The nucleon as a test case to calculate vector-isovector form factors at low energies

Abstract

Abstract. Extending a recent suggestion for hyperon form factors to the nucleon case, dispersion theory is used to relate the low-energy vector-isovector form factors of the nucleon to the pion vector form factor. The additionally required input, i.e. the pion-nucleon scattering amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the nucleons and optionally the Delta baryons. Two methods to include pion rescattering are compared: a) solving the MuskhelishviliOmnès (MO) equation and b) using an N/D approach. It turns out that the results differ strongly from each other. Furthermore the results are compared to a fully dispersive calculation of the (subthreshold) pion-nucleon amplitudes based on Roy-Steiner (RS) equations. In full agreement with the findings from the hyperon sector it turns out that the inclusion of Delta baryons is not an option but a necessity to obtain reasonable results. The magnetic isovector form factor depends strongly on a low-energy constant of the NLO Lagrangian. If it is adjusted such that the corresponding magnetic radius is reproduced, then the results for the corresponding pion-nucleon scattering amplitude (based on the MO equation) agree very well with the RS results. Also in the electric sector the Delta degrees of freedom are needed to obtain the correct order of magnitude for the isovector charge and the corresponding electric radius. Yet quantitative agreement is not achieved. If the subtraction constant that appears in the solution of the MO equation is not taken from nucleon+Delta chiral perturbation theory but adjusted such that the electric radius is reproduced, then one obtains also in this sector a pion-nucleon scattering amplitude that agrees well with the RS results.

Dispersion-theoretical analysis of the electromagnetic form factors of the nucleon: Past, present and future

“…The extracted proton charge radius is consistent with our result, but as noted in Ref. [59], this approach is subject to uncertainties in the ρ-region, different from the exact representation used in the papers discussed above.…”

Electromagnetic transition form factors and Dalitz decays of hyperons

“…The isoscalar and isovector form factors of the nucleon have all non-vanishing "charges". One can define an isoscalar and an isovector radius based on (42), see, e.g., [3,19]. Those two radii are positive and in the order of 1 fm, in full agreement with (43).…”

“…From a technical point of view, these relations are easy to deduce from the definitions of the helicity amplitudes (3). Later, the constraint (4) will be very important for our model independent low-energy parametrization of the transitions.…”

Study on Vibrational-Gamma Soft Properties in 124Te Nucleus

“…The B (E2) data of Pd [102][103][104][105][106][107][108][109][110][111][112] and Ru 96-102 nuclei were examined [12][13][14]. Several vibrational-gamma soft properties IBM calculations have been reported that dealt with the IBM and IVBM models [15][16][17][18][19]. The aim of the present work is to interpret the collective behavior of yrast state of 124 Te nucleus by D-G, IBM-1, BM, and IVBM models.…”