Magnetic dipole moment of the Δ(1232) in chiral perturbation theory

Abstract

The magnetic dipole moment of the ∆(1232) is calculated in the framework of manifestly Lorentzinvariant baryon chiral perturbation theory in combination with the extended on-mass-shell renormalization scheme. As in the case of the nucleon, at leading order both isoscalar and isovector anomalous magnetic moments are given in terms of two low-energy constants. In contrast to the nucleon case, at next-to-leading order the isoscalar anomalous magnetic moment receives a (real) loop contribution. Moreover, due to the unstable nature of the ∆(1232), at next-to-leading order the isovector anomalous magnetic moment not only receives a real but also an imaginary loop contribution.

Chiral effective-field theory in theΔ(1232)region. II. Radiative pion photoproduction

“…We note here that numerically our results are different from an analogous EFT calculation of Hacker et al [27]. Their result for the isoscalar and isovector absorptive magnetic moments is given by [27]: ∆ performed in [27], which are justified from the point of view of the power-counting used in that work. Besides those expansions, the numerical value of Im µ…”

“…∆ is further reduced in [27] due to a smaller value of the πN∆-coupling. The value h 2 A ≃ 8.12 used in our calculations (corresponding with Γ ∆ = 0.115 GeV), must be compared with the coupling (2g) 2 ≃ 5.08 used in Ref.…”

“…The value h 2 A ≃ 8.12 used in our calculations (corresponding with Γ ∆ = 0.115 GeV), must be compared with the coupling (2g) 2 ≃ 5.08 used in Ref. [27].…”

Hadron structure from lattice quantum chromodynamics

“…On the basis of the δ-expansion scheme detailed in [PP03], the m π -dependence of the magnetic moment of the ∆-baryon has been calculated in a covariant way to NLO [PV05]. A study of the magnetic moment of the ∆-baryon using the extended on-mass-shell renormalization scheme in relativistic BChPT has been presented in [HWGS06].…”

Magnetic dipole, electric quadrupole and magnetic octupole moments of the Δ baryons in light cone QCD sum rules

“…The radiative pion production on the nucleon (γN → πNγ ′ ) with the aim of the determination of the magnetic dipole moment of the ∆ + (1232) has been studied in the frame work of Chiral effective-field theory in [4]. The magnetic dipole moment for ∆ baryons is calculated in the framework of the static quark model (SQM) [5], relativistic quark models (RQM) [6], QCD sum rules (QCDSR) [7,8], Chiral quark-soliton models (ChQSM) [9], heavy baryon Chiral perturbation theory (HBChPT) [10,11], a phenomenological quark model (PQM) which nonstatic effects of pion exchange and orbital excitation are included [12], Lattice QCD [13,14,15,16] and Chiral effective-field theory [17]. The magnetic dipole, electric quadrupole and magnetic octupole moments of these baryons is also calculated in [18] in the spectator quark formalism based on a simple ∆ wave function corresponding to a quark-diquark system in an S-state.…”