Without any further adjusting of parameters, a relativistic constituent quark model, successful in the description of the data for the nucleon elastic form factors and of the dominant contribution for the nucleon to Delta electromagnetic transition, is used here to predict the dominant electromagnetic form factors of the Delta baryon. The model is based on a simple Delta wave function corresponding to a quark-diquark system in an S-state. The results for E0 and M1 are consistent both with experimental results and lattice calculations. The remaining form factors E2 and M3 vanish, given the symmetric structure taken for the Delta.
We develop a methodology that enables us to extract accurately the electromagnetic Delta form factors and their momentum dependence. We test our approach in the quenched approximation as a preparation for a study using dynamical fermions. Our calculation of the four form factors covers pion masses between about 410 MeV and 560 MeV on lattices with a size of 2.9 fm and a lattice spacing 0.09 fm. From the form factors we are able to obtain estimates of the magnetic moment and the charge radius of the Delta, which we compare to existing experimental and theoretical results.Our non-zero result for…
We investigate the electromagnetic form factors of the Delta and the Omega baryons within the Poincare-covariant framework of Dyson-Schwinger and Bethe-Salpeter equations. The three-quark core contributions of the form factors are evaluated by employing a quark-diquark approximation. We use a consistent setup for the quark-gluon dressing, the quark-quark bound-state kernel and the quark-photon interaction. Our predictions for the multipole form factors are compatible with available experimental data and quark-model estimates. The current-quark mass evolution of the static electromagnetic prope…
Lattice results on the N to Delta electromagnetic, axial-vector and pseudoscalar form factors are evaluated using dynamical staggered sea quarks and domain wall valence quarks for pion masses in the range of 580-350 MeV, as well as, dynamical and quenched Wilson fermions for similar pion masses.
The C2/M1 ratio of the electromagnetic N->Delta(1232) transition, which is important for determining the geometric shape of the nucleon, is shown to be related to the neutron elastic form factor ratio G_C^n/G_M^n. The proposed relation holds with good accuracy for the entire range of momentum transfers where data are available.
The electromagnetic form factors of the Delta baryon are evaluated within the framework of a covariant spectator quark model, where S and D-states are included in the $Δ$ wave function. We predict all the four Delta multipole form factors: the electric charge GE0, the magnetic dipole GM1, the electric quadrupole GE2 and the magnetic octupole GM3. We compare our predictions with other theoretical calculations. Our results are compatible with the available experimental data and recent lattice QCD data.
We perform a relativistic chiral effective-field theory calculation of the pion electroproduction off the nucleon ($e^- N \to e^- N π$) in the Delta(1232)-resonance region. After fixing the three low-energy constants, corresponding to the magnetic (M1), electric (E2), and Coulomb (C2) $γNΔ$ couplings, our calculation provides a prediction for the momentum-transfer and pion-mass dependence of the $γNΔ$ form factors. The prediction for the pion-mass dependence resolves the discrepancy between the recent lattice QCD results and the experimental value for the "C2/M1 ratio" at low $Q^2$.
We study the N-Delta-gamma transition in the Dyson-Schwinger approach. The nucleon and Delta baryons are treated as quark-diquark bound states, where the ingredients of the electromagnetic transition current are computed self-consistently from the underlying dynamics in QCD. Although our approach does not include pion-cloud effects, we find that the electric and Coulomb quadrupole form-factor ratios R_EM and R_SM show good agreement with experimental data. This implies that the deformation from a spherical charge distribution inside both baryons can be traced back to the appearance of p waves …
We discuss the techniques to extract the electromagnetic Delta form factors in Lattice QCD. We evaluate these form factors using dynamical fermions with smallest pion mass of about 350 MeV. We pay particular attention to the extraction of the electric quadrupole form factor that signals a deformation of the Delta. The magnetic moment of the $Δ$ is extrapolated using a chiral effective field theory. Using the form factors we evaluate the transverse density distributions in the infinite momentum frame showing deformation in the Delta.
A relativistic quark model and a new set of wave functions of nucleon and Delta have been used to study the electromagnetic propertities of (1/2)^+ baryons and photoelectric production of Delta(1236).
We study nucleon-to-delta electromagnetic transition form factors and relations between them within the framework of holographic dual model of QCD proposed by Sakai and Sugimoto. In this setup, baryons appear as topological solitons of the five dimensional holographic gauge theory that describes a tower of mesons and their interactions. We find a relativistic extension of the nucleon-delta-vector meson interaction vertices and use these to calculate transition form factors from holographic QCD. We observe that at low momentum transfer, magnetic dipole, electric and Coulomb quadrupole form fact…
The inclusion of two-body exchange currents in the constituent quark model leads to several new relations between the electromagnetic form factors of the nucleon and Delta(1232). These are:(i) the neutron charge form factor can be expressed as the difference between proton and Delta+ charge form factors, and (ii) the N->Delta charge quadrupole (C2) transition form factor is connected to the charge monopole (C0) form factor of the neutron. The latter relation is used to estimate the charge radius of constituent quarks. Furthermore, we find that exchange currents do not modify the SU(6) relation…
In kaon decay, electromagnetic radiative corrections can generate shifts in the apparent Delta I = 3/2 amplitude of order alpha A_0/A_2 ~ 22 alpha. In order to know the true Delta I = 3/2 amplitude for comparison with lattice calculations and phenomenology, one needs to subtract off this electromagnetic effect. We provide a careful estimate of the electromagnetic shift in the amplitude, which shows that it is smaller than naive expectations, with a fractional shift of delta A_2/A_2 = -0.016 +- 0.01.
We discuss the chiral behavior of nucleon and Delta(1232) electromagnetic properties within the framework of a SU(2) covariant baryon chiral perturbation theory. Our one-loop calculation is complete to the order p^3 and p^4/Delta with Delta as the Delta(1232)-nucleon energy gap. We show that the magnetic moment of a resonance can be defined through the linear energy shift only when an additional relation between the involved masses and the applied magnetic field strength is fulfilled. Singularities and cusps in the pion mass dependence of the Delta(1232) electromagnetic moments reflect a non-f…
We present a calculation of the three-quark core contribution to nucleon and Delta-baryon masses and Delta electromagnetic form factors in a Poincare-covariant Faddeev approach. A consistent setup for the dressed-quark propagator, the quark-quark, quark-'diquark' and quark-photon interactions is employed, where all ingredients are solutions of their respective Dyson-Schwinger or Bethe-Salpeter equations in a rainbow-ladder truncation. The resulting Delta electromagnetic form factors concur with present experimental and lattice data.
We study baryons as three-body systems using the QCD degrees of freedom in the framework of covariant Bethe-Salpeter equations. The interaction among quarks is reduced to a vector-vector interaction via a single dressed-gluon exchange (Rainbow-Ladder truncation). The formalism allows for the study of the hadron spectrum as well as their internal properties. We will present the calculation of electromagnetic properties of spin-3/2 baryons. The model independent features of our results are assessed using two different models for the dressings.
We examine the electromagnetic properties of the Delta(1232) resonance within the self-consistent chiral quark-soliton model. In particular we present the Delta form factors of the vector-current GE0, GE2 and GM1 for a momentum-transfer range of $Q^{2} \leq 1GeV^{2}$. We apply the symmetry-conserving quantization of the soliton and take 1/N_c rotational corrections into account. Values for the magnetic moments of all decuplet baryons as well as for the N-Delta transition are given. Special interest is also given to the electric quadrupole moment of the Delta.
The electromagnetic form factors of the Delta and Omega baryons are calculated in the framework of Poincare-covariant bound-state equations. The quark-quark interaction is truncated to a single dressed-gluon exchange where for the dressings we use two different models and compare the results. The calculation predicts an oblate shape for the electric charge distribution and a prolate shape for the magnetic dipole distribution. We also identify the necessity of including pion-cloud corrections at low photon-momentum transfer.
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.
We review the description of the lowest-energy nucleon excitation -- the $Δ$(1232)-resonance. Much of the recent experimental effort has been focused on the precision measurements of the nucleon-to-$Δ$ transition by means of electromagnetic probes. We confront the results of these measuremnts with the state-of-the-art calculations based on chiral effective-field theories (EFT), lattice QCD, large-$N_c$ relations, perturbative QCD, and QCD-inspired models. We also discuss the link of the nucleon-to-$Δ$ form factors to generalized parton distributions (GPDs). Some of the theoretical approaches a…
An expansion of the electromagnetic form factors of the nucleon and Delta(1232) in small momentum transfer and pion mass is performed in a manifestly-covariant EFT framework consistent with chiral symmetry and analyticity. We present the expressions for the nucleon and Delta(1232) electromagnetic form factors, charge radii, and electromagnetic moments in the framework of SU(2) baryon chiral perturbation theory, with nucleon and Delta(1232)-isobar degrees of freedom, to next-to-leading order. Motivated by the results for the proton electric radius obtained from the muonic-hydrogen atom and elec…
Relations between nucleon, $Δ$ and nucleon-$Δ$ electromagnetic properties associated with chiral physics which have been derived in a pure large-$N_c$ limit are greatly modified in a combined large $N_c$ and chiral limits; the large $N_c$ relations are valid for $(M_Δ-M_N)/m_π<<1$. The E2/M1 ratio for the nucleon-$Δ$ transition is shown to scale as $ε^{-1}$ (with $ε\sim 1/N_c$, $ε\sim m_π/Λ$ with $Λ$ a typical hadronic scale) in the combined large $N_c$ and chiral expansions as opposed to $N_c^{-2}$ in the pure large $N_c$ expansion.
We examine the large-$N_c$ relations which express the electromagnetic $N$-to-$Δ$ transition quantities in terms of the electromagnetic properties of the nucleon. These relations are based on the known large-$N_c$ relation between the $N\to Δ$ electric quadrupole moment and the neutron charge radius, and a newly derived large-$N_c$ relation between the electric quadrupole ($E2$) and Coulomb quadrupole ($C2$) transitions. Extending these relations to finite, but small, momentum transfer we find that the description of the electromagnetic $N\toΔ$ ratios ($R_{EM}$ and $R_{SM}$) in terms of the nu…
We consider here a manifestly covariant quark model of the nucleon and the Delta, where one quark is off-shell and the other two quarks form an on-shell diquark pair. Using this model, we have shown previously that the nucleon form factors and the dominant form factor for the gamma N -> Delta transition (the magnetic dipole (M1) form factor) can be well described by nucleon and Delta wave functions with S-state components only. In this paper we show that non-vanishing results for the small electric (E2) and Coulomb (C2) quadrupole form factors can be obtained if D-state components are added to…
The three electromagnetic form factors of the $Δ(1232)$ resonance, $G^*_M(q^2)$, $G^*_E(q^2)$, and $G^*_C(q^2)$ are obtained in the space-like region using a Dual Resonance Model realization of QCD in the large $N_c$ limit (Dual-${QCD}_{\infty}$). Each form factor involves a single free parameter which is fixed by fitting data on $G^*_M(q^2)$, and on the ratios $R_{EM}(q^2)$ and $R_{SM}(q^2)$. Good agreement with experiment is obtained for all three quantities. Results are then used to predict the $q^2$-dependence of the chiral effective-field theory form factors $g_M(q^2)$, $g_E(q^2)$, and $g…
A covariant quark model, based both on the spectator formalism and on vector meson dominance, and previously calibrated by the physical data, is here extended to the unphysical region of the lattice data by means of one single extra adjustable parameter - the constituent quark mass in the chiral limit. We calculated the Nucleon (N) and the gamma N -> Delta form factors in the universe of values for that parameter described by quenched lattice QCD. A qualitative description of the Nucleon and gamma N -> Delta form factors lattice data is achieved for light pions.
We extend a covariant model, tested before in the spacelike region for the physical and lattice QCD regimes, to a calculation of the gamma* N -> Delta reaction in the timelike region, where the square of the transfered momentum, q^2, is positive (q^2>0). We estimate the Dalitz decay Delta -> Ne+e- and the Delta distribution mass distribution function. The results presented here can be used to simulate the NN -> NNe+e- reactions at moderate beam kinetic energies.
We study the momentum and the quark mass dependence of the axial nucleon to Delta(1232) transition form factors in the framework of non-relativistic chiral effective field theory to leading-one-loop order. The outcome of our analysis provides a theoretical guidance for chiral extrapolations of lattice QCD results with dynamical fermions.
We evaluate the N to Delta axial transition form factors in lattice QCD in the quenched theory, with two degenerate flavors of dynamical Wilson fermions and using domain wall valence fermions with staggered sea quark configurations. We predict the ratio $C_5^A(q^2)/C_3^V(q^2)$ relevant to the parity violating asymmetry and check the validity of the off-diagonal Goldberger-Treiman relation.
Within the dynamical model of Refs. [Phys. Rev. C54, 2660 (1996); C63, 055201 (2001)], we perform an analysis of recent data of pion electroproduction reactions at energies near the Delta(1232) resonance. We discuss possible interpretations of the extracted bare and dressed gamma N --> Delta form factors in terms of relativistic constituent quark models and Lattice QCD calculations. Possible future developments are discussed.
Information on the intrinsic deformation of the proton can be obtained by studying the electromagnetic p-->Delta+ quadrupole transition. Recent experiments have shown that the electric quadrupole (E2) strength in gamma p --> Delta+ is about 10 times larger than predicted by the simple quark model using only one-body currents. Our analysis provides evidence for the dominance of exchange currents in the N-->Delta quadrupole transition and identifies the physical mechanism leading to the observed E2 strength.
The N to Delta transition form factors GM1, GE2 and GC2 are evaluated using dynamical MILC configurations and valence domain wall fermions at three values of quark mass corresponding to pion mass 606 MeV, 502 MeV and 364 MeV on lattices of spatial size $20^3$ and $28^3$. The unquenched results are compared to those obtained at similar pion mass in the quenched theory.
We investigate the axial-vector nucleon-to-delta transition form factors in the framework of relativistic baryon chiral perturbation theory at the one-loop order using the complex-mass renormalization scheme. We determine the available six free parameters by fitting to an empirical parametrization of the form factors obtained from the BNL neutrino bubble chamber experiments. A unique feature of our calculation is the prediction of a non-vanishing form factor $C_3^A(Q^2)$. Moreover, our results show a surprising sensitivity to the coupling constant $\texttt{g}_1$ of the leading-order Lagrangian…
We present a coupled system of integral equations for the pi pi --> Nbar N and Kbar K --> Nbar N S-waves derived from Roy-Steiner equations for pion-nucleon scattering. We discuss the solution of the corresponding two-channel Muskhelishvili-Omnes problem and apply the results to a dispersive analysis of the scalar form factor of the nucleon fully including Kbar K intermediate states. In particular, we determine the corrections Delta_sigma and Delta_D, which are needed for the extraction of the pion-nucleon sigma term from pi N scattering, and show that the difference Delta_D - Delta_sigma=(-1.…
We investigate the model dependence and the importance of choice of database in extracting the {\it physical} nucleon-Delta(1232) electromagnetic transition amplitudes, of interest to QCD and baryon structure, from the pion photoproduction observables. The model dependence is found to be much smaller than the range of values obtained when different datasets are fitted. In addition, some inconsistencies in the current database are discovered, and their affect on the extracted transition amplitudes is discussed.
Recent data allow a new parametrization of the neutron charge form factor G_En. A parameter-free quark model relation between G_En and the N->Delta quadrupole form factor is used to predict the latter from the G_En data. In particular, the neutron charge radius is related to N->Delta quadrupole moment, while the fourth moment of G_En connects to the N->Delta quadrupole transition radius. From the latter we derive an experimental value for the charge radius of the light constituent quarks. Finally, the C2/M1 ratio in pion electroproduction is predicted from the elastic neutron form factor data.
The non-perturbative renormalization of four-quark operators plays a significant role in lattice studies of flavor physics. For this purpose, we define regularization-independent symmetric momentum-subtraction (RI/SMOM) schemes for Delta S=1 flavor-changing four-quark operators and provide one-loop matching factors to the MS-bar scheme in naive dimensional regularization. The mixing of two-quark operators is discussed in terms of two different classes of schemes. We provide a compact expression for the finite one-loop amplitudes which allows for a straightforward definition of further RI/SMOM …
We calculate the form factors of the electromagnetic nucleon-to-$Δ$-resonance transition to third chiral order in manifestly Lorentz-invariant chiral effective field theory. For the purpose of generating a systematic power counting, the complex-mass scheme is applied in combination with the small-scale expansion. We fit the results to available empirical data.
The leading one-loop corrections to the gravitational form factors of the delta resonance are calculated in the framework of chiral effective field theory. Various contributions to the energy-momentum tensor and the renormalization of the low-energy constants are worked out. Using the small scale expansion, expressions for static quantities are obtained and the real and imaginary parts of the gravitational form factors are calculated numerically.
For more than 50 years the Delta N gamma form factors have been studied experimentally, theoretically, and phenomenologically. Although there has been substantial progress in understanding their behavior, there remains much work to be done. A major tool used in many investigations is the Jones-Scadron Delta rest frame parametrization of the three Delta N gamma form factors. We point out that many studies utilizing this parametrization may not account for Wigner rotations and the consequent helicity mixing that ensues when the Delta is not at rest.
We consider the QCD sum rules approach for Delta-isobar magnetic form factor in the infra-red region $0<Q^2<1GeV^2$. The QCD sum rules in external variable field are used. The obtained formfactor is in agreement with quark model predictions for the Delta-isobar magnetic moment.
We consider the electromagnetic transition form factors of the Roper resonance in the framework of an effective field theory of pions, nucleons and delta and Roper resonances as explicit degrees of freedom. Due to the lack experimental data in the region of applicability of low energy effective field theory we fit available free coupling constants and compare obtained results compare to the predictions of a theoretical model.
It is suggested that the falloff in Qsq of the P to Delta magnetic form factor GM* is related to the recently observed falloff of the elastic electric form factor GEp/GMp. Calculation is carried out in the framework of a GPD mechanism.
We develop a formally covariant quark-diquark model of the nucleon. The nucleon is treated as a bound state of a constituent quark and a diquark interacting via a quark exchange. We include both scalar and axial-vector diquarks. The underlying Bethe-Salpeter equation is transformed into a pair of coupled Salpeter equations. The space- and timelike electromagnetic form factors of the nucleon are calculated in the Mandelstam formalism for squared momentum transfers up to 3 (GeV/c)^2 above threshold. The model is applied also to the Delta(3/2).
The axial N-> Delta(1232) transition form factors are calculated within the light cone QCD sum rules method. A comparison of our results with predictions of lattice theory and quark model calculations is pre- sented.
We utilize a light-front relativistic quark model (LF RQM) to predict the 3q core contribution to the electroexcitation amplitudes for the Delta(1232)P33, N(1440)P11, N(1520)D13, and N(1535)S11 up to Q2= 12GeV2. The parameters of the model have been specified via description of the nucleon electromagnetic form factors in the approach that combines 3q and pion-cloud contributions in the LF dynamics.
Recent progress on the extraction of electromagnetic properties of nucleon resonance excitation through pion photo- and electroproduction is reviewed. Cross section data measured at MAMI, ELSA, and CEBAF are analyzed and compared to the analysis of other groups. On this basis, we derive longitudinal and transverse transition form factors for most of the four-star nucleon resonances. Furthermore, we discuss how the transition form factors can be used to obtain empirical transverse charge densities. Contour plots of the thus derived densities are shown for the Delta, Roper, S11, and D13 nucleon …
The N-Delta axial form factors are determined from neutrino induced pion production ANL & BNL data by using a state of the art theoretical model, which accounts both for background mechanisms and deuteron effects. We find violations of the off diagonal Goldberger-Treiman relation at the level of 2 sigma which might have an impact in background calculations for T2K and MiniBooNE low energy neutrino oscillation precision experiments.
We report a theoretical study of the axial Nucleon to Delta(1232) ($N\toΔ$) transition form factors up to one-loop order in relativistic baryon chiral perturbation theory. We adopt a formalism in which the $Δ$ couplings obey the spin-3/2 gauge symmetry and, therefore, decouple the unphysical spin-1/2 fields. We compare the results with phenomenological form factors obtained from neutrino bubble chamber data and in quark models.
Recently we considered the electromagnetic decays of the orbitally-excited SU(6) 70-plet baryons in large-N_c QCD, fitting to the helicity amplitudes measured in photoproduction experiments. Using the results of this analysis, we predict the helicity amplitudes for the decays N^* \to Δγand Δ^* \to Δγ. These decays can be studied at a number of new experimental facilities, and thus provide another nontrivial test of the lowest order large-N_c predictions.
We review some basic properties of the N-Delta transition axial amplitudes and relate them to the strong pi-N-Delta form-factor. In models with the pion cloud we derive a set of constraints on the pion wave function which guaranty the correct behaviour of the amplitudes in the vicinity of the pion pole. Corrections due to the spurious center-of-mass motion are calculated to the leading order in the inverse baryon mass. We give explicit expressions for the amplitudes in the Cloudy Bag Model and show that they rather strongly underestimate the experimental values.
The γ* N -> Δ(1232) transition is a window on hadron shape deformation, the applicability of perturbative QCD at moderate momentum transfers, and the influence of nonperturbative phenomena on hadronic observables. We explain that the Ash-convention magnetic transition form factor must fall faster than the neutron's magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and Δ(1232); and show that these quadrupole ratios do approach their predicted asymptotic limits, albeit slowly.
A theoretical framework is suggested for the calculation of gamma* N -> Delta transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the ``soft'' contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The ``minus'' components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular…
The three complex form factors entering the $Δ\to Nγ^\ast$ vertex are calculated to ${\cal O}(ε^3)$ in the framework of a chiral effective theory with explicit $Δ$(1232) degrees of freedom. Furthermore, the role of presently unknown low energy constants that affect the values of EMR and CMR is elucidated.
We compute the Omega- electromagnetic form factors and the decuplet baryon magnetic moments using a quark model application of the Covariant Spectator Theory. Our predictions for the Omega- electromagnetic form factors can be tested in the future by lattice QCD simulations at the physical strange quark mass.
The inclusion of two-body exchange currents in the constituent quark model leads to new relations between the electromagnetic properties of octet and decuplet baryons. In particular, the N->Delta quadrupole transition form factor can be expressed in terms of the neutron charge form factor.
We calculate magnetic moments of nucleons and hyperons and N -> Delta + gamma transition characteristics using a manifestly Lorentz covariant chiral quark approach for the study of baryons as bound states of constituent quarks dressed by a cloud of pseudoscalar mesons.
We present analytic formulae for the QCD renormalization group factors relating the Wilson coefficients C_i(mu_t) and C_i(mu), with mu_t = O(m_t) and mu < mu_t, of the Delta F=2 dimension six four-quark operators Q_i in the Standard Model and in all of its extensions. Analogous analytic formulae for the QCD factors relating the matrix elements <Q_i(2 GeV)> and <Q_i(mu_K)> with mu_K < 2GeV are also presented. The formulae are given in the NDR scheme. The strongest renormalization-group effects are found for the operators with the Dirac structures (1 - gamma_5)*(1 + gamma_5) and (1 - gamma_5)*(1…
The three complex form factors entering the $Δ\to Nγ^\ast$ vertex are calculated to ${\cal O}(ε^3)$ in the framework of a chiral effective theory with explicit Δ(1232) degrees of freedom included. It is shown that the low q^2 behavior of the form factors is governed by $πN$, $πΔ$ loop effects. Predictions are given for the q^2-dependence of the three transition-multipoles $M1(q^2), E2(q^2), C2(q^2)$. Furthermore, the role of presently unknown low energy constants that affect the values of the multipole ratios EMR(q^2) and CMR(q^2) is elucidated.
