, as δ∆ begins as negligible at backward angles but becomes very large and negative and dominant at forward angles, while δN always stays positive and decreases monotonically with increasing ǫ. The total TBE corrections to the extracted values of G s E + βG s M in recent experiments of HAPPEX and G0 are, depending on kinematics, found to be large and range between 13% to −75% but small in the case of A4 experiments.

Physical Review C, 2020

The three electromagnetic form factors for the transition from a 3/2 + Σ * hyperon to the groundstate Λ hyperon are studied. At low energies, combinations of the transition form factors can be deduced from Dalitz decays of the Σ * hyperon to Λ plus an electron-positron pair. It is pointed out how more information can be obtained with the help of the self-analyzing weak decay of the Λ. In particular it is shown that these transition form factors are complex quantities already in this kinematical region. Such measurements are feasible at hyperon factories as for instance the Facility for Antiproton and Ion Research (FAIR). At higher energies, the transition form factors can be measured in electron-positron collisions. The pertinent relations between the transition form factors and the decay distributions and differential cross sections are presented. Using dispersion theory, the low-energy electromagnetic form factors for the Σ *-to-Λ transition are related to the pion vector form factor. The additionally required input, i.e. the two-pion-Σ *-Λ amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the baryons from the octet and the decuplet. A poorly known NLO parameter is fixed to the experimental value of the Σ * → Λγ decay width. Pion rescattering is taken into account by dispersion theory solving a Muskhelishvili-Omnès equation. Subtracted and unsubtracted dispersion relations are discussed. However, in view of the fact that the transition form factors are complex quantities, the current data situation does not allow for a full determination of the subtraction constants. To reduce the number of free parameters, unsubtracted dispersion relations are used to make predictions for the transition form factors in the low-energy space-and timelike regions.

Physical Review C, 2010

We show that the Lagrangian of the free spin-5 2 field in the spinor-tensor representation with the auxiliary spinor field depends on the three arbitrary parameters. The first two parameters are associated with the spin-3 2 and-1 2 sector of the theory while the latter one is related to the auxiliary degrees of freedom. We derive a corresponding propagator of the system which represents (2 x 2) matrix in the (ψµν , ξ) space. The diagonal terms stand for the propagation of the spin-5 2 and auxiliary fields whereas the non-diagonal ones correspond to the ψµν − ξ mixing. The resulting spin-5 2 propagator contains non-pole contributions coming from the spin-3 2 and-1 2 sector of the spinor-tensor representation. A general form of the interaction vertex involving spin-5 2 field is discussed on the example of the πN N * 5 2 coupling. It is demonstrated that lower spin degrees of freedom can be removed from the theory by using higher order derivative coupling.

Physical Review D, 2022

Physical Review D, 2015

We present the calculation of the hyperon forward spin polarizability γ0 using manifestly Lorentz covariant baryon chiral perturbation theory including the intermediate contribution of the spin 3/2 states. As at the considered order the extraction of γ0 is a pure prediction of chiral perturbation theory, the obtained values are a good test for this theory. After including explicitly the decuplet states, our SU(2) results have a very good agreement with the experimental data and we extend our framework to SU(3) to give predictions to the hyperons' γ0 values. Prominent are the Σ − and Ξ − baryons as their photon transition to the decuplet is forbidden in SU(3) symmetry and therefore they are not sensitive to the explicit inclusion of the decuplet in the theory.

Physical Review D, 2014

We present an analysis of the lowest-lying decuplet baryon masses in the covariant baryon chiral perturbation theory with the extended-on-mass-shell scheme up to next-to-next-to-next-to-leading order. In order to determine the 14 low-energy constants, we perform a simultaneous fit of the n f = 2 + 1 lattice QCD data from the PACS-CS, QCDSF-UKQCD, and HSC Collaborations, taking finite-volume corrections into account self-consistently. We show that up to next-to-next-to-next-to-leading order one can achieve a good description of the lattice QCD and experimental data. Surprisingly, we note that the current lattice decuplet baryon masses can be fitted rather well by the next-to-leading order baryon chiral perturbation theory, which, however, misses the experimental data a little bit. Furthermore, we predict the pion-and strangeness-sigma terms of the decuplet baryons by use of the Feynman-Hellmann theorem.

Physical Review C, 2011

We address the issue of consistent interactions for off-shell fermion fields of arbitrary spin. These interactions play a crucial role in the quantum hadrodynamical description of high-spin baryon resonances in hadronic processes. The Rarita-Schwinger description of high-spin fermion fields involves unphysical degrees of freedom, associated with their lower-spin content. These enter the interaction if not eliminated outright. The invariance condition of the interaction under the unconstrained Rarita-Schwinger gauge removes the lower-spin content of the fermion propagator and leads to a consistent description of the interaction. We develop the most general, consistent interaction structure for high-spin fermions. We find that the power of the momentum dependence of a consistent interaction rises with the spin of the fermion field. This leads to unphysical structures in the energy dependence of the computed tree-level cross sections when the short-distance physics is cut off with standard hadronic form factors. A novel, spin-dependent hadronic form factor is proposed that suppresses the unphysical artifacts.

Physical Review D, 2020