Abstract:
I discuss the problem of formulating the baryon chiral perturbation theory ($\chi$PT) in the presence of a light resonance, such as the $\Delta(1232)$, the lightest nucleon resonance. It is shown how to extend the power counting of $\chi$PT to correctly account for the resonant contributions. Recent applications of the resulting chiral effective-field theory to the description of pion production reactions in $\Delta$-resonance region are briefly reviewed.

Abstract:
We perform a relativistic chiral effective field theory calculation of the radiative pion photoproduction ($\gamma p \to \pi^0 p \gamma'$) in the $\Delta$-resonance region, to next-to-leading order in the ``delta-expansion''. This work is aimed at a model-independent extraction of the $\Delta^+$ magnetic moment from new precise measurements of this reaction. It also predicts the chiral behavior of $\Delta$'s magnetic moment, which can be used to extrapolate the recent lattice QCD results to the physical point.

Abstract:
Recent chiral EFT calculations of nucleon polarizabilities reveal a problem in the current empirical determination of proton's electromagnetic polarizabilities. We also report on the progress in the empirical determination of the $\Delta$(1232)-resonance magnetic moment in the process of $\gamma p \to p \pi^0 \gamma'$ measured at MAMI.

Abstract:
We present an ongoing project to assess the importance of D-waves and the $\Delta (1232)$ resonance for descriptions of neutral pion photoproduction in Heavy Baryon Chiral Perturbation Theory. This research has been motivated by data published by the A2 and CB-TAPS collaborations at MAMI [1]. This data has reached unprecedented levels of accuracy from threshold through to the $\Delta$ resonance. Accompanying the experimental work, there has also been a series of publications studying the theory that show that, to go beyond an energy of $E_\gamma=170$ MeV, it is necessary to include other aspects, in particular the $\Delta (1232)$ as a degree of freedom [2] and possibly higher partial waves [3].

Abstract:
We study the chiral behavior of the nucleon and $\Delta$-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the $\pi N$ and $\pi\Delta$ one-loop contributions to the mass and field-renormalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the $\pi N$-loop corrections compare favorably with the lattice QCD data for the pion-mass dependence of the nucleon and $\Delta$ masses, while inclusion of the $\pi \Delta$ loops tends to spoil this agreement.

Abstract:
The influence of an initial momentum on the appearance of "quantum resonances" in the delta-kicked rotor system is explored experimentally. We show that for certain initial momenta, a resonance can be negated entirely, whereas at others a resonance can be made to appear. At a larger number of kicks, all resonances are shown to narrow. We show that as a consequence, the individual "diffraction peaks" may split. We compare our results to numerical simulations as well as analytical theory.

Abstract:
We present a theoretical study of the radiative pion photoproduction on the nucleon ($\gamma N \to \pi N \gamma'$) in the $\De$-resonance region, with the aim to determine the magnetic dipole moment (MDM) of the $\Delta^+(1232)$. The study is done within the framework of chiral effective-field theory where the expansion is performed (to next-to-leading order) in the $\delta$ power-counting scheme which is an extension of chiral perturbation theory to the $\Delta$-resonance energy region. We present the results for the absorptive part of the $\Delta$ MDM, as well as perform a sensitivity study of the dependence of $\gamma N \to \pi N \gamma'$ observables on the real part of the $\Delta$ MDM. We find that an asymmetry for circular polarization of the photon beam may provide a model-independent way to measure the $\Delta$ MDM.

Abstract:
We present a theoretical study of the radiative pion photoproduction on the nucleon ($\gamma N \to \pi N \gamma'$) in the $\De$-resonance region, with the aim to determine the magnetic dipole moment (MDM) of the $\Delta^+(1232)$. The study is done within the framework of chiral effective-field theory where the expansion is performed (to next-to-leading order) in the $\delta$ power-counting scheme which is an extension of chiral perturbation theory to the $\Delta$-resonance energy region. We present the results for the absorptive part of the $\Delta$ MDM, as well as perform a sensitivity study of the dependence of $\gamma N \to \pi N \gamma'$ observables on the real part of the $\Delta$ MDM. We find that an asymmetry for circular polarization of the photon beam may provide a model-independent way to measure the $\Delta$ MDM.

Abstract:
We perform a relativistic chiral effective-field theory calculation of the pion electroproduction off the nucleon ($e^- N \to e^- N \pi$) in the Delta(1232)-resonance region. After fixing the three low-energy constants, corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) $\gamma N\Delta $ couplings, our calculation provides a prediction for the momentum-transfer and pion-mass dependence of the $\gamma N\Delta $ form factors. The prediction for the pion-mass dependence resolves the discrepancy between the recent lattice QCD results and the experimental value for the "C2/M1 ratio" at low $Q^2$.

Abstract:
Chiral corrections to the delta axial charge are determined using heavy baryon chiral perturbation theory. Knowledge of this axial coupling is necessary to assess virtual-delta contributions to nucleon and delta observables. We give isospin relations useful for a lattice determination of the axial coupling. Furthermore we detail partially quenched chiral corrections, which are relevant to address partial quenching and/or mixed action errors in lattice calculations of the delta axial charge.