Delta Isobar Research Articles

Parity and time-reversal violating nuclear forces with explicit Δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta $$\\end{document}-excitations

We emphasize the usefulness of treating delta resonances as explicit degrees of freedom in applications of chiral effective field theory (EFT) to parity-violating and time-reversal-violating (PVTV) nuclear interactions. Compared with the delta-less framework, the explicit inclusion of the delta isobar allows one to resum certain types of contributions to the PVTV two-pion exchange two- and three-nucleon potentials without at the same time introducing any unknown parameters up to next-to-next-to-leading order in the EFT expansion. We provide the corresponding expressions for the delta contributions in momentum and coordinate spaces and compare the convergence of the EFT expansion in both formulations.

Enhancement of deltaful two-pion exchange nuclear forces

The role of the delta isobar degrees of freedom in nucleon–nucleon scattering is revisited. We attempt to understand why the dimensionally regularized two-pion exchanges with the explicit delta isobar is much stronger than the ones with spectral function regularization. When the cut-off value of spectral function regularization is varied, the isoscalar central component exhibits a rather large cut-off variation. This reveals a surprisingly large numerical factor of the deltaful two-pion exchange potentials. The power counting is adjusted accordingly and we discuss the results and how to improve upon this finding.

Three Body Calculation of theΔΔDibaryon CandidateD03(2370)

The D(03) dibaryon is generated dynamically as a resonance pole in a pion-nucleon-Delta' three-body model, where Delta' is a stable Delta baryon. Using separable interactions dominated by the Delta(1232) isobar for pion-nucleon and by the D(12) isobar for nucleon-Delta', where D(12) is the nucleon-Delta 2150 MeV dibaryon deduced in and constrained by 1D2 pp scattering, the model reduces to an effective two-body problem for Delta-Delta' which is solved. The mass and width of D(03) are found close to those of the I(JP)=0(3+) resonance peak observed by WASA@COSY in pion-production pn collisions at 2.37 GeV.

Chiral three-nucleon force at N4LO. II. Intermediate-range contributions

We derive the subleading contributions to the two-pion-one-pion exchange and ring three-nucleon force topologies emerging at next-to-next-to-next-to-next-to-leading order in chiral effective field theory. The resulting expressions do not involve any unknown parameters. To study convergence of the chiral expansion we work out the most general operator structure of a local isospin-invariant three-nucleon force. Using the resulting operator basis with 22 independent structures, we compare the strength of the corresponding potentials in configuration space for individual topologies at various orders in the chiral expansion. As expected, the subleading contributions from the two-pion-one-pion-exchange and ring diagrams are large which can be understood in terms of intermediate excitation of the Delta(1232) isobar.

Heavy-particle formalism with Foldy-Wouthuysen representation

Utilizing the Foldy-Wouthuysen representation, we use a bottom-up approach to construct heavy-baryon Lagrangian terms, without employing a relativistic Lagrangian as the starting point. The couplings obtained this way feature a straightforward $1/m$ expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications with two examples in the context of chiral effective field theory: the pion-nucleon coupling, which reproduces the results in the literature, and the pion-nucleon-delta coupling, which does not employ the Rarita-Schwinger field for describing the delta isobar, and hence does not invoke any spurious degrees of freedom. In particular, we point out that one of the subleading $\pi N \Delta$ couplings used in the literature is, in fact, redundant, and discuss the implications of this. We also show that this redundant term should be dropped if one wants to use low-energy constants fitted from $\pi N$ scattering in calculations of $NN\to NN\pi$ reactions.

Dilepton production in proton-proton and quasifree proton-neutron reactions at 1.25 GeV

We investigate the pp --> pp e+e- and quasifree pn --> pn e+e- reactions within an effective Lagrangian model at the laboratory kinetic energy of 1.25 GeV for which experimental data have recently been reported by the HADES Collaboration. The model uses a meson-exchange approximation to describe the initial nucleon-nucleon (NN) scattering. Contributions to the reaction amplitudes are included from the NN bremsstrahlung as well as from the excitation, propagation and radiative decay of the Delta(1230) isobar state. It is found that the HADES data on the e+e- invariant mass distribution in the pp --> pp e+e- reaction are reproduced excellently by our model where the Delta isobar term dominates the spectrum. However, the quasifree pn --> pn e+e- cross sections are underpredicted in the invariant mass region of 0.40 - 0.55 GeV/c^2 even after including contributions of the eta Dalitz decay and the subthreshold production and decay of the rho^0 meson via the baryonic resonance N*(1520). In the case of the quasifree pn --> pn e+e- reaction, a strong sensitivity to the pion electromagnetic form factor is observed which helps to bring the calculated cross sections closer to the data in the higher dilepton mass region.

Role of the [formula omitted] in pion–deuteron scattering at threshold within chiral effective field theory

We investigate the role of the delta isobar in the reaction πd→πd at threshold in chiral effective field theory. We discuss the corresponding power counting and argue that this calculation completes the evaluation of diagrams up to the order χ3/2, with χ the ratio of the pion to the nucleon mass. The net effect of all delta contributions at this order to the pion–deuteron scattering length is δaπdΔ=(2.4±0.4)×10−3mπ−1.

Neutron Star Matter Including Delta Isobars**The project supported by National Natural Science Foundation of China under Grant Nos. 10047001 and 10275029, the State Key Basic Research Development Program under Grant No. G2000-0774-07, and the CAS Knowledge Innovation Project under Grant No. KJCX2-N11

In this paper a new phase structure of neutron star matter including nucleons and delta isobars is presented. Particle fractions populated and pion condensations in neutron star matter are investigated in this model. The existence of the pion condensations can postpone the appearance of delta isobars. We found that both the pion condensation and reduce of the ratio of delta isobar to nucleons couplings can soften the corresponding equation of state. The maximum masses and their corresponding radii of neutron stars are calculated, and the obtained values are in observational region.

Relativistic treatment of bremsstrahlung in the process pp → ppγ with allowance for isobar channels and possibility of discriminating between different types of nucleon-nucleon interaction

A relativistic quasipotential formalism for describing electromagnetic processes involving nucleons that takes into account an explicit coupling to the NΔ (1232 MeV) and NN* (1440 MeV) channels is developed. On one hand, this formalism is a relativistic generalization of the Lomon-Ray approach to describing nucleon-nucleon scattering within a framework explicitly including isobar degrees of freedom; on the other hand, it relies on the formalism developed by Lev [F.M. Lev, hep-ph/9403222] within relativistic quantum mechanics for constructing the electromagnetic-current operator for interacting particles. The formalism makes it possible to obtain a consistent description of a two-nucleon system in the energy region extending up to 1 GeV. It is applied to describing the reaction pp → ppγ over a kinematical region in which corrections associated with a virtual delta isobar are of importance. The sensitivity of this reaction to the type of the short-range component of the nucleon-nucleon potential and the possibility of discriminating between the Moscow potential and meson-exchange potentials on the basis of experimental data are confirmed.

Role of baryonic resonances in the dilepton emission in nucleon-nucleon collisions

Within an effective Lagrangian model, we present calculations for cross sections of the dilepton production in proton-proton and proton-neutron collisions at laboratory kinetic energies in 1-5 GeV range. Production amplitudes include contributions from the nucleon-nucleon bremsstrahlung as well as from the mechanism of excitation, propagation, and radiative decay of Delta(1232) and N*(1520) intermediate baryonic resonances. It is found that the delta isobar terms dominate the cross sections in the entire considered beam energy range. Our calculations are able to explain the data of the DLS collaboration on the dilepton production in proton-proton collisions for beam energies below 1.3 GeV. However, for incident energies higher than this the inclusion of contributions from other dilepton sources like Dalitz decay of pi0 and eta mesons, and direct decay of rho and omega mesons is necessary to describe the data.

Spectroscopy of resonance decays in high-energy heavy-ion experiments

Invariant mass distributions of the hadronic decay products from resonances formed in relativistic heavy ion collision (RHIC) experiments are investigated with a view to disentangle the effects of thermal motion and the phase space of decay products from those of intrinsic changes in the structure of resonances at the freeze-out conditions. Analytic results of peak mass shifts for the cases of both equal and unequal mass decay products are derived. The shift is expressed in terms of the peak mass and width of the vacuum or medium-modified spectral functions and temperature. Examples of expected shifts in meson (e.g., rho, omega, and sigma) and baryon (e.g., Delta) resonances that are helpful to interpret recent RHIC measurements at BNL are provided. Although significant downward mass shifts are caused by widened widths of the $\rho-$meson in medium, a downward shift of at least 50 MeV in its intrinsic mass is required to account for the reported downward shift of 60-70 MeV in the peak of the rho-invariant mass distribution. An observed downward shift from the vacuum peak value of the Delta distinctively signals a significant downward shift in its intrinsic peak mass, since unlike for the rho-meson, phase space functions produce an upward shift for the Delta isobar.

ω→π0γ∗, ρ→πγ∗, and π0→γγ∗ decays in nuclear medium

We calculate the medium modification of the pi-omega-rho vertex and analyze its significance for the pi^0 -> gamma gamma*, omega -> pi^0 gamma*, and rho -> pi gamma* decays in nuclear matter. We use a relativistic hadronic approach at zero temperature and in the leading-density limit, and consider decays of particles at rest with respect to the medium. It is shown that for the pi^0 -> gamma gamma* the effects of the Delta isobar cancel almost exactly the effects of the nucleon ph excitations, such that the net medium effect is small. On the contrary, for the decays omega -> pi^0 gamma* and rho -> pi gamma* we find a sizeable increase of the partial widths at virtualities of the photon in the range 0.3-0.6 GeV. The effect has direct significance for the calculation of dilepton yields from the Dalitz decays in relativistic heavy-ion collisions.

What is the structure of the Roper resonance?

We investigate the structure of the nucleon resonance N^*(1440) (Roper) within a coupled-channel meson exchange model for pion-nucleon scattering. The coupling to pipiN states is realized effectively by the coupling to the sigmaN, piDelta and rhoN channels. The interaction within and between these channels is derived from an effective Lagrangian based on a chirally symmetric Lagrangian, which is supplemented by well known terms for the coupling of the Delta isobar, the omega meson and the 'sigma', which is the name given here to the strong correlation of two pions in the scalar-isoscalar channel. In this model the Roper resonance can be described by meson-baryon dynamics alone; no genuine N^*(1440) (3 quark) resonance is needed in order to fit piN phase shifts and inelasticities.

Complete one-loop analysis of the Nucleon's spin polarizabilities

We present a complete one-loop analysis of the four nucleon spin polarizabilities in the framework of heavy baryon chiral-perturbation theory. The first nonvanishing contributions to the isovector and first corrections to the isoscalar spin polarizabilities are calculated. No unknown parameters enter these predictions. We compare our results to various dispersive analyses. We also discuss the convergence of the chiral expansion and the role of the delta isobar.

Erratum: Elementary1H(p,p′π+)nreaction [Phys. Rev. C58, 1614 (1998)

A detailed study of the elementary p(p,p$'\pi^{+}$)n reaction is presented using the delta isobar model. In this model, in the first step one of the two protons in the initial state gets excited to $\Delta $. This, in the second step, decays into a nucleon and a pion. For the $pp \to N\Delta$ step the parametrized form of the DWBA t-matrix of Jain and Santra, which reproduces most of the available data on $pp \to n\Delta^{++}$, is used. The cross-sections studied include the outgoing proton momentum spectra in coincidence with the pion, the outgoing pion momentum spectra and the integrated total cross-section. We find that all the calculated numbers are in good agreement with the corresponding measured cross sections.

NN→NNπ reaction near threshold in a covariant one-boson-exchange model

We calculate the cross sections for the $p(p,n\pi^{+})p$ and $p(p,p\pi^{0})p$ reactions for proton beam energies near threshold in a covariant one-boson-exchange model, which incorporates the exchange of $\pi$, $\rho$, $\sigma$ and $\omega$ mesons and treats both nucleon and delta isobar as intermediate states. The final state interaction effects have also been included. The $\omega$ meson exchange is found to contribute significantly at these energies, which, along with other meson exchanges, provides an excellent agreement with the data. The cross sections at beam energies $\leq$ 300 MeV are almost free from the contributions of the $\Delta$ isobar excitation.

Pion production in proton-proton collisions in a covariant one-boson-exchange model

Motivated by the renewed interest in studying the pion production on nuclei with protons at few GeV incident energies, we investigate the pion production in proton-proton collisions over an energy range of 300 $MeV$ to 2 $GeV$. Starting from a realistic one-boson exchange model with parameters fitted to the amplitudes of the elastic nucleon-nucleon scattering, we perform fully covariant calculations for the total, double and triple differential cross-sections of the $p(p,n\pi^+)p$ and $p(p,p\pi^0)p$ reactions. The calculations incorporate the exchange of $\pi, \rho,\omega$ and $\sigma$ mesons and treat nucleon and delta isobar as intermediate states. We obtain a reasonably good agreement with the experimental data in the entire range of beam energies. The form of the covariant delta propagator, the cut-off parameter for the $\pi NN$ and $\pi N\Delta$ vertex form factors and the energy dependence of the delta isobar decay width is investigated.

Formula omitted] ratio for the γN → Δ transition in the chiral quark soliton model

We calculate the electric quadrupole to magnetic dipole transition ratio E2 M1 for the reaction γN → Δ (1232) in the chiral quark soliton model. The calculated E2 M1 ratio is in a good agreement with the very new experimental data. We obtain non-zero negative value for the electric quadrupole N - Δ transition moment, which suggests an oblate deformed charge structure of the nucleon or/and the delta isobar. Other observables related to this quantity, namely the N - Δ mass splitting, the isovector charge radius, and isovector magnetic moment, are properly reproduced as well.

QCD sum rules for Delta isobar in nuclear matter.

The self-energies of $\Delta$ isobar propagating in nuclear matter are calculated using the finite-density QCD sum-rule methods. The calculations show that the Lorentz vector self-energy for the $\Delta$ is significantly smaller than the nucleon vector self-energy. The magnitude of the $\Delta$ scalar self-energy is larger than the corresponding value for the nucleon, which suggests a strong attractive net self-energy for the $\Delta$; however, the prediction for the scalar self-energy is very sensitive to the density dependence of certain in-medium four-quark condensate. Phenomenological implications for the couplings of the $\Delta$ to the nuclear scalar and vector fields are briefly discussed.

Exclusive pion production in proton-nucleus collisions and the relativistic two nucleon dynamics

The exclusive pion production in a proton-nucleus collision, leading to two-body final states, is examined in a fully covariant two-nucleon model. We focus on the amplitudes which are dominated by the Δ(1232) resonance. Retaining the full covariant forms of the πNN and πNΔ vertices and employing a relativistic propagator for the delta isobar, expressions for various reaction amplitudes are derived. The bound state nucleon wave functions are obtained by solving the Dirac equation with appropriate scalar and vector potentials whereas the continuum wave functions are approximated by plane waves. The sensitivity of the calculated cross sections to the in-medium self-energy of the intermediate pion is investigated. It is found that the relative magnitudes of the so called target-emission and projectile-emission amplitudes depend strongly on the pion self-energy. A comparison with the available data for the 12C and 16O targets at the incident proton energy of 800 MeV supports our conclusions.