We present and discuss predictions for a cross section of bulk and single-particle properties in symmetric nuclear matter based on recent high-quality nucleon-nucleon potentials at N3LO and including all subleading three-nucleon forces. We begin with the equation of state and its saturation properties and proceed to the single-nucleon potential. We also explore short-range correlations as seen through the defect function. The various predictions which we present have a common foundation in an internally consistent ab initio approach.
We present predictions for the neutron matter equation of state, from leading to fourth order of chiral effective field theory, using recently developed, accurate chiral nucleon-nucleon potentials. We find the impact of subleading three-neutron forces to be mild and attractive. We also show order-by-order predictions for the symmetry energy, and discuss its density dependence in relation to empirical constraints.
Recently, we have shown that the continuity equation for the nuclear vector and axial current operators acquires additional terms if the latter depend on the energy transfer. We analyze in detail the electromagnetic single-nucleon four-current operators and verify the validity of the modified continuity equation for all one- and two-nucleon contributions up to fourth order in the chiral expansion. We also derive, for the first time, the leading contribution to the three-nucleon charge operator which appears at this order. Our study completes the derivation of the electroweak nuclear currents t…
We extract the statistical uncertainties for the pion-nucleon ($πN$) low energy constants (LECs) up to fourth order $\mathcal{O}(Q^4)$ in the chiral expansion of the nuclear effective Lagrangian. The LECs are optimized with respect to experimental scattering data. For comparison, we also present an uncertainty quantification that is based solely on \pin{} scattering phase shifts. Statistical errors on the LECs are critical in order to estimate the subsequent uncertainties in \textit{ab initio} modeling of light and medium mass nuclei which exploit chiral effective field theory. As an example o…
We analyze the longest-range two-pion exchange contributions to the three-nucleon force at leading-loop order in the framework of heavy-baryon chiral effective field theory with explicit $Δ(1232)$ degrees of freedom. All relevant low-energy constants which appear in the calculation are determined from pion-nucleon scattering. Comparing our results with the ones obtained in the $Δ$-less theory at N4LO, we find effects of the $Δ$ isobar for this particular topology to be rather well represented in terms of resonance saturation of various low-energy constants in the $Δ$-less approach.
We extend our previous analysis of the unitarized pion-nucleon scattering amplitude including up to fourth order terms in Heavy Baryon Chiral Perturbation Theory. We pay special attention to the stability of the generated Delta(1232 resonance, the convergence problems and the power counting of the chiral parameters.
We report neutron star predictions based on our most recent equations of state. These are derived from chiral effective field theory, which allows for a systematic development of nuclear forces, order by order. We utilize high-quality two-nucleon interactions and include all three-nucleon forces up to fourth order in the chiral expansion. Our ab initio predictions are restricted to the domain of applicability of chiral effective field theory. However, stellar matter in the interior of neutron stars can be up to several times denser than normal nuclear matter at saturation, and its composition …
We present the first nucleon-nucleon potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory. Charge-dependence is included up to next-to-leading order of the isospin-violation scheme. The accuracy for the reproduction of the NN data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials. Since NN potentials of order three and less are known to be deficient in quantitative terms, the present work shows that the fourth order is necessary and sufficient for a reliable NN potential derived from chiral effective Lagr…
We analyse elastic-pion nucleon scattering to fourth order in heavy baryon chiral perturbation theory, extending the third order study published in Nucl. Phys. A640 (1998) 199. We use various partial wave analyses to pin down the low-energy constants from data in the physical region. The S-wave scattering lengths are consistent with recent determinations from pionic hydrogen and deuterium. We find an improved description of the P-waves. We also discuss the pion-nucleon sigma term and problems related to the prediction of the subthreshold parameters.
We present the complete derivation of the nuclear axial charge and current operators as well as the pseudoscalar operators to fourth order in the chiral expansion relative to the dominant one-body contribution using the method of unitary transformation. We demonstrate that the unitary ambiguity in the resulting operators can be eliminated by the requirement of renormalizability and by matching of the pion-pole contributions to the nuclear forces. We give expressions for the renormalized single-, two- and three-nucleon contributions to the charge and current operators and pseudoscalar operators…
We extend our previous study of elastic pion-nucleon scattering in the framework of chiral perturbation theory by performing a combined analysis of the reactions $πN \to πN$ and $πN \to ππN$. The calculation is carried out to fourth order in the chiral expansion using the heavy baryon approach and the covariant formulation supplemented with a modified version of the extended on-mass-shell renormalization scheme. We demonstrate that a combined fit to experimental data in both channels leads to a reduced amount of correlations between the low-energy constants. A satisfactory description of the e…
We calculate the amplitude T_1 for forward doubly-virtual Compton scattering in heavy-baryon chiral perturbation theory, to fourth order in the chiral expansion and with the leading contribution of the gammaNDelta form factor. This provides a model-independent expression for the amplitude in the low-momentum region, which is the dominant one for its contribution to the Lamb shift. It allows us to significantly reduce the theoretical uncertainty in the proton polarisability contributions to the Lamb shift in muonic hydrogen. We also stress the importance of consistency between the definitions o…
We present a calculation of the fourth-order (NLO) contribution to spin-dependent forward Compton scattering in heavy-baryon chiral perturbation theory. No low-energy constants, except for the anomalous magnetic moments of the nucleon, enter at this order. The fourth-order piece of the spin polarisability of the proton turns out to be almost twice the size of the leading piece, with the opposite sign. This leads to the conclusion that no prediction can currently be made for this quantity.
This presentation reviews recent guiding themes in the broad context of nuclear physics, from developments in chiral effective field theory applied to nuclear systems, via the phases and structures of QCD, to matter under extreme conditions in heavy-ion collisions and neutron stars.
We present a calculation of the fourth-order (NLO) contribution to spin-dependent Compton scattering in heavy-baryon chiral perturbation theory, and we give results for the four spin polarisabilities. No low-energy constants, except for the anomalous magnetic moments of the nucleon, enter at this order. For forward scattering the fourth-order piece of the spin polarisability of the proton turns out to be almost twice the size of the leading piece, with the opposite sign. This leads to the conclusion that no prediction can currently be made for this quantity. For backward scattering the fourth-…
We construct the minimal effective chiral pion-nucleon SU(2) Lagrangian at fourth order in the chiral expansion. The Lagrangian contains 118 in principle measurable terms. We develop both the relativistic as well as the heavy baryon formulation of the effective field theory. For the latter, we also work out explicitly all 1/m corrections at fourth order. We display all relevant relations needed to find the linearly independent terms.
We present a calculation of the fourth-order (NLO) contribution to spin-dependent Compton scattering in heavy-baryon chiral perturbation theory, and we give results for the four spin polarisabilities. These results have been presented before, in hep-ph/0002133. Here we address the issue of whether one-particle reducible graphs in the heavy baryon theory contribute to the polarisabilities.
We recently developed a Bayesian framework for parameter estimation in general effective field theories. Here we present selected results from using that framework to estimate parameters with a nucleon-nucleon (NN) potential derived using chiral effective field theory ($χ$EFT): the semi-local NN potential of Epelbaum, Krebs, and Meißner (EKM). There are many NN scattering data, up to high energies, and with rather small errors, so imposing a penalty for unnatural low-energy constants (LECs) usually has a small effect on the fits. In contrast, we have found that including an estimate of higher …
We extend a recent chiral approach to nuclear matter by including the most general (momentum-independent) NN-contact interaction. Iterating this two-parameter contact-vertex with itself and with one-pion exchange the emerging energy per particle exhausts all terms possible up-to-and-including fourth order in the small momentum expansion. The equation of state of pure neutron matter, $\bar E_n(k_n)$, can be reproduced very well up to quite high neutron densities of $ρ_n=0.5\fmd$ by adjusting the strength of a repulsive $nn$-contact interaction. Binding and saturation of isospin-symmetric nuclea…
Embedded in the historical context, we review recent progress in the development of nucleon-nucleon (NN) potentials based upon chiral effective field theory. A major breakthrough is the construction of the first NN potential at next-to-next-to-next-to-leading order (fourth order) of chiral perturbation theory (ChPT). The accuracy of this potential concerning the reproduction of the NN data below 290 MeV lab. energy is comparable to the one of phenomenological high-precision potentials. Since NN potentials of order three or less of ChPT are known to be deficient in quantitative terms, the recen…
We calculate the $T$-matrices of elastic pion-nucleon ($πN$) scattering up to fourth order in SU(3) heavy baryon chiral perturbation theory. The pertinent low-energy constants are determined by fitting to $πN$ phase shifts below 200 MeV pion laboratory momentum in the physical region. The scattering lengths and scattering volumes are extracted from the chiral amplitudes, and turn out to be in good agreement with those of other approaches and the available experimental values. We also discuss the subthreshold parameters and the related issues. On the basis of the various phase shifts, the thres…
A number of papers recently have used fourth-order chiral perturbation theory to extrapolate lattice data for the nucleon mass; the process seems surprisingly successful even for large pion masses. This paper shows that the inclusion of the fifth-order terms spoils the agreement.
The physics of the QCD phase diagram is discussed in view from heavy-ion collisions, compact astrophysical phenomena, lattice QCD and chiral effective models. We find that (T,mu_B) region probed in heavy-ion collisions and the black hole formation processes covers most of the critical point locations predicted in recent lattice QCD Monte-Carlo simulations and chiral effective models of QCD. We also discuss the consistency of the statistical model results and dynamical model description.
A personal overview on the present status of SU(3) chiral perturbation theory in the baryonic sector is given. Recent developments are presented and remaining challenges are pointed out.
We calculate properties of A=6 system using the accurate charge-dependent nucleon-nucleon (NN) potential at fourth order of chiral perturbation theory. By application of the ab initio no-core shell model (NCSM) and a variational calculation in the harmonic oscillator basis with basis size up to 16 hbarOmega we obtain the 6Li binding energy of 28.5(5) MeV and a converged excitation spectrum. Also, we calculate properties of 10B using the same NN potential in a basis space of up to 8 hbarOmega. Our results are consistent with results obtained by standard accurate NN potentials and demonstrate a …
We give a general overview about the approaches to study the phase diagram of QCD. Thereafter, we examine the evolution of a fireball in a chiral fluid dynamic model including nonequilibrium effects.
The Jülich-Bonn group aims at an extensive study of the baryon-baryon ($BB$) interaction involving strange baryons ($Λ$, $Σ$, $Ξ$) within SU(3) chiral effective field theory. An overview of achievements and new developments over the past few years is provided. The topics covered are: 1) Derivation of the leading charge-symmetry breaking (CSB) interaction for the $ΛN$ system and its application in a study of CSB effects in $A$=$4$ $Λ$-hypernuclei. 2) Updated results for the $ΞN$ interaction at NLO and predictions for $Ξ^- p$ correlation functions. 3) Extension of the $ΛN$-$ΣN$ interaction to ne…
Predictions of the existence of well-defined deeply bound pionic atom states for heavy nuclei and the eventual observation of such states by the (d,3He) reaction have revived interest in the pion-nucleus interaction at threshold and in its relation to the corresponding pion-nucleon interaction. Explanation of the 'anomalous' s-wave repulsion in terms of partial restoration of chiral symmetry and/or in terms of energy-dependence effects have been tested in global fits to pionic atom data and in a recent dedicated elastic scattering experiment. The role of neutron density distributions in this c…
Based on a chiral approach to nuclear matter, we calculate the quartic term in the expansion of the equation of state of isospin-asymmetric nuclear matter. The contributions to the quartic isospin asymmetry energy $A_4(k_f)$ arising from $1π$-exchange and chiral $2π$-exchange in nuclear matter are calculated analytically together with three-body terms involving virtual $Δ(1232)$-isobars. From these interaction terms one obtains at saturation density $ρ_0 = 0.16\,$fm$^{-3}$ the value $A_4(k_{f0})= 1.5\,$MeV, more than three times as large as the kinetic energy part. Moreover, iterated $1π$-exch…
To obtain an understanding of the structure and reactions of nuclear systems from first principles has been a long-standing goal of nuclear physics. In this respect, few- and many-body systems provide a unique laboratory for studying nuclear interactions. During the past decades, the development of accurate representations of the nuclear force has undergone substantial progress. Particular emphasis has been devoted to chiral effective field theory (EFT), a low-energy effective representation of quantum chromodynamics (QCD). Within chiral EFT, many studies have been carried out dealing with the…
An overview of Chiral Perturbation Theory calculations in the mesonic sector at the two Loop level is given. Discussed in some detail are the partially quenched case relevant for lattice QCD, the general fitting procedures and $ππ$,$πK$ scattering as well as the determination of $V_{us}$ and $K_{\ell3}$ decays.
We construct the general Lagrangian for relativistic and heavy baryon chiral perturbation theory with virtual photons to fourth order. We work out the electromagnetic and strong isospin violating contributions to the nucleon self-energy, the nucleon mass and the scalar form factor of the nucleon. Electromagnetic effects for the shift to the Cheng-Dashen point can be as large as 2 MeV. We also discuss the corrections to Weinberg's prediction for the scattering length difference $a(π^0 p) - a(π^0 n)$ and show that they are small.
We calculate electromagnetic neutral pion production off tri-nucleon bound states (3H, 3He) at threshold in chiral nuclear effective field theory to fourth order in the standard heavy baryon counting. We show that the fourth order two-nucleon corrections to the S-wave multipoles at threshold are very small. This implies that a precise measurement of the S-wave cross section for neutral pion production off 3He allows for a stringent test of the chiral perturbation theory prediction for the S-wave electric multipole E_{0+}^{pi0 n}.
We overview two interconnected topics: possible effective restoration of chiral symmetry in highly excited hadrons and possible existence of confined but chirally symmetric matter at low temperatures and high densities.
The baryon masses are examined in SU(3) chiral perturbation theory to third order using the recently proposed infrared regularization scheme. Fourth order is estimated by evaluating the dominant diagram. With this regularization the magnitude of the loop integrals is reduced so that the convergence of the series appears to be better than in the heavy baryon approach.
I discuss recent results on lattice QCD calculations with the main emphasis on the thermodynamics of the crossover region, restoration of the chiral symmetry and fluctuations of conserved charges as indicator of deconfinement, that may also be used to determine the chemical freeze-out conditions in heavy-ion collision experiments.
We present a brief overview on recent developments of theory and phenomenology for novel many-body phenomena related to the chirality and magnetic field, with an emphasis on their experimental implications and possible detection in relativistic nuclear collisions.
We overview a possible mechanism for confining but chirally symmetric matter at low temperatures and large densities. As a new development we employ a diffused quark Fermi surface and show that such diffusion does not destroy possible existence of a confining but chirally symmetric matter at low temperatures and large density.
Threshold neutral pion photoproduction on the deuteron is studied in the framework of baryon chiral perturbation theory beyond next-to--leading order in the chiral expansion. To fourth order in small momenta, the amplitude is finite and a sum of two- and three-body interactions with no undetermined parameters. With accurate theoretical and experimental input from the single nucleon sector for the proton amplitude, we investigate the sensitivity of the threshold cross section to the elementary $γn \to π^0 n$ amplitude. A precise measurement of the threshold cross section for $γd \to π^0 d$ is c…
We analyze elastic-pion nucleon scattering to third order in the so-called small scale expansion. It is based on an effective Lagrangian including pions, nucleons and deltas as active degrees of freedom and counting external momenta, the pion mass and the nucleon-delta mass splitting as small parameters. The fermion fields are considered as very heavy. We present results for phase shifts, threshold parameters and the sigma term. We discuss the convergence of the approach. A detailed comparison with results obtained in heavy baryon chiral perturbation theory to third and fourth order is also gi…
We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is implemented in momentum space and (iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the…
These are the proceedings of the fourth international workshop on "Chiral Dynamics: Theory and Experiment" which was held at the University of Bonn, September 8-13, 2003. The workshop concentrated on the various experimental andtheoretical aspects of chiral dynamics, including for the first time in this series detailed discussions of lattice gauge theory. It consisted of an introductory lecture, plenary talks, working group talks and working group summaries. Included is a short contribution per talk.
A short overview of the current state of Chiral Perturbation Theory is given. This includes a description of the basic assumptions, the usefulness of the external field method is emphasized using a simple lowest order example. Then at next-to-leading order the determination of the parameters is discussed. We also present the status of calculations at ${\cal O}(p^6)$. Finally I present the extension into 3 directions: estimates of the free parameters, inclusion of nonleptonic weak and electromagnetic interactions, and inclusion of non-Goldstone fields in the chiral Lagrangian. Invited Talk at t…
We extend the standard second order effective chiral Lagrangian of pions and nucleons by considering the coupling to an external gravitational field. As an application we calculate one-loop corrections to the one-nucleon matrix element of the energy-momentum tensor to fourth order in chiral counting, and next-to-leading order tree-level amplitude of the pion-production in an external gravitational field. We discuss the relation of the obtained results to experimentally measurable observables. Our expressions for the chiral corrections to the nucleon gravitational form factors differ from those…
We present calculations of differential cross sections for Compton scattering from the proton, using amplitudes calculated to fourth order in heavy baryon chiral perturbation theory. We compare with available data up to 200 MeV. We find that the agreement for angles below 90 degree is acceptable over the whole energy range, but that at more backward angles the agreement decreases above about 100 MeV, and fails completely above the photoproduction threshold.
We present the dominant two- and three-pion-exchange contributions to the nucleon-nucleon interaction at sixth order (next-to-next-to-next-to-next-to-next-to-leading order, N5LO) of chiral perturbation theory. Phase shifts with orbital angular momentum L>=4 are given parameter free at this order and allow for a systematic investigation of the convergence of the chiral expansion. The N5LO contribution is prevailingly repulsive and considerably smaller than the N4LO one, thus, establishing the desired trend towards convergence. Using low-energy constants that were extracted from an analysis of p…
We calculate the threshold $T$ matrices of the light pseudoscalar meson and heavy meson scattering to fourth order in heavy meson chiral perturbation theory. We determine the low-energy constants by fitting to the lattice QCD data points through both the perturbative and iterated methods and obtain the physical scattering lengths in both formalisms. The values of the scattering lengths tend to be convergent at fourth order for most of the channels in the perturbative method. The value of the scattering length for the channel $DK (I=0)$, which involves the bound state $D_{s0}^{*}(2317)$, is obt…
We present a calculation of the $η$-$η'$ mixing in the framework of large-$N_c$ chiral perturbation theory. A general expression for the $η$-$η'$ mixing at next-to-next-to-leading order (NNLO) is derived, including higher-derivative terms up to fourth order in the four momentum, kinetic and mass terms. In addition, the axial-vector decay constants of the $η$-$η'$ system are determined at NNLO. The numerical analysis of the results is performed successively at LO, NLO, and NNLO. We investigate the influence of one-loop corrections, OZI-rule-violating parameters, and $\mathcal{O}(N_c p^6)$ conta…
We investigate the spin-independent part of the virtual Compton scattering (VCS) amplitude off the nucleon within the framework of chiral perturbation theory. We perform a consistent calculation to third order in external momenta according to Weinberg's power counting. With this calculation we can determine the second- and fourth-order structure-dependent coefficients of the general low-energy expansion of the spin-averaged VCS amplitude based on gauge invariance, crossing symmetry and the discrete symmetries. We discuss the kinematical regime to which our calculation can be applied and compar…
We give a brief overview of recent theoretical and experimental results on the chiral magnetic effect and spin polarization effect in heavy-ion collisions. We present updated experimental results for the chiral magnetic effect and related phenomena. The time evolution of the magnetic fields in different models is discussed. The newly developed quantum kinetic theory for massive fermions is reviewed. We present theoretical and experimental results for the polarization of $Λ$ hyperons and the $ρ_{00}$ value of vector mesons.
We analyze the electromagnetic form factors of the nucleon to fourth order in relativistic baryon chiral perturbation theory. We employ the recently proposed infrared regularization scheme and show that the convergence of the chiral expansion is improved as compared to the heavy fermion approach. We also discuss the inclusion of vector mesons and obtain an accurate description of all four nucleon form factors for momentum transfer squared up to Q^2 \simeq 0.4 GeV^2.
We calculate the electromagnetic form factors of the nucleon up to fourth order in manifestly Lorentz-invariant chiral perturbation theory with vector mesons as explicit degrees of freedom. A systematic power counting for the renormalized diagrams is implemented using both the extended on-mass-shell renormalization scheme and the reformulated version of infrared regularization. We analyze the electric and magnetic Sachs form factors, $G_E$ and $G_M$, and compare our results with the existing data. The inclusion of vector mesons results in a considerably improved description of the form factors…
There is an important connection between the low energy theorems of QCD and the energy dependence of the Delta resonance in pi-N scattering, as well as the closely related gamma^{*} N -> pi N reaction. The resonance shape is due not only to the strong pi-N interaction in the p wave but the small interaction in the s wave; the latter is due to spontaneous chiral symmetry breaking in QCD (i.e. the Nambu-Goldstone nature of the pion). A brief overview of experimental tests of chiral perturbation theory and chiral based models is presented
We present an efficient Monte Carlo framework for perturbative calculations of infinite nuclear matter based on chiral two-, three-, and four-nucleon interactions. The method enables the incorporation of all many-body contributions in a straightforward and transparent way, and makes it possible to extract systematic uncertainty estimates by performing order-by-order calculations in the chiral expansion as well as the many-body expansion. The versatility of this new framework is demonstrated by applying it to chiral low-momentum interactions, exhibiting a very good many-body convergence up to f…
We present the two- and three-pion exchange contributions to the nucleon-nucleon interaction which occur at next-to-next-to-next-to-next-to-leading order (N4LO, fifth order) of chiral effective field theory, and calculate nucleon-nucleon scattering in peripheral partial waves with L>=3 using low-energy constants that were extracted from pi-N analysis at fourth order. While the net three-pion exchange contribution is moderate, the two-pion exchanges turn out to be sizeable and prevailingly repulsive, thus, compensating the excessive attraction characteristic for NNLO and N3LO. As a result, the …
The spin structure of the nucleon is analyzed in the framework of a Lorentz-invariant formulation of baryon chiral perturbation theory. The structure functions of doubly virtual Compton scattering are calculated to one-loop accuracy (fourth order in the chiral expansion). We discuss the generalization of the Gerasimov-Drell-Hearn sum rule, the Burkhardt-Cottingham sum rule and moments of these. We give predictions for the forward and the longitudinal-transverse spin polarizabilities of the proton and the neutron at zero and finite photon virtuality. A detailed comparison to results obtained in…
