The reaction pi N -> pi pi N in chiral effective field theory with explicit Delta(1232) degrees of freedom

The reaction pi N -> pi pi N is studied at tree level up to next-to-leading order in the framework of manifestly covariant baryon chiral perturbation theory with explicit Delta(1232) degrees of freedom. Using total cross section data to determine the relevant low-energy constants, predictions are made for various differential as well as total cross sections at higher energies. A detailed comparison of results based on the heavy-baryon and relativistic formulations of chiral perturbation theory with and without explicit Delta degrees of freedom is given.Comment: 30 pages, 13 figure

Complex-mass renormalization in hadronic EFT: applicability at two-loop order

We discuss the application of the complex-mass scheme to multi-loop diagrams in hadronic effective field theory by considering as an example a two-loop self-energy diagram. We show that the renormalized two-loop diagram satisfies the power counting.Comment: 8 pages, 2 figures, version accepted for publication in EPJ

Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look

Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant $\beta$-functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide a clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the $\Delta$-resonance. The explicit inclusion of the leading contributions of the $\Delta$-isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the ones from the recent Roy-Steiner-equation analysis of pion-nucleon scattering

Reconciling threshold and subthreshold expansions for pion-nucleon scattering

Heavy-baryon chiral perturbation theory (ChPT) at one loop fails in relating the pion-nucleon amplitude in the physical region and for subthreshold kinematics due to loop effects enhanced by large low-energy constants. Studying the chiral convergence of threshold and subthreshold parameters up to fourth order in the small-scale expansion, we address the question to what extent this tension can be mitigated by including the $\Delta(1232)$ as an explicit degree of freedom and/or using a covariant formulation of baryon ChPT. We find that the inclusion of the $\Delta$ indeed reduces the low-energy constants to more natural values and thereby improves consistency between threshold and subthreshold kinematics. In addition, even in the $\Delta$-less theory the resummation of $1/m_N$ corrections in the covariant scheme improves the results markedly over the heavy-baryon formulation, in line with previous observations in the single-baryon sector of ChPT that so far have evaded a profound theoretical explanation.Comment: 10 pages, 4 tables, Mathematica notebook with the analytic expressions for threshold and subthreshold parameters included as supplementary material; journal versio

Spin Glass and ferromagnetism in disordered Cerium compounds

The competition between spin glass, ferromagnetism and Kondo effect is analysed here in a Kondo lattice model with an inter-site random coupling $J_{ij}$ between the localized magnetic moments given by a generalization of the Mattis model which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with Grassmann fields have been used to obtain the partition function. The static approximation and the replica symmetric ansatz have also been used. The solution of the problem is presented as a phase diagram giving $T/{J}$ {\it versus} $J_K/J$ where $T$ is the temperature, $J_{K}$ and ${J}$ are the strengths of the intrasite Kondo and the intersite random couplings, respectively. If $J_K/{J}$ is small, when temperature is decreased, there is a second order transition from a paramagnetic to a spin glass phase. For lower $T/{J}$, a first order transition appears between the spin glass phase and a region where there are Mattis states which are thermodynamically equivalent to the ferromagnetism. For very low ${T/{J}}$, the Mattis states become stable. On the other hand, it is found as solution a Kondo state for large $J_{K}/{J}$ values. These results can improve the theoretical description of the well known experimental phase diagram of $CeNi_{1-x}Cu_{x}$.Comment: 17 pages, 5 figures, accepted Phys. Rev.

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the $S$- and $P$-partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the $D$ and $F$ waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.Comment: 41 pages, 12 figures, 7 table