arXiv subjects

G. Ramalho

Publications and source records attributed to G. Ramalho.

At least 37 records · Page 2Linked to original sources

arXiv2019

Low-$Q^2$ empirical parametrizations of the $N^\ast$ helicity amplitudes

The data associated with the electromagnetic excitations of the nucleon ($γ^\ast N \to N^\ast$) are usually parametrized by helicity amplitudes at the resonance $N^\ast$ rest frame. The properties of the $γ^\ast N \to N^\ast$ transition current at low $Q^2$ can be, however, better understood when expressed in terms of structure form factors, particularly near the pseudothreshold, when the magnitude of the photon three-momentum vanishes ($|{\bf q}| =0$). At the pseudothreshold the invariant four-momentum square became $q^2= (M_R-M_N)^2$, well in the timelike region $Q^2 =- q^2 < 0$ [$M_N$ and $M_R$ are the mass of the nucleon and of the resonance, respectively]. In the helicity amplitude representation, the amplitudes have well-defined dependences on $|{\bf q}|$, near the pseudothreshold, and there are correlations between different amplitudes. Those constraints are often ignored in the empirical parametrizations of the helicity amplitudes. In the present work, we show that the structure of the transition current near the pseudothreshold has an impact on the parametrizations of the data. We present a method which modifies analytic parametrizations of the data at low $Q^2$, in order to take into account the constraints of the transition amplitudes near the pseudothreshold. The model dependence of the parametrizations on the low-$Q^2$ data is studied in detail.

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arXiv2019

Octet baryon electromagnetic form factor double ratios $(G_E^\ast/G_M^\ast)/(G_E/G_M)$ in a nuclear medium

The ratios of the baryon electric ($G_E$) to magnetic ($G_M$) form factors, $G_E/G_M$, can provide us with important information on the structure of baryons in vacuum as demonstrated in recent studies for the proton and neutron systems. It has been argued that the corresponding in-medium ratios, $G_E^\ast/G_M^\ast$, can also provide useful information on the electromagnetic structure of baryons in a nuclear medium. Although the ratios may not be measured directly in experiments except for the proton at present, the double ratios $(G_E^\ast/G_M^\ast)/(G_E/G_M)$ can be directly related to the polarization-transfer measurements of bound baryons. In the present work we estimate, for the first time, the double ratios $(G_E^\ast/G_M^\ast)/(G_E/G_M)$ for all the members of octet baryons in symmetric nuclear matter in the range $Q^2=0$--3 GeV$^2$, where $Q^2=- q^2$ with $q$ being the four-momentum transfer.

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arXiv2019

Combined parametrization of the neutron electric form factor and the $γ^\ast N \to Δ(1232)$ quadrupole form factors

Models based on $SU(6)$ symmetry breaking and large $N_c$ limit provide relations between the pion cloud contributions to the $γ^\ast N \to Δ(1232)$ quadrupole form factors, electric ($G_E$) and Coulomb ($G_C$), and the neutron electric form factor $G_{En}$, suggesting that those form factors are dominated by the same physical processes. Those relations are improved in order to satisfy a fundamental constraint between the electric and Coulomb quadrupole form factors in the long wavelength limit, when the photon three-momentum vanishes (Siegert's theorem). Inspired by those relations, we study alternative parametrizations for the neutron electric form factor. The parameters of the new form are then determined by a combined fit to the $G_{En}$ and the $γ^\ast N \to Δ(1232)$ quadrupole form factor data. We obtain a very good description of the $G_E$ and $G_C$ data when we combine the pion cloud contributions with small valence quark contributions to the $γ^\ast N \to Δ(1232)$ quadrupole form factors. The best description of the data is obtained when the second momentum of $G_{En}$ is $r_n^4 \simeq -0.4$ fm$^4$. We conclude that the square radii associated with $G_E$ and $G_C$, $r_E^2$ and $r_C^2$, respectively, are large, revealing the long extension of the pion cloud. We conclude also that those square radii are related by $r_E^2 - r_C^2 = 0.6 \pm 0.2$ fm$^2$. The last result is mainly the consequence of the pion cloud effects and Siegert's theorem.

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arXiv2018

Nucleon resonances in Compton scattering

We calculate the nucleon resonance contributions to nucleon Compton scattering, including all states with J^P = 1/2^{+-} and J^P = 3/2^{+-} where experimental data for their electromagnetic transition form factors exist. To this end, we construct a tensor basis for the Compton scattering amplitude based on electromagnetic gauge invariance, crossing symmetry and analyticity. The corresponding Compton form factors provide a Lorentz-invariant description of the process in general kinematics, which reduces to the static and generalized polarizabilities in the appropriate kinematic limits. We derive the general forms of the offshell nucleon-to-resonance transition vertices that implement electromagnetic and spin-3/2 gauge invariance, which automatically also defines onshell transition form factors that are free of kinematic constraints. We provide simple fits for those form factors, which we use to analyze the resulting Compton form factors and extract their contributions to the nucleon's polarizabilities. Apart from the Delta(1232), the resonance contributions to the scalar and spin polarizabilites are very small, although the N(1520) could play a role for the proton's magnetic polarizability.

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arXiv2018

Covariant quark model for the electromagnetic structure of light nucleon resonances

We present estimates from the covariant spectator quark model for the electromagnetic transition form factors for the resonances $N(1440)\frac{1}{2}^+$, $N(1535)\frac{1}{2}^-$, $N(1520)\frac{3}{2}^-$ and $Δ(1232)\frac{3}{2}^+$, at intermediate and large square momentum transfer ($Q^2$). The calculations associated to the $N(1440)\frac{1}{2}^+$, $N(1535)\frac{1}{2}^-$ and $N(1520)\frac{3}{2}^-$ states are based exclusively on the parametrizations derived for the nucleon. In the case of the $Δ(1232)\frac{3}{2}^+$ (isospin 3/2), we use lattice QCD data to estimate the radial structure, and take into account the well known effects associated with the pion cloud dressing of the baryons. Our estimates are based mainly on the valence quark degrees of freedom and are in good agreement with the data for $Q^2 > 2$ GeV$^2$, with a few exceptions. The present predictions can be tested in a near future for large $Q^2$ at the Jefferson Lab -- 12 GeV upgrade.

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arXiv2018

$N^\ast$ Form Factors based on a Covariant Quark Model

We discuss the results of the covariant spectator quark model for the several $γ^\ast N \to N^\ast$ transitions, where $N$ is the nucleon and $N^\ast$ a nucleon excitation. More specifically, we present predictions for the form factors and transition amplitudes associated with the resonances $N(1440)1/2^+$, $N(1535)1/2^-$, $N(1520)3/2^-$, $Δ(1620)1/2^-$ and $N(1650)1/2^-$. The estimates based on valence quark degrees of freedom are compared with the available data, particularly with the recent Jefferson Lab data at low and large momentum transfer ($Q^2$). In general, the estimates are in good agreement with the empirical data for $Q^2 >2$ GeV$^2$, with a few exceptions. The results are discussed in terms of the role of the valence quarks and the meson cloud excitations for the different resonances $N^\ast$. We also review our results for the resonance $Δ(1232)3/2^+$ and discuss the relevance of the pion cloud component for the magnetic dipole form factor and the electric and Coulomb quadrupole form factors.

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arXiv2018

New low-$Q^2$ measurements of the $γ^\ast N \to Δ(1232)$ Coulomb quadrupole form factor, pion cloud parametrizations and Siegert's theorem

The novel measurements of the $γ^\ast N \to Δ(1232)$ Coulomb quadrupole form factor in the range $Q^2=0.04$--0.13 GeV$^2$ changed the trend of the previous data. With the new data the electric and Coulomb form factors are both in remarkable agreement with estimates of the pion cloud contributions to the quadrupole form factors at low $Q^2$. The pion cloud contributions to the electric and Coulomb form factors can be parametrized by the relations $G_E \propto G_{En}/ \left(1 + \frac{Q^2}{2M_Δ(M_Δ-M)}\right)$ and $G_C \propto G_{En}$, where $G_{En}$ is the neutron electric form factor, and $M$, $M_Δ$ are the nucleon and $Δ$ masses, respectively. Those parametrizations are in full agreement with Siegert's theorem, which states that $G_E= \frac{M_Δ-M}{2M_Δ} G_C$ at the pseudothreshold, when $Q^2=-(M_Δ-M)^2$, and improve previous parametrizations. Also a small valence quark component estimated by a covariant quark model contributes to this agreement. The combination of the new data with the new parametrization for $G_E$ concludes an intense period of studying the $γ^\ast N \to Δ(1232)$ quadrupole form factors at low $Q^2$, with the agreement between theory and data.

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arXiv2018

Holographic estimate of the meson cloud contribution to nucleon axial form factor

We use light-front Holography to estimate the valence quark and the meson cloud contributions to the nucleon axial form factor. The free couplings of the holographic model are determined by the empirical data and by the information extracted from lattice QCD. The holographic model provides a good description of the empirical data when we consider a meson cloud mixture of about 30\% in the physical nucleon state. The estimate of the valence quark contribution to the nucleon axial form factor compares well with the lattice QCD data for small pion masses. Our estimate of the meson cloud contribution to the nucleon axial form factor has a slower falloff with the square momentum transfer compared to typical estimates from quark models with meson cloud dressing.

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arXiv2018

Valence quark contributions for the $γ^\ast N \to N(1440)$ form factors from Light-Front holography

The structure of the nucleon and the first radial excitation of the nucleon, the Roper, $N(1440)$, is studied within the formalism of Light-Front holography. The nucleon elastic form factors and $γ^\ast N \to N(1440)$ transition form factors are calculated under the assumption of the dominance of the valence quark degrees of freedom. Contrary to the previous studies, the bare parameters of the model associated with the valence quark are fixed by the empirical data for large momentum transfer ($Q^2$) assuming that the corrections to the three-quark picture (meson cloud contributions) are suppressed. The $γ^\ast N \to N(1440)$ transition form factors are then calculated without any adjustable parameters. Our estimates are compared with results from models based on valence quarks and others. The model compares well with the $γ^\ast N \to N(1440)$ transition form factor data, suggesting that meson cloud effects are not large, except in the region $Q^2< 1.5$ GeV$^2$. In particular, the meson cloud contributions for the Pauli form factor are small.

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arXiv2017

Analytic parametrizations of the $γ^\ast N \to N(1440)$ form factors inspired by Light-Front holography

We present analytic parametrizations for the $γ^\ast N \to N(1440)$ form factors derived from light-front holography in leading twist approximation. The new parametrizations describe the electromagnetic form factors using analytic functions dependent on the masses of the $ρ$ meson and respective radial excitations, as well as the masses of the nucleon and the resonance $N(1440)$. The free parameters of the model, associated with three independent couplings, are interpreted as bare couplings, and are fixed by the nucleon data for large $Q^2$. The proposed parametrizations compare remarkably well with the empirical data for $Q^2 > 2$ GeV$^2$, corroborating the dominant role of the valence quark degrees of freedom in the $γ^\ast N \to N(1440)$ transition.

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arXiv2017

Semirelativistic approximation to the $γ^\ast N \to N(1520)$ and $γ^\ast N \to N(1535)$ transition form factors

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.

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arXiv2017

$γ^\ast N \to N^\ast(1520)$ form factors in the timelike regime

The covariant spectator quark model, tested before in a variety of electromagnetic baryon excitations, is applied here to the $γ^\ast N \to N^\ast(1520)$ reaction in the timelike regime. The transition form factors are first parametrized in the spacelike region in terms of a valence quark core model together with a parametrization of the meson cloud contribution. The form factor behavior in the timelike region is then predicted, as well as the $N^\ast(1520) \to γN$ decay width and the $N^\ast (1520)$ Dalitz decay, $N^\ast (1520) \to e^+ e^- N$. Our results may help in the interpretation of dielectron production from elementary $pp$ collisions and from the new generation of HADES results using a pion beam. In the $q^2=0$--1 GeV$^2$ range we conclude that the {\it QED approximation} (a $q^2$ independent form factor model) underestimates the electromagnetic coupling of the $N^\ast(1520)$ from 1 up to 2 orders of magnitude. We conclude also that the $N^\ast (1520)$ and the $Δ(1232)$ Dalitz decay widths are comparable.

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arXiv2016

Parametrizations of the $γ^\ast N \to Δ(1232)$ quadrupole form factors and Siegert's theorem

The large $N_c$ limit provides relations that can be used to calculate the $γ^\ast N \to Δ(1232)$ quadrupole form factors at low and intermediate $Q^2$ under the assumption of the pion cloud dominance. There are two limitations in those parametrizations. First, the parametrization of the Coulomb quadrupole form factor underestimate the low $Q^2$ data. Second, when extrapolated for the timelike region, the form factors violate Siegert's theorem by terms of the order $1/N_c^2$. We propose here corrections to the parametrization of the electric quadrupole form factor, which violate Siegert's theorem only by terms of the order $1/N_c^4$. Combining the improved large $N_c$ pion cloud parametrizations with the valence quark contributions based on a covariant quark model for the quadrupole transition form factors, we obtain an extrapolation to the timelike region consistent with Siegert's theorem, and accomplish also a very good description of the data.

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arXiv2016

Empirical parametrizations of the resonance amplitudes based on the Siegert's theorem

We present parametrizations of the $γ^\ast N \to N(1535)1/2^-$, $γ^\ast N \to N(1520)3/2^-$ and $γ^\ast N \to Δ(1232)3/2^+$ 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 $γ^\ast N \to Δ(1232)3/2^+$ 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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arXiv2016

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

We present some predictions for the $γ^\ast N \to N^\ast$ transition amplitudes, where $N$ is the nucleon, and $N^\ast$ 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 $γ^\ast N \to N^\ast$ transition amplitudes, where $N^\ast$ is a member of the $SU(6)$-multiplet $[70,1^-]$. The results for the $γ^\ast N \to N(1520)$ and $γ^\ast N \to N(1535)$ transition amplitudes are used as input to the calculation of the amplitudes $A_{1/2}$, $A_{3/2}$, associated with the $γ^\ast N \to N(1650)$, $γ^\ast N \to N(1700)$, $γ^\ast N \to Δ(1620)$, and $γ^\ast N \to Δ(1700)$ transitions. Our estimates are compared with the available data. In order to facilitate the comparison with future experimental data at high $Q^2$, we derived also simple parametrizations for the amplitudes, compatible with the expected falloff at high $Q^2$.

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arXiv2016

Improved empirical parametrizations of the $γ^\ast N \to Δ(1232)$ and $γ^\ast N \to N(1520)$ helicity amplitudes and the Siegert's theorem

In the nucleon electroexcitation reactions, $γ^\ast N \to R$, where $R$ is a nucleon resonance ($N^\ast$), the electric amplitude $E$, and the longitudinal amplitude $S_{1/2}$, are related by $E \propto \fracω{|{\bf q}|}S_{1/2}$, at the pseudo-threshold limit ($|{\bf q}| \to 0$), where $ω$ and $|{\bf q}|$ are respectively the energy and the magnitude of three-momentum of the photon. The previous relation is usually refereed as the Siegert's theorem. The form of the electric amplitude, defined in terms of the transverse amplitudes $A_{1/2}$ and $A_{3/2}$, and the explicit coefficients of the relation, depend on the angular momentum and parity ($J^P$) of the resonance $R$. The Siegert's theorem is the consequence of the structure of the electromagnetic transition current, which induces constraints between the electromagnetic form factors in the pseudo-threshold limit. In the present work, we study the implications of the Siegert's theorem for the $γ^\ast N \to Δ(1232)$ and $γ^\ast N \to N(1520)$ transitions. For the $γ^\ast N \to N(1520)$ transition, in addition to the relation between electric amplitude and longitudinal amplitude, we obtain also a relation between the two transverse amplitudes: $A_{1/2}= A_{3/2} /\sqrt{3}$, at the pseudo-threshold. % The constraints at the pseudo-threshold are tested for the MAID2007 parametrizations of the reactions under discussion. New parametrizations for the amplitudes $A_{1/2}$, $A_{3/2}$ and $S_{1/2}$, for the $γ^\ast N \to Δ(1232)$ and $γ^\ast N \to N(1520)$ transitions, valid for small and large $Q^2$, are proposed. The new parametrizations are consistent with both: the pseudo-threshold constraints (Siegert's theorem) and the empirical data.

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arXiv2016

Improved empirical parametrizations of the $γ^\ast N \to N(1535)$ transition amplitudes and the Siegert's theorem

Some empirical parametrizations of the $γ^\ast N \to N(1535)$ transition amplitudes violates the Siegert's theorem, that relates the longitudinal and the transverse amplitudes, in the pseudo-threshold limit (nucleon and resonance at rest). In the case of the electromagnetic transition from the nucleon (mass $M$) to the resonance $N(1525)$ (mass $M_R$), the Siegert's theorem is sometimes expressed by the relation $|{\bf q}| A_{1/2}= λS_{1/2}$ in the pseudo-threshold limit, when the photon momentum $|{\bf q}|$ vanishes, and $λ= \sqrt{2} (M_R -M)$. In this article, we argue that the Siegert's theorem should be expressed by the relation $A_{1/2} = λ\frac{S_{1/2}}{ |{\bf q}|}$, in the limit $|{\bf q}| \to 0$. This result is a consequence of the relation $S_{1/2} \propto |{\bf q}|$, when $|{\bf q}| \to 0$, as suggested by the analysis of the transition form factors and by the orthogonality between the nucleon and $N(1535)$ states. We propose then new empirical parametrizations for the $γ^\ast N \to N(1535)$ helicity amplitudes, that are consistent with the data and the Siegert's theorem. The proposed parametrization follow closely the MAID2007 parametrization, except for a small deviation in the amplitudes $A_{1/2}$ and $S_{1/2}$ when $Q^2 < 1.5$ GeV$^2$.

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arXiv2016

Axial form factors of the octet baryons in a covariant quark model

We study the weak interaction axial form factors of the octet baryons, within the covariant spectator quark model, focusing on the dependence of four-momentum transfer squared, Q^2. In our model the axial form factors G_A(Q^2) (axial-vector form factor) and G_P(Q^2) (induced pseudoscalar form factor), are calculated based on the constituent quark axial form factors and the octet baryon wave functions. The quark axial current is parametrized by the two constituent quark form factors, the axial-vector form factor g_A^q(Q^2), and the induced pseudoscalar form factor g_P^q(Q^2). The baryon wave functions are composed of a dominant S-state and a P-state mixture for the relative angular momentum of the quarks. First, we study in detail the nucleon case. We assume that the quark axial-vector form factor g_A^q(Q^2) has the same function form as that of the quark electromagnetic isovector form factor. The remaining parameters of the model, the P-state mixture and the Q^2-dependence of g_P^q(Q^2), are determined by a fit to the nucleon axial form factor data obtained by lattice QCD simulations with large pion masses. In this lattice QCD regime the meson cloud effects are small, and the physics associated with the valence quarks can be better calibrated. Once the valence quark model is calibrated, we extend the model to the physical regime, and use the low Q^2 experimental data to estimate the meson cloud contributions for G_A(Q^2) and G_P(Q^2). Using the calibrated quark axial form factors, and the generalization of the nucleon wave function for the other octet baryon members, we make predictions for all the possible weak interaction axial form factors G_A(Q^2) and G_P(Q^2) of the octet baryons. The results are compared with the corresponding experimental data for G_A(0), and with the estimates of baryon-meson models based on SU(6) symmetry.

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