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The long-range terms of the subleading chiral three-nucleon force [published in Phys.\,Rev.\,C77, 064004 (2008)] are specified to the case of three neutrons. From these $3n$-interactions an effective density-dependent neutron-neutron potential $V_\text{med}$ in pure neutron matter is derived. Following the division of the pertinent 3n-diagrams into two-pion exchange, two-pion-one-pion exchange and ring topology, all self-closings and concatenations of two neutron-lines to an in-medium loop are evaluated. The momentum and $k_n$-dependent potentials associated with the spin-operators $1,\, \vec\sigma_1\!\cdot\!\vec\sigma_2,\, \vec\sigma_1\!\cdot\!\vec q\, \vec\sigma_2\!\cdot\!\vec q,\, i( \vec\sigma_1\!+\!\vec\sigma_2)\!\cdot \! (\vec q\!\times \! \vec p\,),\, (\vec\sigma_1\!\cdot\!\vec p\,\vec\sigma_2\!\cdot\!\vec p+\vec\sigma_1\!\cdot\!\vec p\,'\, \vec\sigma_2\!\cdot\!\vec p\,')$ and $ \vec\sigma_1\!\cdot \! (\vec q\!\times \! \vec p\,)\vec\sigma_2\!\cdot \! (\vec q\!\times \! \vec p\,)$ are expressed in terms of functions, which are either given in closed analytical form or require at most one numerical integration. The subsubleading chiral 3N-force is treated in the same way. The obtained results for $V_\text{med}$ are helpful to implement the long-range chiral three-body forces into advanced neutron matter calculations., Comment: 14 pages, 1 figure, section 7 updated. arXiv admin note: text overlap with arXiv:1903.03183

From the subsubleading chiral three-nucleon force [intermediate-range contributions, published in Phys. Rev. C\,87, 054007 (2013)] a density-dependent NN-interaction $V_\text{med}$ is derived in isospin-symmetric nuclear matter. Following the division of the pertinent 3N-diagrams into two-pion-one-pion exchange topology and ring topology, one evaluates for these all selfclosings and concatenations of nucleon-lines to an in-medium loop. In the case of the $2\pi 1\pi$-exchange topology, the momentum- and $k_f$-dependent potentials associated with the isospin-operators ($1$ and $\vec\tau_1 \!\cdot\! \vec\tau_2$) and five independent spin-structures require at most one numerical integration. For the more challenging (concatenations of the) ring diagrams proportional to $c_{1,2,3,4}$, one ends up with regularized double-integrals $\int_0^\lambda dr\,r \int_0^{\pi/2} d\psi$ from which the $\lambda^2$-divergence has been subtracted and the logarithmic piece $\sim \ln (m_\pi/\lambda)$ is isolated. The derived semi-analytical results are most helpful to implement the subsubleading chiral 3N-forces into nuclear many-body calculations., Comment: 17 pages, 1 figure, to be published in Phys. Rev. C

We derive from the subleading contributions to the chiral three-nucleon force (long-range terms, published in Phys.\,Rev.\,C\,77, 064004 (2008)) a density-dependent two-nucleon interaction $V_\text{med}$ in isospin-symmetric, spin-saturated nuclear matter. Following the division of the pertinent 3N-diagrams into two-pion exchange topology, two-pion-one-pion exchange topology and ring topology, we evaluate for these all self-closings and concatenations of nucleon-lines to an in-medium loop. The momentum and $k_f$-dependent potentials associated with the isospin operators ($1$ and $\vec\tau_1\!\cdot\!\vec\tau_2$) and five independent spin-structures are expressed in terms of functions, which are either given in closed analytical form or require at most one numerical integration. In the same way we treat the $2\pi$-exchange 3N-force up to fourth order. Our results for $V_\text{med}$ are most helpful to implement the long-range subleading chiral 3N-forces into nuclear many-body calculations., Comment: 19 pages, 1 figure, 1 table, typo in eq.(82) corrected

We derive from the subleading contributions to the chiral three-nucleon force (short-range terms and relativistic corrections, published in Phys. Rev. C84, 054001 (2011)) a density-dependent two-nucleon interaction $V_\text{med}$ in isospin-symmetric nuclear matter. The momentum and $k_f$-dependent potentials associated with the isospin operators ($1$ and $ \vec\tau_1\!\cdot\!\vec\tau_2$) and five independent spin-structures are expressed in terms of loop functions, which are either given in closed analytical form or require at most one numerical integration. Our results for $V_\text{med}$ are most helpful to implement subleading chiral 3N-forces into nuclear many-body calculations., Comment: 16 pages, 5 figures

The nucleon-nucleon interaction arising from the exchange of three pions and the excitation of $��(1232)$-isobars in intermediate states is studied. Approximating the $��$-propagator by the inverse $��$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., 12 pages, 9 figures

An improved density-matrix expansion is used to calculate the nuclear energy density functional from chiral two- and three-nucleon interactions. The two-body interaction comprises long-range one- and two-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition we employ the leading order chiral three-nucleon interaction with its parameters $c_E, c_D$ and $c_{1,3,4}$ fixed in calculations of nuclear few-body systems. With this input the nuclear energy density functional is derived to first order in the two- and three-nucleon interaction. We find that the strength functions $F_\nabla(\rho)$ and $F_{so}(\rho)$ of the surface and spin-orbit terms compare in the relevant density range reasonably with results of phenomenological Skyrme forces. However, an improved description requires (at least) the treatment of the two-body interaction to second order. This observation is in line with the deficiencies in the nuclear matter equation of state $\bar E(\rho)$ that remain in the Hartree-Fock approximation with low-momentum two- and three-nucleon interactions., Comment: 16 pages, 12 figures, submitted to Eur. Phys. J. A

The temperature dependence of the chiral condensate in isospin-symmetric nuclear matter at varying baryon densities is investigated starting from a realistic free energy density of the correlated nuclear many-body system. The framework is thermal in-medium chiral effective field theory which permits a systematic calculation of the quark mass dependence of the free energy density. One- and two-pion exchange processes, virtual $\Delta(1232)$-isobar excitations and Pauli blocking corrections are treated up to and including three-loop order. It is found that nuclear matter remains in the Nambu-Goldstone phase with spontaneously broken chiral symmetry at least in the range of temperatures $T\lesssim 100\,$MeV and baryon densities up to about twice the density of normal nuclear matter., Comment: 4 pages, 3 figures, submitted to Physical Review Letters

We calculate in chiral perturbation theory the double-pion photoproduction processes $\pi^-\gamma \to \pi^- \pi^0\pi^0$ and $\pi^-\gamma\to \pi^+\pi^-\pi^-$ at low energies. At leading order these reactions are governed by the chiral pion-pion interaction. The next-to-leading order corrections arise from pion-loop diagrams and chiral-invariant counterterms involving the low-energy constants $\bar\ell_1,\, \bar\ell_2,\, \bar\ell_3$ and $\bar\ell_4$. The pertinent production amplitudes $A_1$ and $A_2$ depending on five kinematical variables are given in closed analytical form. We find that the total cross section for neutral pion-pair production $\pi^-\gamma \to\pi^-\pi^0\pi^0$ gets enhanced in the region $\sqrt{s}< 7m_\pi$ by a factor $1.5 - 1.8$ by the next-to-leading order corrections. In contrast to this behavior the total cross section for charged pion-pair production $\pi^-\gamma\to \pi^+ \pi^-\pi^-$ remains almost unchanged in the region $\sqrt{s}< 6m_\pi$ in comparison to its tree-level result. Although the dynamics of the pion-pair production reactions is much richer, this observed pattern can be understood from the different influence of the chiral corrections on the pion-pion final state interaction ($\pi^+\pi^- \to \pi^0\pi^0$ versus $\pi^-\pi^- \to \pi^-\pi^-$). We present also results for the complete set of two-pion invariant mass spectra. The predictions of chiral perturbation theory for the $\pi^-\gamma\to 3\pi$ processes can be tested by the COMPASS experiment which uses Primakoff scattering of high-energy pions in the Coulomb field of a heavy nucleus to extract cross sections for $\pi^-\gamma$ reactions with various final states., Comment: 19 pages, 14 figures, submitted to Nuclear Physics A

We calculate in chiral perturbation theory the double-pion photoproduction processes $��^-��\to ��^- ��^0��^0$ and $��^-��\to ��^+��^-��^-$ at low energies. At leading order these reactions are governed by the chiral pion-pion interaction. The next-to-leading order corrections arise from pion-loop diagrams and chiral-invariant counterterms involving the low-energy constants $\bar\ell_1,\, \bar\ell_2,\, \bar\ell_3$ and $\bar\ell_4$. The pertinent production amplitudes $A_1$ and $A_2$ depending on five kinematical variables are given in closed analytical form. We find that the total cross section for neutral pion-pair production $��^-��\to��^-��^0��^0$ gets enhanced in the region $\sqrt{s}< 7m_��$ by a factor $1.5 - 1.8$ by the next-to-leading order corrections. In contrast to this behavior the total cross section for charged pion-pair production $��^-��\to ��^+ ��^-��^-$ remains almost unchanged in the region $\sqrt{s}< 6m_��$ in comparison to its tree-level result. Although the dynamics of the pion-pair production reactions is much richer, this observed pattern can be understood from the different influence of the chiral corrections on the pion-pion final state interaction ($��^+��^- \to ��^0��^0$ versus $��^-��^- \to ��^-��^-$). We present also results for the complete set of two-pion invariant mass spectra. The predictions of chiral perturbation theory for the $��^-��\to 3��$ processes can be tested by the COMPASS experiment which uses Primakoff scattering of high-energy pions in the Coulomb field of a heavy nucleus to extract cross sections for $��^-��$ reactions with various final states., 19 pages, 14 figures, submitted to Nuclear Physics A

We present a shell model calculation for the beta decay of 14-C to the 14-N ground-state, treating the relevant nuclear states as two 0p-holes in an 16-O core. Employing the universal low-momentum nucleon-nucleon potential V(low-k) only, one finds that the Gamow-Teller matrix element is too large to describe the known (very long) lifetime of 14-C. As a novel approach to the problem, we invoke the chiral three-nucleon force (3NF) at leading order and derive from it a density-dependent in-medium NN interaction. Including this effective in-medium NN interaction, the Gamow-Teller matrix element vanishes for a nuclear density close to that of saturated nuclear matter. The genuine short-range part of the three-nucleon interaction plays a particularly important role in this context, since the medium modifications to the pion propagator and pion-nucleon vertex (due to the long-range 3NF) tend to cancel out in the relevant observable. We discuss also uncertainties related to the off-shell extrapolation of the in-medium NN interaction. Using the off-shell behavior of V(low-k) as a guide, we find that these uncertainties are rather small., 22 pages, 11 figures

A previously derived relativistic energy density functional for nuclei, based on low-energy in-medium chiral dynamics, is generalized to implement constraints from chiral SU(3) effective field theory and applied to $\Lambda$ hypernuclei. Density-dependent central and spin-orbit mean fields are calculated for a $\Lambda$ hyperon using the SU(3) extension of in-medium chiral perturbation theory to two-loop order. Long range $\Lambda N$ interactions arise from kaon-exchange and from two-pion-exchange with a $\Sigma$ hyperon in the intermediate state. Short-distance dynamics is encoded in contact interactions. They include scalar and vector mean fields reflecting in-medium changes of quark condensates, constrained by QCD sum rules. The $\Lambda$ single particle orbitals are computed for a series of hypernuclei from $^{13}_{\Lambda}$C to $^{208}_{\Lambda}$Pb. The role of a surface (derivative) term is studied. Its strength is found to be compatible with a corresponding estimate from in-medium chiral perturbation theory. Very good agreement with hypernuclear spectroscopic data is achieved. The smallness of the $\Lambda$-nuclear spin-orbit interaction finds a natural explanation in terms of an almost complete cancellation between short-range scalar/vector contributions and longer range terms generated by two-pion exchange., Comment: 30 pages, 5 figures, elsart class, minor corrections, to be published in Nuclear Physics A

A previously introduced relativistic energy density functional, successfully applied to ordinary nuclei, is extended to hypernuclei. The density-dependent mean field and the spin-orbit potential are consistently calculated for a $\Lambda$ hyperon in the nucleus using the SU(3) extension of in-medium chiral perturbation theory. The leading long range $\Lambda N$ interaction arises from kaon-exchange and $2\pi$-exchange with $\Sigma$ hyperon in the intermediate state. Scalar and vector mean fields reflecting in-medium changes of the quark condensates are constrained by QCD sum rules. The model, applied to oxygen as a test case, describes spectroscopic data in good agreement with experiment. In particular, the smallness of the $\Lambda$ spin-orbit interaction finds a natural explanation in terms of an almost complete cancellation between scalar-vector background contributions and long-range terms generated by two-pion exchange., Comment: 10 pages, 2 figures, elsart class. Minor revisions

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the two-pion exchange nucleon-nucleon interaction that is generated by the isovector spin-flip $����NN$ contact-vertex proportional to the large low-energy constant $c_4\simeq 3.4 $GeV$^{-1}$. We find that the respective $2����$-exchange potentials contain sizeable isospin-breaking components which reach up to -4% of corresponding isovector $2��$-exchange potentials. The typical values of these novel charge-independence breaking spin-spin and tensor potentials are $-0.11 $MeV and $0.09 $MeV, at a nucleon distance of $r=m_��^{-1}=1.4 $fm. The charge-symmetry breaking spin-spin and tensor potentials come out a factor of 2.4 smaller. Our analytical results for these presumably dominant isospin-violating spin-spin and tensor NN-forces are in a form such that they can be easily implemented into phase-shift analyses and few-body calculations., 7 pages, 1 figure, 2 tables, to be published in Physical Review C: Brief reports

We present a novel approach to the density dependent mean field and the spin-orbit interaction of a $\Lambda$-hyperon in a nuclear many-body system, based on flavor-SU(3) in-medium chiral perturbation theory. The leading long-range $\Lambda N$-interaction arises from kaon exchange and from two-pion exchange with a $\Sigma$-hyperon in the intermediate state. The empirical $\Lambda$-nucleus potential depth of about $-28 $MeV is well reproduced with a single cutoff scale, $\bar \Lambda = 0.7 $GeV, effectively representing all short-distance (high-momentum) dynamics not resolved at scales characteristic of the nuclear Fermi momentum. This value of $\bar\Lambda$ is remarkably consistent with the one required to reproduce the empirical saturation point of isospin-symmetric nuclear matter in the same framework. The smallness of the $\Lambda$-nuclear spin-orbit interaction finds a natural (yet novel) explanation in terms of an almost complete cancellation between short-range contributions (properly rescaled from the known nucleonic spin-orbit coupling strength) and long-range terms generated by iterated one-pion exchange with intermediate $\Sigma$-hyperons. The small $\Sigma\Lambda$-mass difference figures prominently in this context., Comment: 9 pages, 4figures

The role of chiral (pion) dynamics in nuclear matter is reviewed. Contributions to the energy per particle from one- and two-pion exchange are calculated systematically, and it is demonstrated that already at order $k^4_f$ in the Fermi momentum, two-pion exchange produces realistic nuclear binding together with very reasonable values for the compressibility and the asymmetry energy. Further implications of these results are discussed., Invited talk presented by W. Weise at the NATO Advanced Research Workshop: The Nuclear Many-Body Problem 2001, 2.-5.6., Brijuni, Croatia

We show that a recent claim (H.Haberzettl, Phys. Rev. Lett. 85 (2000) 3576) that one cannot extract the nucleon weak axial form factor G_A (t) from charged pion threshold electroproduction is incorrect. Thus previous calculations remain valid and threshold charged pion electroproduction experiments can indeed be used to determine G_A (t), and they should certainly be pursued., 2 pp, somewhat more detailed than the comment by P. Guichon, hep-ph/0012126

Present precision measurements of the neutron life time lead to a CKM matrix element $|V_{ud}|$ which is three standard deviations off the value inferred from heavy quark decays etc. We investigate the possibility whether isospin-breaking effects in the neutron-to-proton vector current transition matrix element $< p|V^+_0|n >=1+��g_V$ could eventually close this gap. For that we calculate in chiral perturbation theory the effect of pion and kaon loops on the matrix element $< p|V^+_0|n >$ taking into account the mass differences of the charged and neutral mesons. We find a negligibly small isospin-breaking effect of $��g_V \simeq -4 \cdot 10^{-5}$. The crucial quantity in the analysis of neutron beta-decay precision measurements is thus the radiative correction term $��_R$. Furthermore, we calculate in heavy baryon chiral perturbation theory the SU(3) breaking effects on the vector transition charges of weak semi-leptonic hyperon decays. We find for these quantities channel-dependent relative deviations from the SU(3) limit which range from -10% to $+1%$., 6 pages, 1 figure, to be published in Physical Review C (brief report)

Threshold neutral pion electroproduction on the deuteron is studied in the framework of baryon chiral perturbation theory at next-to-leading order in the chiral expansion. To this order in small momenta, the amplitude is finite and a sum of two- and three-body interactions with no undetermined parameters. We calculate the S-wave multipoles for threshold production and the deuteron S-wave cross section as a function of the photon virtuality. We also discuss the sensitivity to the elementary neutron amplitudes.

We analyze the total cross section data for $pp \to pp\omega$ near threshold measured recently at SATURNE. Using an effective range approximation for the on-shell $pp$ S-wave final state interaction we extract from these data the modulus $|\Omega| = 0.53$ fm$^4$ of the threshold transition amplitude $\Omega$. We present a calculation of various (tree-level) meson exchange diagrams contributing to $\Omega$. It is essential that $\omega$-emission from the anomalous $\omega\rho\pi$-vertex interferes destructively with $\omega$-emission from the proton lines. The contribution of scalar $\sigma$-meson exchange to $\Omega$ turns out to be negligibly small. Without introducing off-shell meson-nucleon form factors the experimental value $|\Omega|=0.53$ fm$^4$ can be reproduced with an $\omega N$-coupling constant of $g_{\omega N}=10.7$. The results of the present approach agree qualitatively with the J\"ulich model. We also perform a combined analysis of the reactions $pp\to pp\pi^0, pn\pi^+, pp\eta, pp\omega$ and $pn\to pn\eta$ near threshold., Comment: Latex-file 6 pages, 2 Figures

Single pion production off nucleons is studied in the framework of relativistic baryon chiral perturbation theory at tree level with the inclusion of the terms from the dimension two effective pion-nucleon Lagrangian. The five appearing low-energy constants are fixed from pion-nucleon scattering data. Despite the simplicity of the approach, most of the existing data for total and differential cross sections as well as for the angular correlation functions for incoming pion kinetic energies up to 400 MeV can be satisfactorily described., Comment: 29 pp, plain LaTeX, uses epsf, 15 figures

Single pion production off nucleons is studied in the framework of relativistic baryon chiral perturbation theory at tree level with the inclusion of the terms from the dimension two effective pion-nucleon Lagrangian. The five appearing low-energy constants are fixed from pion-nucleon scattering data. Despite the simplicity of the approach, most of the existing data for total and differential cross sections as well as for the angular correlation functions for incoming pion kinetic energies up to 400 MeV can be satisfactorily described., 29 pp, plain LaTeX, uses epsf, 15 figures

We calculate the one--loop contributions of order $M_��^4$ to the difference $��_R$ between the on--shell pion--nucleon scattering amplitude $\bar{D}^+(0,2M_��^2)$ at the Cheng--Dashen point $��=0$, $t=2M_��^2$ and the scalar form factor $��(2M_��^2)$ in the framework of heavy baryon chiral perturbation theory. We proof that to this order $��_R$ contains $no$ chiral logarithms and therefore it vanishes simply as $M_��^4$ in the chiral limit. Numerically, we find as an upper limit $��_R \simeq 2\,$MeV., 7 pp, LaTeX, uses epsf, 1 figure in separate PS file

We investigate neutral pion electroproduction off protons in the framework of heavy baryon chiral perturbation theory. The chiral expansion of the S--wave multipoles $E_{0+}$ and $L_{0+}$ is carried out to three orders. There appear several undetermined low--energy constants. Three are taken from a recent study of the new TAPS threshold $\pi^0$ photoproduction data, one is fixed from the proton Dirac form factor and the novel S--wave constants appearing at orders $q^4$ and $q^5$ are determined from a best fit (constrained by resonance exchange) to the recent NIKHEF and MAMI data at photon momentum transfer squared $k^2 = -0.1 \, \, {\rm GeV}^2$. The inclusion of a particular set of dimension five operators is forced upon the fit by a soft--pion theorem which severely constrains the momentum dependence of the longitudinal S--wave multipole $L_{0+}$ at order $q^4$. We give predictions for lower photon virtualities for the various multipoles and differential cross sections. Further improvements are briefly touched upon., Comment: 25 pp, LaTeX, uses epsf and elsart12.sty, 8 figures in 10 PS files

We analyze the new threshold data for neutral pion photoproduction off protons in the framework of heavy baryon chiral perturbation theory. We show that large loop corrections are needed to understand the S--wave multipole $E_{0+}$ and that all pertinent low--energy constants can be understood within the framework of resonance exchange saturation. Previous inconsistencies in the description of this reaction in the threshold region are resolved., Comment: 8 pp, LaTeX/ReVTeX file, 3 figures (in a separate compressed tar files in pi0fig.uu)

We evaluate the S-wave pion--nucleon scattering length $a^-$ in the framework of heavy baryon chiral perturbation theory up--to--and--including terms of order $M_\pi^4$. We show that the order $M_\pi^4$ piece of the isovector amplitude at threshold, $T^-_{\rm thr}$, vanishes exactly. We predict for the isovector scattering length, $0.088 \, M_{\pi^+}^{-1} \le a^- \le 0.096 \, M_{\pi^+}^{-1}$., Comment: 5 pp, LaTeX file, 2 figures (appended as separate compressed tar file, amin.uu)

We evaluate the S-wave pion--nucleon scattering length $a^-$ in the framework of heavy baryon chiral perturbation theory up--to--and--including terms of order $M_��^4$. We show that the order $M_��^4$ piece of the isovector amplitude at threshold, $T^-_{\rm thr}$, vanishes exactly. We predict for the isovector scattering length, $0.088 \, M_{��^+}^{-1} \le a^- \le 0.096 \, M_{��^+}^{-1}$., 5 pp, LaTeX file, 2 figures (appended as separate compressed tar file, amin.uu)

We analyze the new threshold data for neutral pion photoproduction off protons in the framework of heavy baryon chiral perturbation theory. We show that large loop corrections are needed to understand the S--wave multipole $E_{0+}$ and that all pertinent low--energy constants can be understood within the framework of resonance exchange saturation. Previous inconsistencies in the description of this reaction in the threshold region are resolved., 8 pp, LaTeX/ReVTeX file, 3 figures (in a separate compressed tar files in pi0fig.uu)

The effective field theory for collective rotations of triaxially deformed nuclei is generalized to odd-mass nuclei by including the angular momentum of the valence nucleon as an additional degree of freedom. The Hamiltonian is constructed up to next-to-leading order within the effective field theory formalism. The applicability of this Hamiltonian is examined by describing the wobbling bands observed in the lutetium isotopes $^{161,163,165,167}$Lu. It is found that by taking into account the next-to-leading order corrections, quartic in the rotor angular momentum, the wobbling energies $E_{\textrm{wob}}$ and spin-rotational frequency relations $\omega(I)$ are better described than with the leading order Hamiltonian., Comment: 19 pages, 6 figures