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The Delta(1232) Resonance in Chiral Effective Field Theory  [PDF]
Vladimir Pascalutsa
Physics , 2007, DOI: 10.1016/j.ppnp.2007.12.023
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.
Magnetic moment of the Delta(1232)-resonance in chiral effective field theory  [PDF]
Vladimir Pascalutsa,Marc Vanderhaeghen
Physics , 2004, DOI: 10.1103/PhysRevLett.94.102003
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.
Nucleon polarizabilities and Delta-resonance magnetic moment in chiral EFT  [PDF]
Vladimir Pascalutsa
Physics , 2010, DOI: 10.1063/1.3647162
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.
Impact of the Delta (1232) resonance on neutral pion photoproduction in chiral perturbation theory  [PDF]
Lloyd W. Cawthorne,Judith A. McGovern
Physics , 2015,
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].
The nucleon and Delta-resonance masses in relativistic chiral effective-field theory  [PDF]
Vladimir Pascalutsa,Marc Vanderhaeghen
Physics , 2005, DOI: 10.1016/j.physletb.2006.03.023
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.
The initial momentum dependence of the quantum resonance in the delta-kicked rotor  [PDF]
J-A. Currivan,A. Ullah,M. D. Hoogerland
Physics , 2008, DOI: 10.1209/0295-5075/85/30005
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.
Chiral effective-field theory in the Delta(1232) region: II. radiative pion photoproduction
Pascalutsa, Vladimir;Vanderhaeghen, Marc
High Energy Physics - Phenomenology , 2007, DOI: 10.1103/PhysRevD.77.014027
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.
Chiral effective-field theory in the Delta(1232) region: II. radiative pion photoproduction  [PDF]
Vladimir Pascalutsa,Marc Vanderhaeghen
Physics , 2007, DOI: 10.1103/PhysRevD.77.014027
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.
Electromagnetic Nucleon-to-Delta Transition in Chiral Effective-Field Theory  [PDF]
Vladimir Pascalutsa,Marc Vanderhaeghen
Physics , 2005, DOI: 10.1103/PhysRevLett.95.232001
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 $Q^2$.
Chiral Corrections and the Axial Charge of the Delta  [PDF]
Fu-Jiun Jiang,Brian C. Tiburzi
Physics , 2008, DOI: 10.1103/PhysRevD.78.017504
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.
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