We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. Our calculation treats systematically the effects from $1π$-exchange, iterated $1π$-exchange, and irreducible $2π$-exchange with intermediate $Δ$-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass $M^*(ρ)$ entering the energy density functional is identical to the one of Fermi-liquid theory when employing the improved density-matrix expansion. The strength $F_\nabla(ρ)$ of the $(\vec\nabla ρ)^2$ surface-term as provided by the pion-exchange dynamics is in good agreement with that of phenomenological Skyrme forces in the density region $ρ_0/2 <ρ<ρ_0$. The spin-orbit coupling strength $F_{so}(ρ)$ receives contributions from iterated $1π$-exchange (of the ``wrong sign'') and from three-nucleon interactions mediated by $2π$-exchange with virtual $Δ$-excitation (of the ``correct sign''). In the region around $ρ_0/2 \simeq 0.08 $fm$^{-3}$ where the spin-orbit interaction in nuclei gains most of its weight these two components tend to cancel, thus leaving all room for the short-range spin-orbit interaction. The strength function $F_J(ρ)$ multiplying the square of the spin-orbit density comes out much larger than in phenomenological Skyrme forces and it has a pronounced density dependence.
Historic steps in the emergence, the derivation and the use of three-nucleon forces, genuine and effective, for calculations of few-nucleon systems and of the structure of heavier nuclei are recalled. The research focus is on few-nucleon systems. The need of three-nucleon forces for a successful description of some data and the remaining puzzles of other data, not explainable despite the inclusion of three-nucleon forces, are discussed.
We examine possibilities of pion condensation with zero momentum (s-wave condensation) in neutron stars by using the pion-nucleus optical potential U and the relativistic mean field (RMF) models. We use low-density phenomenological optical potentials parameterized to fit deeply bound pionic atoms or pion-nucleus elastic scatterings. Proton fraction (Y_p) and electron chemical potential (mu_e) in neutron star matter are evaluated in RMF models. We find that the s-wave pion condensation hardly takes place in neutron stars and especially has no chance if hyperons appear in neutron star matter and…
The scattering amplitude of the pion-nucleon elastic scattering is calculated by the lowest-order approximation of the perturbative expansion with the non-perturbative term. The self-energy of nucleon is determined so as to give the scattering parameters of the $S$-wave. It is shown that the scattering process mediated by the $σ$-meson plays a decisive role together with the pseudovector pion interaction.
The electromagnetic form factor of proton is studied following our previous calculation of the anomalous magnetic moment. The non-perturbative term is incorporated to correct the $Q^2$ dependence.
A calculation of the pion-production operator up to next-to-next-to-leading order for s-wave pions is performed within chiral effective field theory. In the previous study [Phys. Rev. C 85, 054001 (2012)] we discussed the contribution of the pion-nucleon loops at the same order. Here we extend that study to include explicit Delta degrees of freedom and the 1/m_N^2 corrections to the pion-production amplitude. Using the power counting scheme where the Delta-nucleon mass difference is of the order of the characteristic momentum scale in the production process, we calculate all tree-level and loo…
We study the perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering for p- and d-waves within the effective field theory approach. The one pion exchange potential is fully iterated at the leading order in the expansion, a choice generating a consistent and well-defined power counting that we explore in detail. The results show that perturbative chiral two pion exchange reproduces the data up to a center-of-mass momentum of k_cm ~300 MeV at NNLO and that the effective field theory expansion convergences up to k_cm ~ 350 MeV.
We outline the modified formulation of baryon chiral effective field theory for nucleon-nucleon scattering and discuss the issue of a possible power counting violation by the nucleon mass. We also present the results for the quark mass dependence of the $^1S_0$ and $^3S_1$ scattering lengths and the deuteron binding energy at leading order.
In the Yukawa model for nuclear forces, a simple relation between the charged and neutral pion-nucleon coupling constants is derived. The relation implies that the charged pion-nucleon coupling constant is larger than the neutral one since the np interaction is stronger than the pp interaction. The derived value of the charged pion-nucleon constant shows a very good agreement with one of the recent experimental values. The relative splitting between the charged and neutral pion-nucleon coupling constants is predicted to be practically the same as that between the charged and neutral pion masse…
Pion photoproduction amplitudes are calculated from a set of equations that have been derived by coupling an external photon to all places in a dressed pion-nucleon vertex. The calculation is consistent with gauge invariance, charge conservation, unitarity and covariance. To provide input to the photoproduction amplitude, a photon-nucleon vertex is calculated from a set of equations derived by complete attachment of photons to a dressed nucleon propagator. We check the accuracy of this vertex by extracting its nucleon electromagnetic form factors.
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.
We show how to renormalize chiral two pion exchange perturbatively if one pion exchange has already been fully iterated at leading order. This particular choice corresponds to the implementation of the counting proposal of Nogga, Timmermans and van Kolck at subleading orders. We illustrate why the perturbative treatment of the two pion exchange contributions is mandatory in order to avoid certain inconsistencies in Weinberg's counting. In addition, renormalizability implies modifications of the power counting which we explore for the particular case of the singlet channel.
We study the perturbative renormalizability of chiral two pion exchange for the singlet and triplet channels within effective field theory, provided that the one pion exchange piece of the interaction has been fully iterated. We determine the number of counterterms/subtractions needed in order to obtain finite results when the cut-off is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that chiral two pion exchange can be treated perturbatively up to a center-of-mass momentum of k ~ 200-300 MeV in the singlet channel and k ~ 300-400 in …
The procedure for deriving the Ward-Takahashi identity is applied to the pseudovector coupling pion-nucleon system in which the isovector and axial-vector current does not conserved. The relation is given in closed form although it is more complicated than that of the quantum electrodynamics. The application to the propagator has revealed the interesting results.
A dynamical investigation of the nucleon-nucleon (NN) interaction by using the resonating group method (RGM) in a chiral SU(3) quark model has been revisited. The considered quark-quark interaction includes, besides the one-gluon exchange (OGE) and the phenomenological confinement potential, the nonet scalar and pseudoscalar meson exchanges derived from the spontaneous SU(3) chiral symmetry breaking. The physical consistency requirement that the wave functions of single baryons satisfy the minimums of the Hamiltonian has been strictly imposed in determination of the model parameters. The calcu…
We investigate p-wave pion production in nucleon-nucleon collisions up to next-to-next-to-leading order in chiral effective field theory. In particular, we show that it is possible to describe simultaneously the p-wave amplitudes in the $pn\to ppπ^-$, $pp\to pnπ^+$, $pp\to dπ^+$ channels by adjusting a single low-energy constant accompanying the short-range operator which is available at this order. This study provides a non-trivial test of the applicability of chiral effective field theory to reactions of the type $NN\to NNπ$.
We propose a new, renormalizable approach to nucleon-nucleon scattering in chiral effective field theory based on the manifestly Lorentz invariant form of the effective Lagrangian without employing the heavy-baryon expansion. For the pion-less case and for the formulation based on perturbative pions, the new approach reproduces the known results obtained by Kaplan, Savage and Wise. Contrary to the standard formulation utilizing the heavy-baryon expansion, the nonperturbatively resummed one-pion exchange potential can be renormalized by absorbing all ultraviolet divergences into the leading S-w…
We derive the leading one-loop contribution to the one-pion exchange and short-range two-nucleon electromagnetic current operator in the framework of chiral effective field theory. The derivation is carried out using the method of unitary transformation. Explicit results for the current and charge densities are given in momentum and coordinate space.
We show on two examples, namely a calculation for charge symmetry breaking in pn->d pi^0 that allows one to extract the quark mass difference induced part of the proton--neutron mass difference and a high precision calculation for pion--deuteron scattering and its implications for the value of the charged pion--nucleon coupling constant, how QCD tests can be performed from low energy hadronic observables.
We present the first application of the Basis Light-Front Quantization method to a simple chiral model of the nucleon-pion system as a relativistic bound state for the physical proton. The light-front mass-squared matrix of the nucleon-pion system is obtained within a truncated basis. The mass and the corresponding light-front wave function (LFWF) of the proton are computed by numerical diagonalization of the resulting mass-squared matrix. With the boost invariant LFWF, we calculate the probability density distribution of the pion's longitudinal momentum fraction and the Dirac form factor of t…
