Electromagnetic interactions in a chiral effective lagrangian for nuclei

Abstract

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentzinvariant effective field theory contains nucleons, pions, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The theory exhibits a nonlinear realization of SU (2) L × SU (2) R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.

Neutrinoproduction of photons and pions from nucleons in a chiral effective field theory for nuclei

“…V iµ and A iµ are the isovector vector current and the isovector axial-vector current, respectively. We do not discuss "seagull" terms of higher order in the couplings because they do not enter in our calculations [10,24]. Here:…”

“…1) at tree level; loops are not included; only diagrams with contact structure are included 3 . Because of VMD, we can extrapolate the current to nonzero Q 2 [10,20]. The results are given below, and the explicit calculations are shown in Appendix B.…”

“…Here we use a recently proposed Lorentz-covariant * Electronic address: xilzhang@indiana.edu meson-baryon effective field theory (EFT) that was originally motivated by the nuclear many-body problem [3][4][5][6][7][8][9][10]. (This formalism is often called quantum hadrodynamics or QHD.)…”

Electroweak Interactions in a Chiral Effective Lagrangian for Nuclei

“…The motivation for this EFT and illustrations of some calculated results are discussed in Refs. (Furnstahl et al, 1997;Hu et al, 2007;Huertas, 2002;McIntire et al, 2007;McIntire, 2008;Serot, 2007;2010), for example. This QHD EFT has also been applied to a discussion of the isovector axial-vector current in nuclei (Ananyan et al, 2002).…”

“…In this work, we focus on the introduction of EW interactions in the QHD EFT, with the Delta (1232) resonance (∆) included as manifest degrees of freedom. To realize the symmetries of QCD in QHD EFT, including both chiral symmetry SU(2) L ⊗ SU(2) R and discrete symmetries, we apply the background-field technique (Gasser & Leutwyler, 1984;Serot, 2007). Based on the EW synthesis in the Standard Model, a proper substitution of background fields in terms of EW gauge bosons in the lagrangian, as constrained by the EW interactions of quarks (Donoghue et al, 1992), leads to EW interactions of hadrons at low energy.…”