Effective Lagrangian Approach to pion photoproduction from the nucleon

Abstract

We present a pion photoproduction model on the free nucleon based on an Effective Lagrangian Approach (ELA) which includes the nucleon resonances ($\Delta(1232)$, N(1440), N(1520), N(1535), $\Delta (1620)$, N(1650), and $\Delta (1700)$), in addition to Born and vector meson exchange terms. The model incorporates a new theoretical treatment of spin-3/2 resonances, first introduced by Pascalutsa, avoiding pathologies present in previous models. Other main features of the model are chiral symmetry, gauge invariance, and crossing symmetry. We use the model combined with modern optimization techniques to assess the parameters of the nucleon resonances on the basis of world data on electromagnetic multipoles. We present results for electromagnetic multipoles, differential cross sections, asymmetries, and total cross sections for all one pion photoproduction processes on free nucleons. We find overall agreement with data from threshold up to 1 GeV in laboratory frame.Comment: Misprints corrected. 60 pages. 33 figures.5 tables. Accepted for publication in Annals of Physics (NY

Properties of nucleon resonances by means of a genetic algorithm

“…The internal structure of the nucleonic excitations shows up in the values of the electromagnetic coupling constants that appear in the Lagrangian. The model displays chiral symmetry, gauge invariance, and crossing symmetry, and incorporates a consistent treatment of the interaction with spin-3/2 particles that avoids well-known pathologies of previous models [13,14,21]. Furthermore, the dressing of the resonances is considered by means of a phenomenological width which takes into account decays into one and two π 's and one η.…”

“…We prefer to use the helicity amplitudes (for their definition and connection with coupling constants see Refs. [13,14,20]) to define the ranges, instead of the electromagnetic coupling constants. We allow them to vary in the range [−1, 1] GeV −1/2 .…”

“…II we briefly present the model for pion photoproduction on free nucleons from threshold up to 1.2 GeV developed in Refs. [13][14][15]. In Sec.…”

“…Recently, in nuclear and particle physics, more credit is being given to modern optimization procedures [11][12][13][14][15][16] and to error estimations on the parameters stemming from the fits. Modern and sophisticated optimization techniques such as simulated annealing [17] and genetic algorithms (GA) [18] have been developed over the last twenty years and have been applied to problems which are impossible to tackle with conventional tools.…”

Threshold Neutral Pion Photoproduction on the Proton

“…This choice is due to the fact that, since the total cross section of the π 0 production off the proton is very small close to threshold, the ∆(1232) resonance could have a quite important contribution [15], whose effect becomes ever clearer when moving to energies closer to its mass [16]. The effect of the inclusion of this resonance has been thoroughly studied in [17][18][19][20][21][22][23][24]. We show that, although we are not including any additional fitting constants, the dynamics of the ∆(1232) resonance is a sufficient addition to well describe the experimental input even at photon energies higher than 200 MeV.…”