Transition form factors: γ*+p→Δ(1232) , Δ(1600)

Lu, Y.; Chen, C.; Cui, Z. -F.; Roberts, C. D.; Schmidt, S. M.; Segovia, J.; Zong, H. -S.

doi:10.1103/PhysRevD.100.034001

Title: Transition form factors: $γ^{*} + p \to Δ (1232)$ , $Δ (1600)$

Abstract

We report that electroproduction form factors describing the $γ^{*} p \to Δ^{+} (1232)$ , $Δ^{+} (1600)$ transitions are computed using a fully dynamical diquark-quark approximation to the Poincaré-covariant three-body bound-state problem in relativistic quantum field theory. In this approach, the $Δ (1600)$ is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the $Δ (1232)$ . Precise measurements of the $γ^{*} p \to Δ^{+} (1232)$ transition already exist on $0 \leq Q^{2} ≲ 8 {GeV}^{2}$ , and the calculated results compare favorably with the data outside the meson-cloud domain. The predictions for the $γ^{*} p \to Δ^{+} (1600)$ magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to $Q^{2} \approx 6 m_{p}^{2}$ , enabling a meaningful direct comparison with experiment once analysis of existing data is completed. In both cases, the electric quadrupole form factor is particularly sensitive to deformation of the $Δ$ -baryons. Interestingly, while the $γ^{*} p \to Δ^{+} (1232)$ transition form factors are larger in magnitude than those for $γ^{*} p \to Δ^{+} (1600)$ in some neighborhood of the real photon point, this ordering is reversed on $Q^{2} ≳ 2 m_{p}^{2}$ , suggesting that the $γ^{*} p \to Δ^{+} (1600)$ transition is more localized in configuration space.

Authors:

Lu, Y. ^[1]; Chen, C. ^[2]; Cui, Z. -F. ^[1];

^[3]; Schmidt, S. M. ^[4]; Segovia, J. ^[5]; Zong, H. -S. ^[6]

Nanjing Univ. (China)
Universidade Estadual Paulista, São Paulo (Brazil)
Argonne National Lab. (ANL), Lemont, IL (United States)
Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich (Germany)
Universidad Pablo de Olavide, Sevilla (Spain)
Nanjing Univ. (China); Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing (China)

Publication Date:: 2019-08-05

Research Org.:: Argonne National Lab. (ANL), Argonne, IL (United States)

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

OSTI Identifier:: 1560671

Alternate Identifier(s):: OSTI ID: 1547958

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 100; Journal Issue: 3; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Lu, Y., Chen, C., Cui, Z. -F., Roberts, C. D., Schmidt, S. M., Segovia, J., and Zong, H. -S. Transition form factors: γ*+p→Δ(1232) , Δ(1600).  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevD.100.034001.

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                    Lu, Y., Chen, C., Cui, Z. -F., Roberts, C. D., Schmidt, S. M., Segovia, J., & Zong, H. -S. Transition form factors: γ*+p→Δ(1232) , Δ(1600).  United States.  https://doi.org/10.1103/PhysRevD.100.034001

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                    Lu, Y., Chen, C., Cui, Z. -F., Roberts, C. D., Schmidt, S. M., Segovia, J., and Zong, H. -S. Mon .  
"Transition form factors: γ*+p→Δ(1232) , Δ(1600)".  United States.  https://doi.org/10.1103/PhysRevD.100.034001.  https://www.osti.gov/servlets/purl/1560671.

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@article{osti_1560671,

  title        = {Transition form factors: γ*+p→Δ(1232) , Δ(1600)},

  author       = {Lu, Y. and Chen, C. and Cui, Z. -F. and Roberts, C. D. and Schmidt, S. M. and Segovia, J. and Zong, H. -S.},

  abstractNote = {We report that electroproduction form factors describing the γ*p→Δ+(1232), Δ+(1600) transitions are computed using a fully dynamical diquark-quark approximation to the Poincaré-covariant three-body bound-state problem in relativistic quantum field theory. In this approach, the Δ(1600) is an analogue of the Roper resonance in the nucleon sector, appearing as the simplest radial excitation of the Δ(1232). Precise measurements of the γ*p→Δ+(1232) transition already exist on 0≤Q2≲8 GeV2, and the calculated results compare favorably with the data outside the meson-cloud domain. The predictions for the γ*p→Δ+(1600) magnetic dipole and electric quadrupole transition form factors are consistent with the empirical values at the real photon point, and extend to Q2≈6mp2, enabling a meaningful direct comparison with experiment once analysis of existing data is completed. In both cases, the electric quadrupole form factor is particularly sensitive to deformation of the Δ-baryons. Interestingly, while the γ*p→Δ+(1232) transition form factors are larger in magnitude than those for γ*p→Δ+(1600) in some neighborhood of the real photon point, this ordering is reversed on Q2≳2mp2, suggesting that the γ*p→Δ+(1600) transition is more localized in configuration space.},

  doi          = {10.1103/PhysRevD.100.034001},

  journal      = {Physical Review D},

  number       = 3,

  volume       = 100,

  place        = {United States},

  year         = {2019},

  month        = {8}

}

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FIG. 1: Faddeev equation: a linear integral equation for the matrix-valued function Ψ, being the Faddeev amplitude for a baryon of total momentum P = p_q + p_d, which expresses the relative momentum correlation between the dressed-quarks and -nonpointlike-diquarks within the baryon. The shaded rectangle demarcates the kernel of themore »

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Dynamical generation of resonances in the $P 33$ partial wave
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Golli, B.; Osmanović, H.; Širca, S.
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Drawing insights from pion parton distributions
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Title: Transition form factors: γ * + p → Δ ( 1232 ) , Δ ( 1600 )

Abstract

Citation Formats

Figures / Tables:

Natural constraints on the gluon-quark vertex journal, February 2017

Systematic study of longitudinal and transverse helicity amplitudes in the hypercentral constituent quark model journal, December 2012

Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach journal, May 2012

Nucleon Mass from a Covariant Three-Quark Faddeev Equation journal, May 2010

Multipole γN-Δ form factors and resonant photo- and electroproduction journal, November 1973

Evidence for a P 11 Pion-Nucleon Resonance at 556 MeV journal, March 1964

Process-Independent Effective Coupling: From QCD Green’s Functions to Phenomenology journal, July 2018

New results from the studies of the N ( 1440 ) 1 / 2 + , N ( 1520 ) 3 / 2 − , and Δ ( 1620 ) 1 / 2 − resonances in exclusive e p → e ′ p ′ π + π − electroproduction with the CLAS detector journal, February 2016

Quark-model identification of baryon ground and resonant states journal, June 2008

Three Lectures on Hadron Physics journal, April 2016

Nucleon spin structure at very high x journal, November 2013

Diquarks journal, October 1993

Review of Particle Physics journal, August 2018

Evidence for an N * Resonance at 1425 MeV journal, November 1964

Investigation of the Conjectured Nucleon Deformation at Low Momentum Transfer journal, January 2005

Parton distribution amplitudes: Revealing correlations within the proton and Roper journal, August 2018

Electromagnetic N - Δ transition at high Q 2 journal, November 1986

Baryons as relativistic three-quark bound states journal, November 2016

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Hadronisation of QCD journal, January 1989

Spectrum of Light- and Heavy-Baryons journal, April 2019

Measurements of e p → e ′ π + n at 1.6 < W < 2.0 GeV and extraction of nucleon resonance electrocouplings at CLAS journal, April 2015

π - and K -meson Bethe-Salpeter amplitudes journal, December 1997

Δ → N γ * Coulomb quadrupole amplitude in PQCD journal, January 2004

Excited state baryon spectroscopy from lattice QCD journal, October 2011

Pseudovector components of the pion, π 0 → γ γ , and F π ( q 2 ) journal, December 1998

Dynamical coupled-channels model of π N scattering in the W ⩽ 2 GeV nucleon resonance region journal, December 2007

N → Δ transition and proton polarizabilities from measurements of p ( γ → , γ ) , p ( γ → , π 0 ) , and p ( γ → , π + ) journal, July 2001

Pion-nucleon interactions between Tlab = 300 and Tlab = 700 MeV journal, January 1964

Measurement of the Recoil Polarization in the p ( e → , e ′ p → ) π 0 Reaction at the Δ ( 1232 ) Resonance journal, April 2001

Bethe-Salpeter study of vector meson masses and decay constants journal, October 1999

Dissecting nucleon transition electromagnetic form factors journal, October 2016

Disentangling the Dynamical Origin of P 11 Nucleon Resonances journal, January 2010

Photoproduction amplitudes of P 11 and P 33 baryon resonances in the quark model journal, September 1992

Electromagnetic $${\varvec{N}}^{\varvec{*}}$$ N ∗ Transition Form Factors in the ANL-Osaka Dynamical Coupled-Channels Approach journal, March 2018

Nucleon electromagnetic form factors from the covariant Faddeev equation journal, July 2011

Nucleon and $${\Delta}$$ Δ Elastic and Transition Form Factors journal, October 2014

Dynamical study of the Δ excitation in N ( e , e ′ π ) reactions journal, March 2001

Poincaré-covariant analysis of heavy-quark baryons journal, June 2018

Quark models of baryon masses and decays journal, January 2000

Process-independent strong running coupling journal, September 2017

The pion: an enigma within the Standard Model journal, May 2016

Insights into the γ * N → Δ transition journal, September 2013

Bridging a gap between continuum-QCD and ab initio predictions of hadron observables journal, March 2015

Parity partners in the baryon resonance spectrum journal, July 2017

Meson exchange contributions to the nucleon mass in the Faddeev approach to the NJL model journal, July 1998

Structure of the nucleon’s low-lying excitations journal, February 2018

Baryon Structure and QCD journal, January 1989

Completing the Picture of the Roper Resonance journal, October 2015

Electroexcitation of the Δ ( 1232 ) 3 2 + and Δ ( 1600 ) 3 2 + in a light-front relativistic quark model journal, September 2015

Light baryons and their excitations journal, November 2016

Nucleon-to-Roper electromagnetic transition form factors at large Q 2 journal, February 2019

Calculation of diquark masses in QCD journal, November 1987

Measurements of the γ * p → Δ reaction at low Q 2 : Probing the mesonic contribution journal, August 2008

Electromagnetic properties for arbitrary spin particles: Natural electromagnetic moments from light-cone arguments journal, June 2009

Genuine quark state versus dynamically generated structure for the Roper resonance journal, March 2018

Experimental study of the P 11 ( 1440 ) and D 13 ( 1520 ) resonances from the CLAS data on e p → e ′ π + π − p ′ journal, September 2012

Dynamical coupled-channels effects on pion photoproduction journal, April 2008

Progress in the Calculation of Nucleon Transition form Factors journal, June 2016

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Electromagnetic transition form factors of baryons in the space-like momentum region journal, March 2018

Electroexcitation of nucleon resonances from CLAS data on single pion electroproduction journal, November 2009

Total Cross Sections of Positive Pions in Hydrogen journal, March 1952

Elastic and Transition Form Factors of the Δ(1232) journal, December 2013

Ordinary and Exchange Scattering of Negative Pions by Hydrogen journal, March 1952

Progress towards understanding baryon resonances journal, June 2013

Quark-diquark approximation of the three-quark structure of baryons in the quark confinement model journal, December 1990

Developments of the Jülich–Bonn Dynamical Coupled-Channel Analysis journal, October 2018

Pion-nucleon phase shifts and resonances journal, September 1964

Understanding the nucleon as a Borromean bound-state journal, November 2015

Energy-Dependent Pion-Nucleon Phase-Shift Analysis journal, April 1965

Effective Masses of Diquarks journal, June 2002

Baryon Structure and QCD: Nucleon Calculations journal, January 1989

Hadronization of quark flavor dynamics journal, July 1990

Perspective on rainbow-ladder truncation journal, April 2008

π + photoproduction on the proton for photon energies from 0.725 to 2.875 GeV journal, June 2009

Title: Transition form factors: $γ^{*} + p \to Δ (1232)$ , $Δ (1600)$

Natural constraints on the gluon-quark vertex
journal, February 2017

Systematic study of longitudinal and transverse helicity amplitudes in the hypercentral constituent quark model
journal, December 2012

Nucleon to delta electromagnetic transition in the Dyson-Schwinger approach
journal, May 2012

Nucleon Mass from a Covariant Three-Quark Faddeev Equation
journal, May 2010

Multipole γN-Δ form factors and resonant photo- and electroproduction
journal, November 1973

Evidence for a $P_{11}$ Pion-Nucleon Resonance at 556 MeV
journal, March 1964

Process-Independent Effective Coupling: From QCD Green’s Functions to Phenomenology
journal, July 2018

New results from the studies of the $N (1440) 1 / 2^{+}, N (1520) 3 / 2^{-}$ , and $Δ (1620) 1 / 2^{-}$ resonances in exclusive $e p \to e^{'} p^{'} π^{+} π^{-}$ electroproduction with the CLAS detector
journal, February 2016

Quark-model identification of baryon ground and resonant states
journal, June 2008

Three Lectures on Hadron Physics
journal, April 2016

Nucleon spin structure at very high x
journal, November 2013

Diquarks
journal, October 1993

Review of Particle Physics
journal, August 2018

Evidence for an $N^{*}$ Resonance at 1425 MeV
journal, November 1964

Investigation of the Conjectured Nucleon Deformation at Low Momentum Transfer
journal, January 2005

Parton distribution amplitudes: Revealing correlations within the proton and Roper
journal, August 2018

Electromagnetic N - Δ transition at high $Q^{2}$
journal, November 1986

Baryons as relativistic three-quark bound states
journal, November 2016

Electromagnetic Multipole Moments of Baryons
journal, November 2018

Hadronisation of QCD
journal, January 1989

Spectrum of Light- and Heavy-Baryons
journal, April 2019

Measurements of $e p \to e^{'} π^{+} n$ at $1.6 < W < 2.0$ GeV and extraction of nucleon resonance electrocouplings at CLAS
journal, April 2015

$π$ - and $K$ -meson Bethe-Salpeter amplitudes
journal, December 1997

$\vec{Δ} N γ^{*}$ Coulomb quadrupole amplitude in PQCD
journal, January 2004

Excited state baryon spectroscopy from lattice QCD
journal, October 2011

Pseudovector components of the pion, $π^{0} \to γ γ,$ and $F_{π} {(q}^{2})$
journal, December 1998

Dynamical coupled-channels model of $π N$ scattering in the $W ⩽ 2$ GeV nucleon resonance region
journal, December 2007

$\vec{N} Δ$ transition and proton polarizabilities from measurements of $p (\vec{γ}, γ),$ $p (\vec{γ}, π^{0}),$ and $p (\vec{γ}, π^{+})$
journal, July 2001

Pion-nucleon interactions between Tlab = 300 and Tlab = 700 MeV
journal, January 1964

Measurement of the Recoil Polarization in the $p (\vec{e}, e^{'} \vec{p}) π^{0}$ Reaction at the $Δ (1232)$ Resonance
journal, April 2001

Bethe-Salpeter study of vector meson masses and decay constants
journal, October 1999

Dissecting nucleon transition electromagnetic form factors
journal, October 2016

Disentangling the Dynamical Origin of $P_{11}$ Nucleon Resonances
journal, January 2010

Photoproduction amplitudes of $P_{11}$ and $P_{33}$ baryon resonances in the quark model
journal, September 1992

Electromagnetic $${\varvec{N}}^{\varvec{*}}$$ N ∗ Transition Form Factors in the ANL-Osaka Dynamical Coupled-Channels Approach
journal, March 2018

Nucleon electromagnetic form factors from the covariant Faddeev equation
journal, July 2011

Nucleon and $${\Delta}$$ Δ Elastic and Transition Form Factors
journal, October 2014

Dynamical study of the $Δ$ excitation in ${N (e, e}^{'} π)$ reactions
journal, March 2001

Poincaré-covariant analysis of heavy-quark baryons
journal, June 2018

Quark models of baryon masses and decays
journal, January 2000

Process-independent strong running coupling
journal, September 2017

The pion: an enigma within the Standard Model
journal, May 2016

Insights into the $γ^{*} N \to Δ$ transition
journal, September 2013

Bridging a gap between continuum-QCD and ab initio predictions of hadron observables
journal, March 2015

Parity partners in the baryon resonance spectrum
journal, July 2017

Meson exchange contributions to the nucleon mass in the Faddeev approach to the NJL model
journal, July 1998

Structure of the nucleon’s low-lying excitations
journal, February 2018

Baryon Structure and QCD
journal, January 1989

Completing the Picture of the Roper Resonance
journal, October 2015

Electroexcitation of the $Δ (1232) {\frac{3}{2}}^{+}$ and $Δ (1600) {\frac{3}{2}}^{+}$ in a light-front relativistic quark model
journal, September 2015

Light baryons and their excitations
journal, November 2016

Nucleon-to-Roper electromagnetic transition form factors at large $Q^{2}$
journal, February 2019

Calculation of diquark masses in QCD
journal, November 1987

Measurements of the $γ^{*} p \to Δ$ reaction at low $Q^{2}$ : Probing the mesonic contribution
journal, August 2008

Electromagnetic properties for arbitrary spin particles: Natural electromagnetic moments from light-cone arguments
journal, June 2009

Genuine quark state versus dynamically generated structure for the Roper resonance
journal, March 2018

Experimental study of the $P_{11} (1440)$ and $D_{13} (1520)$ resonances from the CLAS data on $e p \to e^{'} π^{+} π^{-} p^{'}$
journal, September 2012

Dynamical coupled-channels effects on pion photoproduction
journal, April 2008

Progress in the Calculation of Nucleon Transition form Factors
journal, June 2016

Results from the N * Program at Jefferson Lab
journal, May 2011

Electromagnetic transition form factors of baryons in the space-like momentum region
journal, March 2018

Electroexcitation of nucleon resonances from CLAS data on single pion electroproduction
journal, November 2009

Total Cross Sections of Positive Pions in Hydrogen
journal, March 1952

Elastic and Transition Form Factors of the Δ(1232)
journal, December 2013

Ordinary and Exchange Scattering of Negative Pions by Hydrogen
journal, March 1952

Progress towards understanding baryon resonances
journal, June 2013

Quark-diquark approximation of the three-quark structure of baryons in the quark confinement model
journal, December 1990

Developments of the Jülich–Bonn Dynamical Coupled-Channel Analysis
journal, October 2018

Pion-nucleon phase shifts and resonances
journal, September 1964

Understanding the nucleon as a Borromean bound-state
journal, November 2015

Energy-Dependent Pion-Nucleon Phase-Shift Analysis
journal, April 1965

Effective Masses of Diquarks
journal, June 2002

Baryon Structure and QCD: Nucleon Calculations
journal, January 1989

Hadronization of quark flavor dynamics
journal, July 1990

Perspective on rainbow-ladder truncation
journal, April 2008

$π^{+}$ photoproduction on the proton for photon energies from 0.725 to 2.875 GeV
journal, June 2009

Baryon current matrix elements in a light-front framework
journal, April 1995

Colloquium : Roper resonance: Toward a solution to the fifty year puzzle
journal, March 2019

N $$^*$$ ∗ Experiments and Their Impact on Strong QCD Physics
journal, April 2018