Systematic 1/M expansion for spin 3/2 particles in baryon chiral perturbation theory

Starting from a relativistic formulation of the pion-nucleon-delta system, the most general structure of 1/M corrections for a heavy baryon chiral lagrangian including spin 3/2 resonances is given. The heavy components of relativistic nucleons and delta fields are integrated out and their contributions to the next-to-leaing order lagrangians are constructed explicitly. The effective theory obtained admits a systematic expansion in terms of soft momenta, the pion mass $m_\pi$ and the delta-nucleon mass difference $\Delta$. As an application, we consider neutral pion photoproduction at threshold to third order in this small scale expansion

The nucleon mass in N_f=2 lattice QCD: finite size effects from chiral perturbation theory

In the framework of relativistic SU(2)_f baryon chiral perturbation theory we calculate the volume dependence of the nucleon mass up to and including O(p^4). Since the parameters in the resulting finite size formulae are fixed from the pion mass dependence of the large volume nucleon masses and from phenomenology, we obtain a parameter-free prediction of the finite size effects. We present mass data from the recent N_f=2 simulations of the UKQCD and QCDSF collaborations and compare these data as well as published mass values from the dynamical simulations of the CP-PACS and JLQCD collaborations with the theoretical expectations. Remarkable agreement between the lattice data and the predictions of chiral perturbation theory in a finite volume is found.Comment: 23 pages, 5 figures; references added + minor corrections; one more reference added, typo in eq.(25) corrected, additional clarifying remark

Axial and tensor charge of the nucleon with dynamical fermions

We present preliminary results for the axial and tensor charge of the nucleon obtained from simulations with N_f=2 clover fermions. A comparison with chiral perturbation theory is attempted.Comment: Talk presented at Lattice2004(weak), Fermilab, June 21-26, 2004, 3 pages, 3 figures, v2: one reference added, v3: acknowledgement extende

The axial charge of the nucleon on the lattice and in chiral perturbation theory

We present recent Monte Carlo data for the axial charge of the nucleon obtained by the QCDSF-UKQCD collaboration for N_f=2 dynamical quarks. We compare them with formulae from chiral perturbation theory in finite and infinite volume and find a remarkably consistent picture.Comment: 6 pages, 3 figures, talk presented at Lattice2005 (weak matrix elements), needs PoS.cl

Delta(1232) and the polarizabilities of the nucleon

Previous calculations of the polarizabilities of the nucleon within the framework of heavy baryon chiral perturbation theory have included the contribution of the Δ(1232) only in its effects on various contact terms or have been performed in chiral SU(3) where systematic errors are difficult to control. Herein, we perform a corresponding calculation in chiral SU(2) wherein Δ(1232) is treated as an explicit degree of freedom and the expansion is taken to third order in soft momenta, the pion mass, and the quantity MΔ-MN, collectively denoted ε. We present the results of a systematic O(ε3) calculation of forward Compton scattering off the nucleon, extract the electric polarizability α̅ E, the magnetic polarizability β̅ M, and the spin polarizability γ, and compare with available information from experiments and from previous calculations. Concluding with a critical discussion of our results, we point out the necessity of a future O(ε4) calculation

NN, N-DELTA COUPLINGS AND THE QUARK-MODEL

We examine mass-corrected SU(6) symmetry predictions in the quark model relating vector, axial-vector, and strong NN and NΔ couplings, and demonstrate that the experimental NΔ value is significantly higher than predicted in each case. Nevertheless the Goldberger-Treiman relation is satisfied in both sectors. Possible origins of the discrepancy of the quark model predictions with experiments are discussed

Delta(1232) and the polarizabilities of the nucleon

Previous calculations of the polarizabilities of the nucleon within the framework of heavy baryon chiral perturbation theory have included the contribution of the Δ(1232) only in its effects on various contact terms or have been performed in chiral SU(3) where systematic errors are difficult to control. Herein, we perform a corresponding calculation in chiral SU(2) wherein Δ(1232) is treated as an explicit degree of freedom and the expansion is taken to third order in soft momenta, the pion mass, and the quantity MΔ-MN, collectively denoted ε. We present the results of a systematic O(ε3) calculation of forward Compton scattering off the nucleon, extract the electric polarizability α̅ E, the magnetic polarizability β̅ M, and the spin polarizability γ, and compare with available information from experiments and from previous calculations. Concluding with a critical discussion of our results, we point out the necessity of a future O(ε4) calculation

Systematic 1/M expansion for spin 3/2 particles in baryon chiral perturbation theory

Starting from a relativistic formulation of the pion-nucleon-delta system, the most general structure of 1/M corrections for a heavy baryon chiral lagrangian including spin 3/2 resonances is given. The heavy components of relativistic nucleons and delta fields are integrated out and their contributions to the next-to-leaing order lagrangians are constructed explicitly. The effective theory obtained admits a systematic expansion in terms of soft momenta, the pion mass $m_\pi$ and the delta-nucleon mass difference $\Delta$. As an application, we consider neutral pion photoproduction at threshold to third order in this small scale expansion

Heavy baryon chiral perturbation theory with light deltas

We demonstrate how heavy mass methods, previously applied to chiral perturbation theory calculations involving the interactions of nucleons and pions, can be generalized to include interactions with the (1232) in a systematic formalism which we call the `small-scale expansion\u27