Improved empirical parametrizations of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>γ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mi>N</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1232</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>γ</mml:mi><mml:mo>*</mml:mo></mml:msup><mml:mi>N<

Ramalho, G.

doi:10.1103/physrevd.93.113012

Cited by 17 publications

(12 citation statements)

References 63 publications

(145 reference statements)

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“…The functions G i (i = 1, .., 4) are form factor functions that depend on Q 2 , but only three of them are independent. From current conservation [9,28] we conclude that…”

Section: A Helicity Amplitudesmentioning

confidence: 93%

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Semirelativistic approximation to the γN→N(1520) and γN
Ramalho
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2017
Phys. Rev. D
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The representation of the wave functions of the nucleon resonances within a relativistic framework is a complex task. In a nonrelativistic framework the orthogonality between states can be imposed naturally. In a relativistic generalization, however, the derivation of the orthogonality condition between states can be problematic, particularly when the states have different masses. In this work we study the N (1520) and N (1535) states using a relativistic framework. We considered wave functions derived in previous works, but impose the orthogonality between the nucleon and resonance states using the properties of the nucleon, ignoring the difference of masses between the states (semirelativistic approximation). The N (1520) and N (1535) wave functions are then defined without any adjustable parameters and are used to make predictions for the valence quark contributions to the transition form factors. The predictions compare well with the data particularly for high momentum transfer, where the dominance of the quark degrees of freedom is expected. I. INTRODUCTIONIn the last century we learned that the hadrons, including the nucleon (N ) and the nucleon excitations (N * ) are not pointlike particles and have their own internal structure. The structure of those states is the result of the internal constituents, quarks and gluons, and the interactions ruled by Quantum Chromodynamics (QCD). In the last decades experimental facilities such as Jefferson Lab (JLab), MAMI (Mainz) and MIT-Bates have accumulated information (data) about the electromagnetic structure of the nucleon resonances, parametrized in terms of structure form factors for masses up to 3 GeV [1,2].Several theoretical models have been proposed to interpret the nucleon resonance spectrum and the information associated with its internal structure [1][2][3]. Different models provide different parametrizations of the internal structure in terms of the effective degrees of freedom. Some of the more successful models are the constituent quark models (CQM) based on nonrelativistic kinematics like the Karl-Isgur model [3,4] and the Light Front quark models (LFQM) defined in the infinite momentum frame [5][6][7]. In those extreme cases, nonrelativistic models or LFQM, the kinematics is simplified. In general, however, the transition between the nonrelativistic and relativistic regimes is not a trivial task.In this work we discuss the γ * N → N * transition form factors for resonances N * with negative parity. The definition of the wave functions of the nucleon (mass M N ) and a nucleon excitation (mass M R ), in terms of the internal quark degrees of freedom, can be done first in the rest frame of the particle, and extended later for a moving frame using a Lorentz transformation. In a nonrelativistic framework the mass and energy of the state are not relevant for the definition of the states. Moreover, the orthogonality between the nucleon and the resonance N * is ensured, since the wave functions are independent of their masses. To understand the complexity of ...

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“…The functions G i (i = 1, .., 4) are form factor functions that depend on Q 2 , but only three of them are independent. From current conservation [9,28] we conclude that…”

Section: A Helicity Amplitudesmentioning

confidence: 93%

“…The functions G i (i = 1, .., 4) are form factor functions that depend on Q 2 , but only three of them are independent. From current conservation [9,28] we conclude thatAnother useful combination of the form factorsUsing the previous form factors we can express the γ * N → N (1520) helicity amplitudes defined by Eqs. (3.3)-(3.5) as [1, 9]…”

mentioning

confidence: 84%

Semirelativistic approximation to the γN→N(1520) and γN
Ramalho
¹

2017
Phys. Rev. D
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18
2
12
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“…A parametrization of the data (MAID-SG2) [8] compatible with the previous condition is presented in the left panel of Fig. 3.…”

Section: Introductionmentioning

confidence: 85%

“…In addition, at the pseudothreshold the last two amplitudes are related by 1 2 E 2− = λS 1/2 [3,8]. Using the parametrizations for A 1/2 , A 3/2 and S 1/2 one can calculate the transition form factors G M , G E and G C .…”

Section: Introductionmentioning

confidence: 99%

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Empirical Parametrizations of the Resonance Amplitudes Based on the Siegert’s Theorem

Ramalho¹

2017

Proceedings of the 14th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2016)

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We present parametrizations of the γ+ transition amplitudes that are compatible with the analytic constraints at the pseudothreshold (Siegert's theorem). The presented parametrizations also provide a fair description of the experimental data. For the case of the γ * N → ∆(1232)3/2 + transition, we discuss how the pion cloud parametrizations of the electric and the Coulomb quadrupole form factors can be adjusted according to the Siegert's theorem.

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A Relativistic Model for the Electromagnetic Structure of Baryons from the 3rd Resonance Region

Ramalho

2016

Few-Body Syst

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We present some predictions for the γ * N → N * transition amplitudes, where N is the nucleon, and N * is a nucleon excitation from the third resonance region. First we estimate the transition amplitudes associated with the second radial excitation of the nucleon, interpreted as the N (1710) state, using the covariant spectator quark model. After that, we combine some results from the covariant spectator quark model with the framework of the single quark transition model, to make predictions for the γ *

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Improved empirical parametrizations of theγN→Δ(1232)andγN<

Cited by 17 publications

References 63 publications

Semirelativistic approximation to the γN→N(1520) and γN
Ramalho
¹

2017
Phys. Rev. D
Self Cite
18
2
12
0
View full text Add to dashboard Cite

Semirelativistic approximation to the γN→N(1520) and γN
Ramalho
¹

2017
Phys. Rev. D
Self Cite
18
2
12
0
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Empirical Parametrizations of the Resonance Amplitudes Based on the Siegert’s Theorem

A Relativistic Model for the Electromagnetic Structure of Baryons from the 3rd Resonance Region

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Improved empirical parametrizations of theγ*N→Δ(1232)andγ*N<

Cited by 17 publications

References 63 publications

Semirelativistic approximation to the γ*N→N(1520) and γ*NRamalho1 2017Phys. Rev. DSelf Cite182120View full textAdd to dashboardCite

Semirelativistic approximation to the γ*N→N(1520) and γ*NRamalho1 2017Phys. Rev. DSelf Cite182120View full textAdd to dashboardCite

Empirical Parametrizations of the Resonance Amplitudes Based on the Siegert’s Theorem

A Relativistic Model for the Electromagnetic Structure of Baryons from the 3rd Resonance Region

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Improved empirical parametrizations of theγN→Δ(1232)andγN<

Semirelativistic approximation to the γN→N(1520) and γN
Ramalho
¹

2017
Phys. Rev. D
Self Cite
18
2
12
0
View full text Add to dashboard Cite

Semirelativistic approximation to the γN→N(1520) and γN
Ramalho
¹

2017
Phys. Rev. D
Self Cite
18
2
12
0
View full text Add to dashboard Cite