We evaluate the pion and isobar propagators in cold nuclear matter self consistently applying a covariant form of the isobar-hole model. Migdal's vertex correction effects are considered systematically in the absence of phenomenological soft form factors. Saturated nuclear matter is modeled by scalar and vector mean fields for the nucleon. It is shown that the short-range dressing of the pi N Delta vertex has a significant effect on the pion and isobar properties. Using realistic parameters sets we predict a downward shift of about 50 MeV for the Delta resonance at nuclear saturation density. The pionic soft modes are much less pronounced than in previous studies.
We evaluate the in-medium spectral functions for pions, nucleon and isobar resonances in a self consistent and covariant manner. The calculations are based on a recently developed formulation which leads to predictions in terms of the pion-nucleon scattering phase shifts and a set of Migdal parameters describing important short range correlation effects. We do not observe significant softening of pion modes if we insist on reasonable isobar resonance properties but predict a considerable broadening of the N(1440) and N(1520) resonances in nuclear matter. Contrasted results are obtained for the…
Two approaches for analysis of pion photo- and electroproduction on nucleons in the resonance energy region are checked at $Q^2=0$ using the results of GWU(VPI) partial-wave analysis of photoproduction data. The approaches are based on dispersion relations and unitary isobar model. Within dispersion relations good description of photoproduction multipoles is obtained up to $W=1.8 GeV$. Within unitary isobar model, modified with increasing energy by incorporation of Regge poles, and with unified Breit-Wigner parametrization of resonance contributions, good description of photoproduction multipo…
The nucleon-nucleon interaction arising from the exchange of three pions and the excitation of $Δ(1232)$-isobars in intermediate states is studied. Approximating the $Δ$-propagator by the inverse $Δ$N mass-splitting, analytical expressions are derived for the spectral-functions of the isoscalar and isovector central, spin-spin and tensor NN-potentials in momentum-space. A trans- lation of the spectral-functions into coordinate-space potentials reveals that the main effect of these specific exchange and excitation mechanisms is a repulsive isoscalar central NN-potential.
Electron scattering from the three-nucleon bound state with two- and three-body disintegration is described. The description uses the purely nucleonic charge-dependent CD-Bonn potential and its coupled-channel extension CD-Bonn + $Δ$. Exact solutions of three-particle equations are employed for the initial and final states of the reactions. The current has one-baryon and two-baryon contributions and couples nucleonic with $Δ$-isobar channels. $Δ$-isobar effects on the observables are isolated. The $Δ$-isobar excitation yields an effective three-nucleon force and effective two- and three-nucleo…
Radiative nucleon-deuteron capture and two- and three-body photo disintegration of the three-nucleon bound state are described. The description uses the purely nucleonic charge-dependent CD-Bonn potential and its coupled-channel extension CD Bonn + $Δ$. The $Δ$-isobar excitation yields an effective three-nucleon force and effective two- and three-nucleon currents besides other $Δ$-isobar effects; they are mutually consistent. Exact solutions of three-particle equations are employed for the initial and final states of the reactions. The current has one-baryon and two-baryon contributions and co…
The proton-proton bremsstrahlung is investigated within a coupled-channel model with the $Δ$ degree of freedom. The model is consistent with the $NN$ scattering up to 1 GeV and the $γNΔ$ vertex determined in the study of pion photoproduction reactions. It is found that the $Δ$ excitation can significantly improve the agreements with the $pp \rightarrow ppγ$ at $E_{lab}=280$ MeV. Predictions at $E_{lab}=550$ and $800$ MeV are presented for future experimental tests.
A model calculation for pion production in nucleon-nucleon collisions is presented. Direct production, pion rescattering and contributions from pair diagrams are taken into account. The amplitudes for the elementary processes are based on well established microscopic models of nucleon-nucleon and pion-nucleon scattering. The $Δ(1232)$ is included explicitly and is found to play an important role even at energies close to production threshold. A good overall agreement with existing data from the pion production threshold up to the Delta resonance region is achieved.
A new operator for pion photo- and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances ($P_{33}(1232)$, $P_{11}(1440)$, $D_{13}(1520)$, $S_{11}(1535)$, $F_{15}(1680)$, and $D_{33}(1700)$). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The $Q^2$ dependence of electromagnetic resonance vertices is described with appropriate form factors in the electromagnetic helicity amplitudes. Wit…
We investigate effects of nuclear medium on antiquark distribution in nuclei applying the results of a recently developed relativistically-covariant self-consistent model for the pion and the isobar. We take into account Fermi motion including Pauli blocking and binding effects on the nucleons and medium effects on the isobar and pion leading to modest enhancement of the pion light-cone-momentum distribution in large nuclei. As a consequence the Drell-Yan cross-section ratio with respect to the deuteron exceeds one only for small values of the light-cone momentum.
The absorption of π^+ on ^3He in the $Δ$-region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a $πN \to Δ$ vertex and a $NΔ- NN$ transition t-matrix which are calculated from a phenomenological model for NN and πd reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for ^2H and ^3He lie too high in energy in relation to the data. The effect of the final state three-nucleon interaction turns out to be too small for changing…
The excitation of a $Δ$-isobar in a finite nucleus in charge--exchange ($^3\!$He,t) reaction is discussed in terms of a nuclear response function. The medium effects modifying a $Δ$- and a pion propagation were considered for a finite size nucleus. The Glauber approach has been used for distortion of a $^3\!$He and a triton in the initial and the final states. The effects determining the peak positions and its width are discussed. Large displacement width for the $Δ$ - h excitations and considerable contribution of coherent pion production were found for the reaction on $^{12}$C.
We calculate the cross sections for the $p(p,nπ^{+})p$ and $p(p,pπ^{0})p$ reactions for proton beam energies near threshold in a covariant one-boson-exchange model, which incorporates the exchange of $π$, $ρ$, $σ$ and $ω$ mesons and treats both nucleon and delta isobar as intermediate states. The final state interaction effects have also been included. The $ω$ 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 co…
A formalism for representing the fully relativistic propagator of the Rarita-Schwinger field in the nuclear medium is developed. Using a convenient basis for expanding the propagator, or the self energy, it is shown that they can be represented by 40 energy and momentum dependent quantities which can be combined into a 2x2 and a 6x6 matrix. In this way calculations reduce to matrix multiplication. Using the presented formalism the full relativistically covariant contribution of the pion-nucleon loop to the isobar self energy and propagator in isospin-symmetric spin-saturated nuclear medium is …
We extend a recent three-loop calculation of nuclear matter in chiral perturbation theory by including the effects from two-pion exchange with single and double virtual $Δ(1232)$-isobar excitation. Regularization dependent short-range contributions from pion-loops are encoded in a few NN-contact coupling constants. The empirical saturation point of isospin-symmetric nuclear matter, $\bar E_0 = -16 $MeV, $ρ_0 = 0.16 $fm$^{-3}$, can be well reproduced by adjusting the strength of a two-body term linear in density (and weakening an emerging three-body term quadratic in density). The nuclear matte…
gamma N->Delta transition form factors and threshold pi^0 photo- and electroproduction are studied with the new version of MAID and a dynamical model. By re-analyzing the recent Jlab data on p(e,e'p) pi^0 at Q^2 = 2.8 and 4.0 (GeV/c)^2, we find that the hadronic helicity conservation is not yet observed in this region of Q^2. The extracted R_{EM}, starting from a small and negative value at the real photon point, actually exhibits a clear tendency to cross zero and change sign as Q^2 increases, while the absolute value of R_{SM} is strongly increasing. Our analysis indicates that A_{1/2} and S…
We study photoproduction off nuclei based on a self consistent and covariant many body approach for the pion and isobar propagation in infinite nuclear matter. For the first time the t-channel exchange of an in-medium pion is evaluated in the presence of vertex correction effects consistently. In particular the interference pattern with the s-channel in-medium nucleon and isobar exchange contribution is considered. Electromagnetic gauge invariance is kept as a consequence of various Ward identities obeyed by the computation. Adjusting the set of Migdal parameters to the data set we predict an …
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 $p(p,nπ^+)p$ and $p(p,pπ^0)p$ reactions. The calculations incorporate the exchange of $π, ρ,ω$ and $σ$ mesons and treat nucleon a…
We perform a self-consistent relativistic RPA calculation for the isobaric analogue and Gamow-Teller resonances based on relativistic mean field theory results for the ground states of $^{48}$Ca, $^{90}$Zr and $^{208}$Pb. We use the parameter set NL1 for the $σ$, $ω$ and $ρ$ mesons, and experimental values for the pion and nucleon. An extra parameter, related to the intensity of the contact term in the pion-exchange interaction, is crucial to reproduce the latter resonances.
The $NN$ scattering near inelastic threshold is sensitive to the long-range diagonal interaction in the produced isobar channel. Earlier models included meson exchange potentials in the $NN$ sector and connecting that sector to isobar channels, as well as an $R$-matrix description of short-range quark effects. Including the diagonal pion exchange contributions in the $NΔ$ channels coupled to the very inelastic ${}^1D_2$ and ${}^3F_3$ $NN$ channels substantially improves those phase parameters and the observables $Δσ_{L}$ and $Δσ_{T}$. The same improvement is made to the other $I=1$ $NN$ channe…
Puzzling discrepancies between recent pion interferometry data on Au+Au reactions at s^1/2 = 130 and 200 AGeV from RHIC and predictions based on ideal hydrodynamics are analyzed in terms of covariant parton transport theory. The discrepancies of out and longitudinal radii are significantly reduced when the finite opacity of the gluon plasma is taken into account.
The unitary isobar model MAID2007 has been developed to analyze the world data of pion photo- and electroproduction. The model contains both a common background and several resonance terms. The background is unitarized according to the K-matrix prescription, and the 13 four-star resonances with masses below 2 GeV are described by appropriately unitarized Breit-Wigner forms. The data have been analyzed by both single-energy and global fits, and the transverse and longitudinal helicity amplitudes have been extracted for the four-star resonances below 2 GeV. Because of its inherent simplicity, MA…
A covariant model of elastic pion-nucleon scattering based on the Bethe-Salpeter equation is presented. The kernel consists of s- and u-channel nucleon and delta poles, along with rho and sigma exchange in the t-channel. A good fit is obtained to the s- and p-wave phase shifts up to the two-pion production threshold.
We investigate the role of the pion in Covariant Density Functional Theory. Starting from conventional Relativistic Mean Field (RMF) theory with a non-linear coupling of the $σ$-meson and without exchange terms we add pions with a pseudo-vector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bu…
It is shown that the off-shell parameters in the interaction Lagrangian of pions, nucleons, and $Δ$-isobars are redundant in the framework of effective field theories. Our results also suggest the necessity of including the $Δ$ as an explicit dynamical degree of freedom.
We optimize $Δ$-full nuclear interactions from chiral effective field theory. The low-energy constants of the contact potentials are constrained by two-body scattering phase shifts, and by properties of bound-state of $A=2$ to $4$ nucleon systems and nuclear matter. The pion-nucleon couplings are taken from a Roy-Steiner analysis. The resulting interactions yield accurate binding energies and radii for a range of nuclei from $A=16$ to $A=132$, and provide accurate equations of state for nuclear matter and realistic symmetry energies. Selected excited states are also in agreement with data.
In this work improvements to the application of the Gross equation to nuclear systems are tested. In particular we evaluate the two pion exchange diagrams, including the crossed-box diagram, using models developed within the spectator-on-mass-shell covariant formalism. We found that the form factors used in these models induce spurious contributions that violate the unitary cut requirement. We tested then some alternative form-factors in order to preserve the unitarity condition. With this new choice, the difference between the exact and the spectator-on-mass-shell amplitudes is of the order o…
The pion-nucleon interaction in the P33 partial wave is assumed to proceed simultaneously through the excitation of the Delta-isobar and through a phenomenologically introduced non-resonant background potential. The introduction of the background potential allows a more realistic parameterization of the pion-nucleon-Delta vertex compared with the previously used one without background. It also modifies the propagation of the Delta-isobar in the nuclear medium and gives rise to novel effective nucleon-Delta interactions. Their consequences on predictions for observables in the two-nucleon syste…
We calculate the density-dependent spin-asymmetry energy $S(k_f)$ of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to $S(k_f)$ originate from one-pion exchange, iterated one-pion exchange, and (irreducible) two-pion exchange with no, single, and double virtual $Δ$-isobar excitation. We find that the truncation to $1π$-exchange and iterated $1π$-exchange terms (which leads already to a good nuclear matter equation of state) is spin-unstable, since $S(k_{f0})<0$. The inclusion of the chiral $πNΔ$-dynamics guarantees …
We argue that, in contrast to the non-relativistic approach, a relativistic evaluation of the nucleon--hole and delta-isobar--nucleon hole contributions to the pion self-energy incorporates the s-wave scattering, which requires a more accurate evaluation. Therefore relativistic approach containing only these diagrams does not describe appropriately the pion self-energy in isospin symmetric nuclear matter. We conclude that, a correct relativistic approach to the pion self-energy should involve a more sophisticated calculation in order to satisfy the known experimental results on the near-thresh…
For the first time a fully self-consistent charge-exchange relativistic RPA based on the relativistic Hartree-Fock (RHF) approach is established. The self-consistency is verified by the so-called isobaric analog state (IAS) check. The excitation properties and the non-energy weighted sum rules of two important charge-exchange excitation modes, the Gamow-Teller resonance (GTR) and the spin-dipole resonance (SDR), are well reproduced in the doubly magic nuclei $^{48}$Ca, $^{90}$Zr and $^{208}$Pb without readjustment of the particle-hole residual interaction. The dominant contribution of the exch…
The universal curve $σ/A$ of nuclear photoabsorption is investigated within a Fermi gas model of nuclear matter. An energy range from pion threshold up to 400 MeV is considered. The interactions between nucleon, pion, $Δ$-isobar and photon are considered in the non-relativistic approximation with corrections of the order $1/M$ taken into account with respect to proton mass. Analytical expressions are obtained, in which the influence of nuclear correlations, two-nucleon contributions and relativistic corrections is studied explicitely. An extension of the model calculation to nucleon knock-out …
We investigate effects of consistent (conserving the number of degrees of freedom) and inconsistent pion-nucleon-isobar couplings on the isobar propagator in vacuum and in nuclear medium. Using the consistent coupling in conjunction with a convenient basis leads to significant simplification of the isobar vacuum and in-medium self energy and dressed propagator compared to the case of inconsistent interaction. The higher-derivative nature of the consistent interaction requires a suitable compensation by an additional form-factor term or adjustment in the used cut-off values. This modification i…
In symmetrical nuclear matter the solutions of pion dispersion equation are investigated in the complex plane of the pion frequency ω. There are three well-known branches of solutions on the physical sheet : sound, pion and isobar, at the matter density less than the critical one ρ<ρ_c. At ρ>ρ_c the fourth branch appears on the physical sheet. For this branch the condition ω^2_c\leq0 (in general case Reω^2_c\leq0) takes place. This points out the instability of the ground state which is possibly related to the pion condensation.
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 …
The nuclear density functional framework, based on chiral dynamics and the symmetry breaking pattern of low-energy QCD, is extended to the description of collective nuclear excitations. Starting from the relativistic point-coupling Lagrangian previously introduced [Nucl. Phys. A770 (2006) 1], the proton-neutron (quasiparticle) random phase approximation is formulated and applied to investigate the role of chiral pion-nucleon dynamics in excitation modes involving spin and isospin degrees of freedom, e.g. isobaric analog states and Gamow-Teller resonances.
The Covariant Spectator Theory is applied to the description of quarks and the pion. The dressed quark mass function is calculated dynamically in Minkowski space and used in the calculation of the pion electromagnetic form factor. The effects of the mass function on the pion form factor and the different quark-pole contributions to the triangle diagram are analyzed.
In-medium chiral perturbation theory is used to calculate the density dependence of the quark condensate $<\bar qq>$. The corrections beyond the linear density approximation are obtained by differentiating the interaction contributions to the energy per particle of isospin-symmetric nuclear matter with respect to the pion mass. Our calculation treats systematically the effects from one-pion exchange (with $m_π$-dependent vertex corrections), iterated $1π$-exchange, and irreducible $2π$-exchange including intermediate $Δ(1232)$-isobar excitations, with Pauli-blocking corrections up to three-loo…
Coherent pi0 photo- and electroproduction on 4He and 12C nuclei is investigated in the framework of a distorted wave impulse approximation in momentum space. The elementary process is described by the recently developed unitary isobar model. Medium effects are considered by introducing a phenomenological Delta self-energy. The recent experimental data for 4He and 12C can be well described over a wide range of energies and emission angles by the assumption that the Delta-nuclear interaction saturates.
We introduce a covariant approach in Minkowski space for the description of quarks and mesons that exhibits both chiral-symmetry breaking and confinement. In a simple model for the interquark interaction the quark mass function is obtained and used in the calculation of the pion form factor. We study the effects of the mass function and of the different quark pole contributions on the pion form factor.
A new approach to the parameterization of pion form factors is presented and for illustration applied to the pion vector form factor. It has the correct analytic structure, is at low energies consistent with recent high accuracy analyses of $ππ$ scattering phase shifts and, at high energies, maps smoothly onto the well--known, successful isobar model.
The structure of the pion wave function in the relativistic constituent quark model is investigated in the explicitly covariant formulation of light-front dynamics. We calculate the two relativistic components of the pion wave function in a simple one-gluon exchange model and investigate various physical observables: decay constant, charge radius, electromagnetic and transition form factors. We discuss the influence of the full relativistic structure of the pion wave function for an overall good description of all these observables, including both low and high momentum scales.
A systematic approach for the model building of Generalized Parton Distributions (GPDs), based on their overlap representation within the DGLAP kinematic region and a further covariant extension to the ERBL one, is applied to the valence-quark pion's case, using light-front wave functions inspired by the Nakanishi representation of the pion's Bethe-Salpeter amplitudes (BSA). This simple but fruitful pion's GPD model illustrates the general model building technique and, in addition, allows for the ambiguities related to the covariant extension, grounded on the Double Distribution (DD) represent…
The pion electromagnetic form factor at spacelike momentum transfer is calculated in relativistic impulse approximation using the Covariant Spectator Theory. The same dressed quark mass function and the equation for the pion bound-state vertex function as discussed in the companion paper are used for the calculation, together with a dressed quark current that satisfies the Ward-Takahashi identity. The results obtained for the pion form factor are in agreement with experimental data, they exhibit the typical monopole behavior at high-momentum transfer, and they satisfy some remarkable scaling r…
The charge-exchange break-up of polarised deuterons pol{d}p -> {pp}n, where the final {pp} diproton system has a very low excitation energy and hence is mainly in the 1S0 state, is a powerful tool to probe the spin-flip terms in the proton-neutron charge-exchange scattering. Recent measurements with the ANKE spectrometer at the COSY storage ring at 1.6, 1.8, and 2.27 GeV have extended these studies into the pion-production regime in order to investigate the mechanism for the excitation of the Delta(1232) isobar in the pol{d}p -> {pp}X reaction. Values of the differential cross section and two …
The energy dependence of forward pion double charge exchange reactions on light nuclei is studied for both the Ground State transition and the Double-Isobaric-Analog-State transitions. A common characteristic of these double reactions is a resonance-like peak around 50 MeV pion lab energy. This peak arises naturally in a two-step process in the conventional pion-nucleon system with proper handling of nuclear structure and pion distortion. A comparison among the results of different nuclear structure models demonstrates the effects of configuration mixing. The angular distribution is used to fi…
We present a calculation of radiative pion photoproduction in the framework of covariant chiral perturbation theory with explicit $Δ(1232)$ degrees of freedom. The analysis is performed employing the small scale expansion scheme adjusted for the $Δ$ region. Depending on the channel, we include contributions up to next-to-next-to-leading order. We fit the available experimental data for the reaction $ γp\toγpπ^0 $ and extract the value of the $Δ^+$ magnetic moment. Errors from the truncation of the small scale expansion are estimated using the Bayesian approach. We compare our results both with…
The pion form factor is calculated in the framework of the charge-conjugation invariant Covariant Spectator Theory. This formalism is established in Minkowski space and the calculation is set up in momentum space. In a previous calculation we included only the leading pole coming from the spectator quark (referred to as the relativistic impulse approximation). In this paper we also include the contributions from the poles of the quark which interacts with the photon and average over all poles in both the upper and lower half planes in order to preserve charge conjugation invariance (referred t…
We study pion--nucleon scattering with a chiral lagrangian of pions, nucleons, and $Δ$-isobars. The scattering amplitude is evaluated to one-loop $Q^3$ order, where $Q$ is a generic small momentum, using a new approach which is equivalent to heavy baryon chiral perturbation theory. We obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to 100 MeV. A sigma term greater than 45 MeV is favored, but the value is not well determined.
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 a…
We highlight some of the recent advances in the application of chiral effective field theory (chiral EFT) with baryons to the $πN$ scattering process. We recall some problems that cast doubt on the applicability of chiral EFT to $πN$ and show how the relativistic formalism, once the $Δ(1232)$-resonance is included as an explicit degree of freedom, solves these issues. Finally it is shown how this approach can be used to extract the $σ$-terms from phenomenological information.
This paper is the first in a series of three which attempt to resolve the difficulties that have plagued the $NN-πNN$ problem for the past ten years. Various theoretical inconsistencies in the current formulation have been pointed out and this work aims to eliminate these inconsistencies and so, we hope, produce agreement with experiment. This is to be done by using covariant perturbation theory, in which these inconsistencies are not present. The covariant perturbation theory is developed starting from a model Lagrangian, in order to fix notation and phases. It is shown that both old-fashione…
We construct a nuclear interaction in chiral effective field theory with explicit inclusion of the $Δ$-isobar $Δ(1232)$ degree of freedom at all orders up to next-to-next-to-leading order (NNLO). We use pion-nucleon ($πN$) low-energy constants (LECs) from a Roy-Steiner analysis of $πN$ scattering data, optimize the LECs in the contact potentials up to NNLO to reproduce low-energy nucleon-nucleon scattering phase shifts, and constrain the three-nucleon interaction at NNLO to reproduce the binding energy and point-proton radius of $^{4}$He. For heavier nuclei we use the coupled-cluster method to…
This thesis contains two parts. The first part deals with pion-nucleon/meson-baryon scattering in the Kadyshevsky formalism. This formalism is introduced and discussed. Problems may arise when derivative couplings and/or higher spin fields are used, especially when compared to the results in the Feynman formalism: unwanted contact terms pop-up. These terms are cancelled using the Gross and Jackiw or Takahashi and Umezawa method. The final results in both formalisms are therefore equal, causal and covariant. Formal incorporation of pair suppression in the baryon exchange sector is achieved usin…
Employing the covariant baryon chiral perturbation theory, we calculate the leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$ interaction up to order $O(p^3)$. We compare the so-obtained $NN$ phase shifts with $2\leq L\leq 6$ and mixing angles with $2\leq J\leq6$ with those obtained in the nonrelativistic baryon chiral perturbation theory, which allows us to check the relativistic corrections to the medium-range part of $NN$ interactions. We show that the contributions of relativistic TPE are more moderate than those of the nonrelativistic TPE. The relativistic co…
We discuss the formation of $Δ$ isobars in neutron star matter. We show that their threshold density strictly correlates with the density derivative of the symmetry energy of nuclear matter, the $L$ parameter. By restricting $L$ to the range of values indicated by recent experimental and theoretical analysis, i.e. $40$ MeV $\lesssim L \lesssim 62$ MeV, we find that $Δ$ isobars appear at a density of the order of 2$÷$3 times nuclear matter saturation density, i.e. the same range for the appearance of hyperons. The range of values of the couplings of the $Δ$s with the mesons is restricted by the…
We report on recent results of a calculation of the nucleon and delta masses in a covariant bound-state approach, where to the simple rainbow-ladder gluon-exchange interaction kernel we add a pion-exchange contribution to account for pion cloud effects. We observe good agreement with lattice data at large pion masses. At the physical point our masses are too large by about five percent, signaling the need for more structure in the gluon part of the interaction.
We investigate the role of the delta isobar in the reaction $πd\to πd$ 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 (m_pi/M_N)^(3/2), with m_pi (M_N) for the pion (nucleon) mass. The net effect of all delta contributions at this order to the pion-deuteron scattering length is (2.4 +/- 0.4)x 10^(-3) m_pi^{-1}.
