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

Alarcon Soriano, Jose Manuel; Weiss, Christian

doi:10.1103/PhysRevC.96.055206

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 $$N$$ andmore »« less

Authors:

Alarcon Soriano, Jose Manuel ^[1]; Weiss, Christian ^[1]

Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Publication Date:: Mon Nov 20 00:00:00 EST 2017

Research Org.:: Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

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.

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                    Alarcon Soriano, Jose Manuel, & Weiss, Christian. Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor.  United States.  https://doi.org/10.1103/PhysRevC.96.055206

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                    Alarcon Soriano, Jose Manuel, and Weiss, Christian. 2017.  
        "Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor".  United States.  https://doi.org/10.1103/PhysRevC.96.055206.  https://www.osti.gov/servlets/purl/1410288.

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@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},

  url          = {https://www.osti.gov/biblio/1410288},
  journal      = {Physical Review C},

  issn         = {2469-9985},

  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}

}

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Works referencing / citing this record:

CP violation in η muonic decays
journal, January 2019

Sanchez-Puertas, Pablo
Journal of High Energy Physics, Vol. 2019, Issue 1
https://doi.org/10.1007/jhep01(2019)031

Electromagnetic form factors of the transition from the spin-3/2 $Σ$ to the $Λ$ hyperon
journal, January 2020

Junker, Olov; Leupold, Stefan; Perotti, Elisabetta
Physical Review C, Vol. 101, Issue 1
https://doi.org/10.1103/physrevc.101.015206

Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors
text, January 2017

Alarcón, J. M.; Weiss, C.
arXiv
https://doi.org/10.48550/arxiv.1710.06430

Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory
text, January 2018

Alarcón, J. M.; Higinbotham, D. W.; Weiss, C.
arXiv
https://doi.org/10.48550/arxiv.1809.06373

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

Abstract

Citation Formats

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LARGE- N c BARYONS journal, December 1998

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Nucleons with chiral loops journal, October 1988

High-Precision Determination of the Pion-Nucleon σ Term from Roy-Steiner Equations journal, August 2015

Novel evaluation of the two-pion contribution to the nucleon isovector form factors journal, February 2006

Transverse Charge Densities journal, November 2010

Chiral Dynamics in Nucleons and Nuclei journal, June 1995

The g1 problem: Deep inelastic electron scattering and the spin of the proton journal, June 1990

Chiral-Symmetry Breakdown in Large- N Chromodynamics journal, July 1980

Chiral perturbation theory to one loop journal, November 1984

Hyperon forward spin polarizability γ 0 in baryon chiral perturbation theory journal, November 2015

Lattice QCD and the Timelike Pion Form Factor journal, August 2011

Baryons in the expansion journal, November 1979

Quantization of an interacting spin- 3 2 field and the Δ isobar journal, September 1998

On-shell consistency of the Rarita-Schwinger field formulation journal, August 2009

Dispersive analysis of the scalar form factor of the nucleon journal, June 2012

Some General Relations between the Photoproduction and Scattering of π Mesons journal, July 1954

Lepton flavor violation in the Higgs sector and the role of hadronic τ -lepton decays journal, January 2014

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Nucleon and Δ ( 1232 ) form factors at low momentum transfer and small pion masses journal, February 2012

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Hadron properties from QCD sum rules journal, October 1985

Light-front representation of chiral dynamics in peripheral transverse densities journal, July 2015

Improved description of the -scattering phenomenology at low energies in covariant baryon chiral perturbation theory journal, September 2013

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QCD and resonance physics. theoretical foundations journal, February 1979

Remarks on Higgs-boson interactions with nucleons journal, October 1978

The role of resonances in chiral perturbation theory journal, July 1989

Low-energy analysis of the nucleon electromagnetic form factors journal, January 2001

Δ ( 1232 ) resonance in the γ → p → p π 0 reaction at threshold journal, May 2016

Nucleon-nucleon interactions from dispersion relations: Coupled partial waves journal, September 2012

Chiral perturbation theory of muonic-hydrogen Lamb shift: polarizability contribution journal, April 2014

Erratum: π N scattering in relativistic baryon chiral perturbation theory reexamined [Phys. Rev. C 83 , 055205 (2011)] journal, May 2013

Nucleon-nucleon interactions from dispersion relations: Elastic partial waves journal, November 2011

Sigma-term update journal, January 1991

Aspects of chiral pion-nucleon physics journal, April 1997

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Chiral dynamics and peripheral transverse densities journal, January 2014

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Generalized parton distributions journal, December 2003

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journal, July 1999

LARGE- N _c BARYONS
journal, December 1998

Nucleon electroweak form factors: Analysis of their spectral functions
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Spin-flavor structure of large $N_{c}$ baryons
journal, April 1995

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Erratum: $\frac{1}{N_{c}}$ expansion for baryons
journal, March 1995

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journal, January 1991

Field theory of nucleon to higher-spin baryon transitions
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journal, February 2017

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journal, March 1960

The ϱNN vertex in vector-dominance models
journal, September 1975

Chiral dynamics and partonic structure at large transverse distances
journal, December 2009

Octet-baryon axial-vector charges and $S U (3)$ -breaking effects in the semileptonic hyperon decays
journal, September 2014

Chiral perturbation theory: Expansions in the mass of the strange quark
journal, January 1985

Static properties of nucleons in the Skyrme model
journal, December 1983

Theory of the Low-Energy Pion-Pion Interaction
journal, July 1960

Nucleon electromagnetic form factors
journal, October 2007

Chiral and large- $N_{c}$ limits of quantum chromodynamics and models of the baryon
journal, April 1996

Scalar form factors of light mesons
journal, November 2004

Is $SU (2) \otimes SU (2)$ a Better Symmetry than SU(3)?
journal, March 1971

Analysis strategies for general spin-independent WIMP-nucleus scattering
journal, September 2016

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journal, January 1997

Scalar radius of the pion and zeros in the form factor
journal, July 2007

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journal, October 1988

High-Precision Determination of the Pion-Nucleon $σ$ Term from Roy-Steiner Equations
journal, August 2015

Novel evaluation of the two-pion contribution to the nucleon isovector form factors
journal, February 2006

Transverse Charge Densities
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Chiral Dynamics in Nucleons and Nuclei
journal, June 1995

The g1 problem: Deep inelastic electron scattering and the spin of the proton
journal, June 1990

Chiral-Symmetry Breakdown in Large- $N$ Chromodynamics
journal, July 1980

Chiral perturbation theory to one loop
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Hyperon forward spin polarizability $γ_{0}$ in baryon chiral perturbation theory
journal, November 2015

Lattice QCD and the Timelike Pion Form Factor
journal, August 2011

Baryons in the expansion
journal, November 1979

Quantization of an interacting spin- $\frac{3}{2}$ field and the $Δ$ isobar
journal, September 1998

On-shell consistency of the Rarita-Schwinger field formulation
journal, August 2009

Dispersive analysis of the scalar form factor of the nucleon
journal, June 2012

Some General Relations between the Photoproduction and Scattering of $π$ Mesons
journal, July 1954

Lepton flavor violation in the Higgs sector and the role of hadronic $τ$ -lepton decays
journal, January 2014

Renormalization of relativistic baryon chiral perturbation theory and power counting
journal, September 2003

Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis
journal, August 2017

Nucleon and $Δ (1232)$ form factors at low momentum transfer and small pion masses
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Hadron properties from QCD sum rules
journal, October 1985

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journal, July 2015

Improved description of the -scattering phenomenology at low energies in covariant baryon chiral perturbation theory
journal, September 2013

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QCD and resonance physics. theoretical foundations
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Remarks on Higgs-boson interactions with nucleons
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The role of resonances in chiral perturbation theory
journal, July 1989

Low-energy analysis of the nucleon electromagnetic form factors
journal, January 2001

$Δ (1232)$ resonance in the $\vec{γ} p \to p π^{0}$ reaction at threshold
journal, May 2016

Nucleon-nucleon interactions from dispersion relations: Coupled partial waves
journal, September 2012

Chiral perturbation theory of muonic-hydrogen Lamb shift: polarizability contribution
journal, April 2014

Erratum: $π N$ scattering in relativistic baryon chiral perturbation theory reexamined [Phys. Rev. C 83 , 055205 (2011)]
journal, May 2013

Nucleon-nucleon interactions from dispersion relations: Elastic partial waves
journal, November 2011

Sigma-term update
journal, January 1991

Aspects of chiral pion-nucleon physics
journal, April 1997

Spectral functions of isoscalar-scalar and isovector-electromagnetic form factors of the nucleon at two-loop order
journal, August 2003

Hard exclusive reactions and the structure of hadrons
journal, January 2001

Chiral dynamics and peripheral transverse densities
journal, January 2014

Generalized parton distributions and strong forces inside nucleons and nuclei
journal, February 2003

Generalized parton distributions
journal, December 2003

Heavy baryon chiral perturbation theory with light deltas
journal, October 1998

$N / D$ description of two meson amplitudes and chiral symmetry
journal, September 1999

Chiral dynamics and the growth of the nucleon’s gluonic transverse size at small x
journal, March 2004

Chiral dynamics in the presence of bound states: kaon–nucleon interactions revisited
journal, February 2001

The strangeness content of the nucleon from effective field theory and phenomenology
journal, March 2014

Light-front representation of chiral dynamics with Δ isobar and large-N c relations
journal, June 2016

$\frac{1}{N_{c}}$ expansion for baryons
journal, May 1994

Predictive powers of chiral perturbation theory in Compton scattering off protons
journal, November 2009

Chiral unitary mesonâ€“baryon dynamics in the presence of resonances: elastic pionâ€“nucleon scattering
journal, June 2000

On the $\pi\pi$ π π continuum in the nucleon form factors and the proton radius puzzle
journal, November 2016

Low energy analysis of π N →π N
journal, May 2001

A planar diagram theory for strong interactions
journal, April 1974

Leading SU(3)-Breaking Corrections to the Baryon Magnetic Moments in Chiral Perturbation Theory
journal, November 2008

Impact Parameter Space Interpretation for Generalized Parton Distributions
journal, January 2003