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Title: Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor

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 $$t > 4 M_\pi^2$$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $$\pi\pi \rightarrow N\bar N$$ 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 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).
 [1] ;  [1]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Report Number(s):
JLAB-THY-17-2525; DOE/OR/-23177-4275; arXiv:1707.07682
Journal ID: ISSN 2469-9985; PRVCAN
Grant/Contract Number:
AC05-06OR23177; FPA2016-77313-P
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2469-9985
American Physical Society (APS)
Research Org:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Country of Publication:
United States
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Form factors; dispersion relations; chiral effective field theory; scalar operators; 1=Nc expansion
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1409461