Nucleon andΔ(1232)form factors at low momentum transfer and small pion masses

Abstract

An expansion of the electromagnetic form factors of the nucleon and ∆(1232) in small momentum transfer and pion mass is performed in a manifestly-covariant EFT framework consistent with chiral symmetry and analyticity. We present the expressions for the nucleon and ∆(1232) electromagnetic form factors, charge radii, and electromagnetic moments in the framework of SU(2) baryon chiral perturbation theory, with nucleon and ∆-isobar degrees of freedom, to next-to-leading order. Motivated by the results for the proton electric radius obtained from the muonic-hydrogen atom and electron-scattering process, we extract values for the second derivative of the electric form factor which is a genuine prediction of the p 3 BχPT. The chiral behavior of radii and moments is studied and compared to that obtained in the heavy-baryon framework and lattice QCD. The chiral behavior of ∆(1232)-isobar properties exhibits cusps and singularities at the threshold of ∆ → πN decay, and their physical significance is discussed. *

Generalized polarizabilities of the nucleon in baryon chiral perturbation theory

“…As many recent calculations demonstrate (see, e.g., [22][23][24][25][26][27][28][29][30][31]), Bχ PT shows an improved convergence over the analogous HBχ PT calculations, and, as result, a more "natural" description of the nucleon polarizabilities and Compton scattering processes [32][33][34][35][36]. In this paper, we extend the previous Bχ PT calculations of Lensky et al [35][36][37], done for nucleon polarizabilities appearing in real and forward doubly virtual Compton scattering (RCS and VVCS, respectively), to the case of GPs and VCS.…”

Improved description of the -scattering phenomenology at low energies in covariant baryon chiral perturbation theory

“…We have checked that the application of these methods to the EOMS-renormalized amplitude naturally lead to the same values of g πN as those obtained by the direct application of Eq. (35).…”

“…A serious drawback of the IR method is that, in curing the problems of the HB expansion, it runs into its own ones with the analytic properties of the loop integrals [35]. This is related to the fact that the IR resummation of kinetic terms performed on the HB propagators completely omits the inclusion of negative-energy pole or anti-nucleon contribution, violating charge conjugation symmetry and, therefore, causality [36].…”

“…In the first place, we use Lorentz covariant BChPT with a consistent power counting obtained via the extended-onmass-shell (EOMS) renormalization scheme [41,42]. The main advantage of EOMS over the HB and IR schemes is that it preserves the proper analytic structure of the Green functions [35]. Secondly, we explicitly include the ∆(1232) taking into account that, below the resonance region, the diagrams with the ∆ are suppressed in comparison with those with the nucleon [43,39].…”

Threshold Neutral Pion Photoproduction on the Proton

“…We opt for the EOMS regularization scheme, where both these problems are addressed simultaneously, by absorbing their fully analytical expressions into the low-energy constants of the corresponding order [28,29]. The success of this renormalization scheme has been thoroughly studied on many physical observables in [30][31][32][33][34][35][36][37][38][39][40][41]. More specifically, we use the modified minimal subtraction MS scheme [42].…”