Transverse Helicity Amplitudes Research Articles

About the magnitude of the γ*N→N(1520) transverse amplitudes near Q2=0

The γ*N→N(1520) transition has a property that differs from the other low-lying nucleon resonance amplitudes: the magnitude of the transverse helicity amplitudes. The transition helicity amplitudes are defined in terms of square-transfer momentum q2, or Q2=−q2. Near the photon point (Q2=0) there is a significant difference in the magnitude of the transverse amplitudes: A3/2 is very large and A1/2 is very small. This atypical behavior contrasts with the relation between the amplitudes at the pseudothreshold [the limit where the nucleon and the N(1520) are both at rest and Q2<0], where A3/2=A1/2/3, and also in the large-Q2 region, where theory and data suggest that A3/2 is suppressed relative to A1/2. In the present work, we look for the source of the suppression of the A1/2 amplitude at Q2=0. The result is easy to understand in first approximation, when we look into the relation between the transverse amplitudes and the elementary form factors, defined by a gauge-invariant parametrization of the γ*N→N(1520) transition current, near Q2=0. There is a partial cancellation between contributions of two elementary form factors near Q2=0. We conclude, however, that the correlation between the two elementary form factors at Q2=0 is not sufficient to explain the transverse amplitude data below Q2=1 GeV2. The description of the dependence of the transverse amplitudes on Q2 requires the determination of the scale of variation of the elementary form factors in the range Q2=0…0.5 GeV2, a region with almost nonexistent data. We conclude at the end that the low-Q2 data for the transverse amplitudes can be well described when we relate the scale of variation of the elementary form factors with the nucleon dipole form factor. Published by the American Physical Society 2024

Analytical investigation of γN→N*,Δ* transition helicity amplitudes

We study the structure of nonstrange baryons by analytically calculating the electromagnetic transition helicity amplitudes of the nucleon and Δ resonances. We employ an improved hypercentral constituent quark model and obtain the corresponding eigenenergies and eigenfunctions in closed forms. Then, we calculate the transverse and longitudinal helicity amplitudes for nucleon and Δ resonances. The comparison of evaluated observables and experimental data indicates good agreement between the proposed model and available data.

Analytical investigation of electromagnetic transition form factors of nucleon resonances

In this paper, we investigated the transition form factors of nucleon resonances, in an analytical approach. Employing an improved hypercentral constituent quark model, we obtained analytical eigenfunctions which have been used to calculate the transverse and longitudinal helicity amplitudes for nucleon resonances. We compared the evaluated observables with experimental data and it has been shown that the present model provides a good description of the available data.

Electromagnetic Coupling of Negative Parity Nucleon Resonances N (1535) Based on Nonrelativistic Constituent Quark Model

The electromagnetic transition between the nucleon and excited baryons has long been recognized as an important source of information for understanding strong interactions in the domain of quark confinement. We study the electromagnetic properties of the excitation of the negative parity the N*(1535) resonances in the nonrelativistic constituent quark model at large momentum transfers and have performed a calculation the longitudinal and transverse helicity amplitudes. Since the helicity amplitudes depend strongly on the quark wave function in this paper, we consider the baryon as a simple, non-relativistically three-body quark model and also consider a hypercentral potential scheme for the internal baryon structure, which makes three-body forces among three quarks. Since the hyper central potential depends only on the hyper radius, therefore, the Cornell potential which is a combination of the Coulombic-like term plus a linear confining term is considered as the potential for interaction between quarks. In our work, in solving the Schrodinger equation with the Cornell potential, the Nikiforov–Uvarov method employed, and the analytic eigen-energies and eigen-functions obtained. By using the obtained eigen-functions, the transition amplitudes calculated. We show that our results in the range lead to an overall better agreement with the experimental data in comparison with the other three non-relativistic quark models.

Electromagnetic transitions of the Roper resonance $\gamma^{\ast} p \rightarrow p_{11}(1440)$ γ * p → p 11 ( 1440 ) within the nonrelativistic quark model

The Roper resonance, or ( $ \gamma^{\ast}p \rightarrow p_{11} (1440)$ ), is the lowest excited state of the nucleon. We study the scalar and transverse helicity amplitudes for the electroexcitation of the Roper resonance and obtain the $ Q^{2}$ dependence of the helicity amplitudes of the Roper resonance. The helicity amplitudes depend strongly on the quark wave function. In this paper, we consider the baryon as a simple, nonrelativistic three-body quark model and we also consider a hypercentral potential scheme for the internal baryon structure which makes three-body forces among three quarks. The hypercentral potential depends only on the hyperradius which itself is a function of Jacobi relative coordinates that are functions of particle positions ( $ r_{1}$ , $ r_{2}$ , and $ r_{3}$ ). For this purpose, the Cornell potential is regarded as a combination of the Coulombic-like term plus a linear confining term in our work. In solving the Schrodinger equation with the Cornell potential, the Nikiforov-Uvarov (NU) method is employed, and the analytic eigenenergies and eigenfunctions are obtained. By using the obtained eigenfunctions, the transition amplitudes are calculated. Presenting our results in the range $ 0\le Q^{2} (GeV^{2}) \le 5$ in comparison with the predictions obtained in other non-relativistic quark models, our results lead to an overall better agreement with the experimental data, especially in the medium $ Q^{2}$ range.

Effects of a spin-flavour-dependent interaction on light-flavoured baryon helicity amplitudes

This paper is a continuation of a previous work about the effects of a phenomenological flavour-dependent force in a relativistically covariant constituent quark model based on the Salpeter equation on the structure of light-flavoured baryon resonances. Here the longitudinal and transverse helicity amplitudes as studied experimentally in the electro-excitation of nucleon- and Δ-resonances are calculated. In particular the amplitudes for the excitation of three- and four-star resonances as calculated in a previous model A are compared to those of the novel model C as well as to existing and partially new experimental data such as, e.g., determined by the CB-ELSA Collaboration. A brief discussion on some improvements to model C is given after the introduction.

Systematic study of longitudinal and transverse helicity amplitudes in the hypercentral constituent quark model

We report in a systematic way the predictions of the non-relativistic hypercentral Constituent Quark model for the electromagnetic excitations of baryon resonances. The longitudinal and transverse helicity amplitudes are calculated with no free parameters for fourteen resonances, both for proton and neutron. The calculations lead to an overall fair description of data, specially in the medium $Q^2$ range, where quark degrees of freedom are expected to dominate.

Electroexcitation of nucleon resonances from CLAS data on single pion electroproduction

We present results on the electroexcitation of the low mass resonances Delta(1232)P33, N(1440)P11, N(1520)D13, and N(1535)S11 in a wide range of Q2. The results were obtained in the comprehensive analysis of JLab-CLAS data on differential cross sections, longitudinally polarized beam asymmetries, and longitudinal target and beam-target asymmetries for pion electroproduction off the proton. The data were analysed using two conceptually different approaches, fixed-t dispersion relations and a unitary isobar model, allowing us to draw conclusions on the model sensitivity of the obtained electrocoupling amplitudes. The amplitudes for the Delta(1232)P33} show the importance of a meson-cloud contribution to quantitatively explain the magnetic dipole strength, as well as the electric and scalar quadrupole transitions. They do not show any tendency of approaching the pQCD regime for Q2<6 GeV2. For the Roper resonance, N(1440)P11, the data provide strong evidence for this state as a predominantly radial excitation of a 3-quark ground state. Measured in pion electroproduction, the transverse helicity amplitude for the N(1535)S11 allowed us to obtain the branching ratios of this state to the piN and etaN channels via comparison to the results extracted from eta electroproduction. The extensive CLAS data also enabled the extraction of the gamma*p -> N(1520)D13 and N(1535)S11 longitudinal helicity amplitudes with good precision.

Hadronic B decays in the MSSM with large tan β

We present an analysis of non-leptonic B decays in the minimally flavour-violating MSSM with large tan β. We relate the Wilson coefficients of the relevant hadronic scalar operators to leptonic observables, showing that the present limits on the B s →μ + μ − and B +→τ + ν τ branching fractions exclude any visible effect in hadronic decays. We study the transverse helicity amplitudes of B→VV decays, which exhibit an enhanced sensitivity to the scalar operators, showing that even though an order one modification relative to the SM is not excluded in some of these amplitudes, they are too small to be detected at B factories.

Electroexcitation of the Roper resonance for1.7&lt;Q2&lt;4.5GeV2ine→p→enπ+

The helicity amplitudes of the electroexcitation of the Roper resonance are extracted for 1.7<Q2<4.5GeV2 from recent high precision JLab-CLAS cross section and longitudinally polarized beam asymmetry data for π+ electroproduction on protons at W=1.15−1.69 GeV. The analysis is made using two approaches, dispersion relations and a unitary isobar model, which give consistent Q2 behavior of the helicity amplitudes for the γ*p→N(1440)P11 transition. It is found that the transverse helicity amplitude A1/2, which is large and negative at Q2=0, becomes large and positive at Q2≃2GeV2, and then drops slowly with Q2. The longitudinal helicity amplitude S1/2, which was previously found from CLAS e→p→epπ0,enπ+ data to be large and positive at Q2=0.4,0.65GeV2, drops with Q2. Available model predictions for γ*p→N(1440)P11 allow us to conclude that these results provide strong evidence in favor of N(1440)P11 as a first radial excitation of the 3q ground state. The results of the present paper also confirm the conclusion of our previous analysis for Q2<1 GeV2 that the presentation of N(1440)P11 as a qG3 hybrid state is ruled out.Received 3 April 2008DOI:https://doi.org/10.1103/PhysRevC.78.045209©2008 American Physical Society

Unitary isobar model --MAID2007

The unitary isobar model MAID2007 has been developed to analyze the world data of pion photo- and electroproduction. The model contains both a common background and several resonance terms. The background is unitarized according to the K-matrix prescription, and the 13 four-star resonances with masses below 2 GeV are described by appropriately unitarized Breit-Wigner forms. The data have been analyzed by both single-energy and global fits, and the transverse and longitudinal helicity amplitudes have been extracted for the four-star resonances below 2 GeV. Because of its inherent simplicity, MAID2007 is well adopted for predictions and analysis of the observables in pion photo- and electroproduction.

Factorization inB→Kπℓ+ℓ−decays

We derive factorization relations for the transverse helicity amplitudes in $B\ensuremath{\rightarrow}K\ensuremath{\pi}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ at leading order in $\ensuremath{\Lambda}/{m}_{b}$, in the kinematical region with an energetic kaon and a soft pion. We identify and compute a new contribution of leading order in $\ensuremath{\Lambda}/{m}_{b}$ to the $B\ensuremath{\rightarrow}K\ensuremath{\pi}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ amplitude which is not present in the one-body decay $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$. As an application we study the forward-backward asymmetry (FBA) of the lepton momentum angular distribution in $B\ensuremath{\rightarrow}K\ensuremath{\pi}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ decays on and off the ${K}^{*}$ resonance. The FBA in these decays has a zero at ${q}_{0}^{2}={q}_{0}^{2}({M}_{K\ensuremath{\pi}})$, which can be used, in principle, for determining the Wilson coefficients ${C}_{7,9}$ and testing the standard model. We point out that the slope of the ${q}_{0}^{2}({M}_{K\ensuremath{\pi}}^{2})$ curve contains the same information about the Wilson coefficients as the location of the zero, but is less sensitive to unknown nonperturbative dynamics. We estimate the location of the zero at leading order in factorization, and using a resonant model for the $B\ensuremath{\rightarrow}K\ensuremath{\pi}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ nonfactorizable amplitude.

Enhanced Electroweak Penguin Amplitude inB→VVDecays

We discuss a novel electromagnetic penguin contribution to the transverse helicity amplitudes in B decays to two vector mesons, which is enhanced by two powers of mB/Lambda relative to the standard penguin amplitudes. This leads to unique polarization signatures in penguin-dominated decay modes such as B-->rhoK* similar to polarization effects in the radiative decay B-->K*gamma and offers new opportunities to probe the magnitude and chirality of flavor-changing neutral current couplings to photons.

Electromagnetic nucleon-delta transition in the perturbative chiral quark model

We apply the perturbative chiral quark model to the gamma N -> Delta transition. The four momentum dependence of the respective transverse helicity amplitudes A(1/2) and A(3/2) is determined at one loop in the pseudoscalar Goldstone boson fluctuations. Inclusion of excited states in the quark propagator is shown to result in a reasonable description of the experimental values for the helicity amplitudes at the real photon point.

Exchange currents in nucleon electroexcitation

We calculate the scalar and transverse helicity amplitudes for the electromagnetic excitation of nucleon resonances as a function of the photon four-momentum transfer. The helicity amplitudes are decomposed into electromagnetic multipoles and connected to the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}{N}^{*}$ transition form factors. The internal N and ${N}^{*}$ dynamics is described by a constituent quark model (CQM) Hamiltonian with gluon, pion, and $\ensuremath{\sigma}$-meson exchange potentials as residual interactions. The N and ${N}^{*}$-resonance wave functions are obtained by solving the Schr\odinger equation in a harmonic oscillator basis which contains up to $N=2$ excitation quanta. For the electromagnetic current we include, in addition to the one-body current, two-body exchange currents associated with the quark-quark potentials. Exchange currents provide an effective description of the cloud of $q\overline{q}$ pairs, which together with the valence quarks are important degrees of freedom in physical hadrons. We obtain sizable contributions of the two-body exchange currents for nearly all $\ensuremath{\gamma}{\mathrm{NN}}^{*}$ amplitudes. For some observables, e.g., the $C2/M1$ ratio in the $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\Delta}(1232)$ transition, and the $M1$ transition to the ${N}^{*}(1440),$ exchange currents provide the most important contribution.

Role of theD13(1520)resonance inηelectroproduction

We investigate the electroproduction of eta mesons below a center of momentum energy of 1.6 GeV, with particular emphasis on the roles of the N*(1535) and N*(1520) resonances. Using the effective Lagrangian approach, we show that the transverse helicity amplitude of the N*(1535) can be extracted with good accuracy from the new eta electroproduction data, under reasonable assumptions for the strength of the longitudinal helicity amplitude. In addition, although the differential cross section is found to to have a small sensitivity to the N*(1520) resonance, it is shown that a recently completed double polarization experiment is very sensitive to this resonance.

Estimates for forward-backward asymmetry in [formula omitted

Forward-backward charge asymmetry in rare dilepton B-decays is formulated with the assumption of an on-shell b-quark. We find that the asymmetry is expressed in terms of two spatially transverse helicity amplitudes, which are determined by combining the data of D → K ∗ (892) l +ν with heavy flavour symmetry. We estimate the charge asymmetry of B → K ∗ (892) l +l − for large energy leptons against various top masses in the standard model.

Electroproduction of the Roper resonance as a hybrid state.

We derive the ${\mathit{Q}}^{2}$ dependence of the helicity amplitudes of the Roper resonance assuming that it is (1) a radially excited ${\mathit{q}}^{3}$ state, and (2) a ${\mathit{q}}^{3}$G hybrid baryon. Our study shows that for a hybrid baryon assignment the magnitude of the transverse helicity amplitude decreases rapidly as ${\mathit{Q}}^{2}$ increases, and the longitudinal helicity amplitude vanishes. This behavior is quite different from the predictions of the ${\mathit{q}}^{3}$ quark potential model, which assumes a radially excited ${\mathit{q}}^{3}$ assignment. Comparison with data shows that the hybrid interpretation of the Roper resonance is favored. Future experiments at the Continuous Electron Beam Accelerator Facility should be able to clearly distinguish between these two possible assignments.