Nucleon form factors in dispersively improved Chiral Effective Field Theory I: Scalar form factor

Abstract

We propose a method for calculating the nucleon form factors (FFs) of $G$-parity-even operators by combining Chiral Effective Field Theory ($\chi$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $t>4M_{\pi }^2$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $\pi \pi \to N\bar{N}$ partial-wave amplitudes and the timelike pion FF. $\chi$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $\pi \pi$ rescattering in the $t$-channel ($N/D$ method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional $\chi$EFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the $t$-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the $\pi N$ low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-$N_c$ limit of QCD because the $\chi$EFT calculation includes $N$ and $\Delta$ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovector-vector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions).

17 pages and 11 figures

References in corpus (11)

• Nucleon Electromagnetic Form Factors
• Leading SU(3)-breaking corrections to the baryon magnetic moments in Chiral Perturbation Theory
• On the pi pi continuum in the nucleon form factors and the proton radius puzzle
• Three-body Unitarity with Isobars Revisited
• Dispersive analysis of the scalar form factor of the nucleon
• Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering
• Octet-baryon axial-vector charges and SU(3)-breaking effects in the semileptonic hyperon decays
• Gold-plated moments of nucleon structure functions in baryon chiral perturbation theory
• Scalar radius of the pion and zeros in the form factor
• πN scattering in relativistic baryon chiral perturbation theory revisited
• On-shell consistency of the Rarita-Schwinger field formulation

Cited by in corpus (1)

• The electromagnetic form factors of the transition from the spin-3/2 Sigma to the Lambda hyperon