Up toNLO3heavy-baryon chiral perturbation theory calculation for theM1properties

Abstract

M1 properties, comprising magnetic moments and radiative capture of thermal neutron observables, are studied in two-and three-nucleon systems. We use meson exchange current derived up to N 3 LO using heavy baryon chiral perturbation theoryà la Weinberg. Calculations have been performed for several qualitatively different realistic nuclear Hamiltonians, which permits us to analyze model dependence of our results. Our results are found to be strongly correlated with the effective range parameters such as binding energies and the scattering lengths. Taking into account such correlations, the results are in good agreement with the experimental data with small model dependence. YOUNG-HO SONG, RIMANTAS LAZAUSKAS, AND TAE-SUN PARK PHYSICAL REVIEW C 79, 064002 (2009) F JM (r) = j J (qr)Y JM (r), (20) F M JL (r) = j L (qr)Y M J L1 (r), where j L (qr) is the spherical Bessel function; Y JM and Y M J L1are spherical and vector-spherical harmonics, respectively; r is a vector describing the particle (nucleon or meson), which interacts with EM field. Then the electric and magnetic multipoles read064002-4 UP TO N 3 LO HEAVY-BARYON CHIRAL . . . PHYSICAL REVIEW C 79, 064002 (2009) E JM = i J + 1 2J + 1 1/2 F M J J −1 (r) − J 2J + 1 1/2 F M J J +1 (r) · j c + qF M J J (r) · j µ .

Parity violation in radiative neutron capture on the deuteron

“…For low energy neutrons, the expressions for these PV effects could be written in terms of parity conserving magnetic dipole (M1) whereĴ c (x) is a convection current,μ(x) is a magnetization current,ρ(x) is a charge operator, and q = ω is a photon energy. In our calculations, we use the M1 operator up to N 3 LO in chiral order counting, which includes contributions from two-pion exchange and contact currents obtained in heavy baryon chiral perturbation theory [20]. For calculations of E1 amplitudes at the leading order, we use only the E1 charge operator, which is related to 3-vector currents by Siegert's theorem.…”

“…The results of calculations of parity conserving M1 amplitudes for radiative thermal neutron capture on deuteron have been reported in papers [20,21] using a "hybrid" method, where wave functions were obtained from realistic potential models and the current operators were derived from the heavy baryon chiral effective field theory. The results of these calculations can be approximated [20] …”

“…where two low energy constants of the two-body M1 operators are fixed [20] we choose a set of realistic models of nucleon-nucleon interactions, namely: Argonne v18 potential (AV18) [22], INOY potential [23], Reid soft-core potential (Reid) and Nijmegen potential(NijmII) [24]. Also, we have performed calculations for the AV18 potential in conjunction with the Urbana IX three-nucleon force potential [25] (denoted as AV18+UIX).…”

“…Our approach could be considered as a "hybrid" method, similar to the "hybrid" approach in the line of Weinberg's scheme [26,27], which has been successfully applied for the calculations of weak and electromagnetic processes involving three-body and four-body hadronic systems [20,21,[28][29][30][31], and for the calculations of parity violating [15] and time reversal violating effects in elastic n-d scattering [32,33]. It is worth mentioning that alternative calculations of parity violating effects in elastic n-d scattering using pionless EFT [34] are well consistent with the hybrid calculations [15], though more detailed comparison between these two methods is required.…”

“…For M1 amplitude, we use results of N 3 LO EFT calculations [20] which give a total cross section uncertainty better than 3%, including uncertainties from potential model dependencies, cutoff dependencies and higher order corrections. Another possible source for model dependencies is a choice of PV violating potentials, which, for the EFT approach, means the choice of the scalar functions used for the regularization.…”