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Title: Nucleon form factors in dispersively improved chiral effective field theory: 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 $$t > 4 M_\pi^2$$. 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).

Authors:
 [1];  [1]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
Publication Date:
Research Org.:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1410288
Alternate Identifier(s):
OSTI ID: 1409461
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
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 96; Journal Issue: 5; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Form factors; dispersion relations; chiral effective field theory; scalar operators; 1=Nc expansion

Citation Formats

Alarcon Soriano, Jose Manuel, and Weiss, Christian. Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor. United States: N. p., 2017. Web. doi:10.1103/PhysRevC.96.055206.
Alarcon Soriano, Jose Manuel, & Weiss, Christian. Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor. United States. doi:10.1103/PhysRevC.96.055206.
Alarcon Soriano, Jose Manuel, and Weiss, Christian. Mon . "Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor". United States. doi:10.1103/PhysRevC.96.055206.
@article{osti_1410288,
title = {Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor},
author = {Alarcon Soriano, Jose Manuel and Weiss, Christian},
abstractNote = {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).},
doi = {10.1103/PhysRevC.96.055206},
journal = {Physical Review C},
number = 5,
volume = 96,
place = {United States},
year = {Mon Nov 20 00:00:00 EST 2017},
month = {Mon Nov 20 00:00:00 EST 2017}
}

Journal Article:
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  • We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining Chiral Effective Field Theory (more » $$\chi$$EFT) and dispersion analysis. The spectral functions on the two-pion cut at $$t > 4 M_\pi^2$$ are constructed using the elastic unitarity relation and an $N/D$ representation. $$\chi$$EFT is used to calculate the real unctions $$J_\pm^1 (t) = f_\pm^1(t)/F_\pi(t)$$ (ratios of the complex $$\pi\pi \rightarrow N \bar N$$ partial-wave amplitudes and the timelike pion FF), which are free of $$\pi\pi$$ rescattering. Rescattering effects are included through the empirical timelike pion FF $$|F_\pi(t)|^2$$. The method allows us to compute the isovector EM spectral functions up to $$t \sim 1$$ GeV$^2$ with controlled accuracy (LO, NLO, and partial N2LO). With the spectral functions we calculate the isovector nucleon EM FFs and their derivatives at $t = 0$ (EM radii, moments) using subtracted dispersion relations. We predict the values of higher FF derivatives with minimal uncertainties and explain their collective behavior. Finally, we estimate the individual proton and neutron FFs by adding an empirical parametrization of the isoscalar sector. Excellent agreement with the present low-$Q^2$ FF data is achieved up to $$\sim$$0.5 GeV$^2$ for $$G_E$$, and up to $$\sim$$0.2 GeV$^2$ for $$G_M$$. Our results can be used to guide the analysis of low-$Q^2$ elastic scattering data and the extraction of the proton charge radius.« less
  • We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining Chiral Effective Field Theory (more » $$\chi$$EFT) and dispersion analysis. The spectral functions on the two-pion cut at $$t > 4 M_\pi^2$$ are constructed using the elastic unitarity relation and an $N/D$ representation. $$\chi$$EFT is used to calculate the real unctions $$J_\pm^1 (t) = f_\pm^1(t)/F_\pi(t)$$ (ratios of the complex $$\pi\pi \rightarrow N \bar N$$ partial-wave amplitudes and the timelike pion FF), which are free of $$\pi\pi$$ rescattering. Rescattering effects are included through the empirical timelike pion FF $$|F_\pi(t)|^2$$. The method allows us to compute the isovector EM spectral functions up to $$t \sim 1$$ GeV$^2$ with controlled accuracy (LO, NLO, and partial N2LO). With the spectral functions we calculate the isovector nucleon EM FFs and their derivatives at $t = 0$ (EM radii, moments) using subtracted dispersion relations. We predict the values of higher FF derivatives with minimal uncertainties and explain their collective behavior. Finally, we estimate the individual proton and neutron FFs by adding an empirical parametrization of the isoscalar sector. Excellent agreement with the present low-$Q^2$ FF data is achieved up to $$\sim$$0.5 GeV$^2$ for $$G_E$$, and up to $$\sim$$0.2 GeV$^2$ for $$G_M$$. Our results can be used to guide the analysis of low-$Q^2$ elastic scattering data and the extraction of the proton charge radius.« less
  • We present a method for calculating the nucleon form factors of G-parity-even operators. This method combines chiral effective field theory (χEFT) and dispersion theory. Through unitarity we factorize the imaginary part of the form factors into a perturbative part, calculable with χEFT, and a non-perturbative part, obtained through other methods. We consider the scalar and electromagnetic (EM) form factors of the nucleon. The results show an important improvement compared to standard chiral calculations, and can be used in analysis of the low-energy properties of the nucleon.
  • We compute the electromagnetic form factors of the nucleon in quenched lattice QCD, using nonperturbatively improved Wilson fermions, and compare the results with phenomenology and chiral effective field theory.