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).

arXiv comment17 pages and 11 figures

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• Improved Treatment of Dark Matter Capture in Neutron Stars III: Nucleon and Exotic Targets
• Precise determination of proton magnetic radius from electron scattering data
• Fresh extraction of the proton charge radius from electron scattering
• Robust extraction of proton charge radius from electron-proton scattering data
• Hadron and light nucleus radii from electron scattering
• Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors
• Accurate nucleon electromagnetic form factors from dispersively improved chiral effective field theory
• PRad-II: A New Upgraded High Precision Measurement of the Proton Charge Radius
• The electromagnetic form factors of the transition from the spin-3/2 Sigma to the Lambda hyperon
• Advanced extraction of the deuteron charge radius from electron-deuteron scattering data
• Partonic angular momentum in the nucleon's chiral periphery
• $CP$ violation in $\eta$ muonic decays
• Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$
• Nucleon form factors and parton distributions in nonlocal chiral effective theory
• Transverse charge and current densities in the nucleon from dispersively improved chiral effective field theory
• Nucleon axial-vector form factor and radius from future neutrino experiments