We present estimates of the hyperon elastic form factors for the baryon octet and the $Ω^-$ baryon for large four-momentum transfer squared, $q^2$, in the timelike region ($q^2>0$). Experimentally, those form factors can be extracted from the $e^+ e^- \to B \bar B$ and $p \bar p \to B \bar B$ processes, where $B$ stands for a general baryon. Our results are based on calculations of the elastic electromagnetic form factors in the spacelike region ($Q^2 = - q^2 > 0$) within a covariant quark model. To connect the results in the spacelike region to those in the timelike region, we use asymptotic relations between the two regions which are constraints derived from analyticity and unitarity. We calculate the effective form factors $|G(q^2)|$ and compare them with the integrated cross section data $σ_{\rm Born} (q^2)$ from BaBar, BES III, and CLEO. The available data are at the moment restricted to $Λ$, $Σ^0$, $Σ^-$, $Ξ^-$, $Ξ^0$, and $Ω^-$ as well as to $e^+ e^- \to Λ\bar Σ^0 $ and $e^+ e^- \to Σ^0 \bar Λ$ reactions. Our results provide useful reference for future experiments and seem to indicate that the present data are still in the non-perturbative QCD region, while the onset for the asymptotic constraints from analyticity and unitarity happens much before the region of the perturbative QCD falloff of the form factors.
Electromagnetic form factors of hyperons ($Λ$, $Σ$, $Ξ$) in the timelike region, accessible in the reaction $e^+e^- \to \bar YY$, are studied. The focus is on energies close to the reaction thresholds, where the properties of these form factors are significantly influenced by the interaction in the final $\bar YY$ system. This interaction is taken into account in the calculation, utilizing $\bar YY$ potential models that have been constructed by the Jülich group for the analysis of data from the reaction $\bar pp \to \bar YY$ in the past. The enhancement of the effective form factor for energi…
Electric and magnetic timelike form factors of hyperons at large transfer momentum
Soongsil University（崇实大学）；LIP, Laboratório de Instrumentação e Física Experimental de Partículas（粒子物理实验仪器实验室）；Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术研究所）；Universidade Cidade de São Paulo（圣保罗城市大学）
A review of recent precision measurements of the electromagnetic form factors of the mesons, pion and kaon, and the hyperons, $Λ^0$, $Σ^0$, $Σ^+$, $Ξ^-$, $Ξ^0$, $Ω^-$, at large timelike momentum transfers is presented. Evidence is found for diquark correlations in $Λ^0$, $Σ^0$ hyperons.
We present a calculation of the electric and magnetic form factors of ground-state octet and decuplet baryons including strange quarks. We work with a combination of Dyson-Schwinger equations for the quark propagator and covariant Bethe-Salpeter equations describing baryons as bound states of three (non-perturbative) quarks. Our form factors for the octet baryons are in good agreement with corresponding lattice data at finite $Q^2$; deviations in some isospin channels for the magnetic moments can be explained by missing meson cloud effects. At larger $Q^2$ our quark core calculation has predic…
The quasielastic weak production of $Λ$ and $Σ$ hyperons from nucleons and nuclei induced by antineutrinos is studied in the energy region of some ongoing neutrino oscillation experiments in the intermediate energy region. The hyperon nucleon transition form factors determined from neutrino nucleon scattering and an analysis of high precision data on semileptonic decays of neutron and hyperons using SU(3) symmetry have been used. The nuclear effects due to Fermi motion and final state interaction effects due to hyperon nucleon scattering have also been studied. The numerical results for differ…
We study the electromagnetic form factors of $Λ$ hyperon in the timelike region using the recent experimental data in the exclusive production of $\barΛ Λ$ pair in electron-position annihilation. We present a pQCD inspired parametrization of $G_E(s)$ and $G_M(s)$ with only two parameters, and we consider a suppression mechanism of the electric form factor $G_E(s)$ compared to the magnetic form factor $G_M(s)$. The parameters are determined through fitting our parametrization to the effective form factor data in the reaction $e^+e^-\rightarrow \barΛΛ$. Except the threshold region, our parametri…
Even though the Drell-Yan-West formulation is the most rigorous and well-established framework to compute the exclusive processes, its utility has been limited only to the spacelike region because of the intrinsic kinematic constraint $q^+=0$. We present an explicit example demonstrating how one may obtain the necessary information (i.e. nonvalence or so called Z-graph contribution) in the timelike region of exclusive process without encountering a formidable task of direct calculation that has hindered so far the progress in this area. In the analysis of $q\bar{Q}$ bound state form factors us…
The three electromagnetic form factors for the transition from a 3/2+ Sigma* hyperon to the ground-state Lambda hyperon are studied. At low energies, combinations of the transition form factors can be deduced from Dalitz decays of the Sigma* hyperon to Lambda plus an electron-positron pair. It is pointed out how more information can be obtained with the help of the self-analyzing weak decay of the Lambda. In particular it is shown that these transition form factors are complex quantities already in this kinematical region. Such measurements are feasible at hyperon factories as for instance the…
We explore the structure of the spin-1/2 flavor-octet baryons (hyperons) through their electromagnetic transverse densities. The transverse densities describe the distribution of charge and magnetization at fixed light-front time and enable a spatial representation of the baryons as relativistic systems. At peripheral distances b~1/M_pi the transverse densities are computed using a new method that combines chiral effective field theory and dispersion analysis. The peripheral isovector densities arise from two-pion exchange, which includes the rho-meson resonance through elastic unitarity. The …
By the analysis of the world data base of elastic electron scattering on the proton and the neutron (for the latter, in fact, on $^2H$ and $^3He$) important experimental insights have recently been gained into the flavor compositions of nucleon electromagnetic form factors. We report on testing the Graz Goldstone-boson-exchange relativistic constituent-quark model in comparison to the flavor contents in low-energy nucleons, as revealed from electron-scattering phenomenology. It is found that a satisfactory agreement is achieved between theory and experiment for momentum transfers up to $Q^2\si…
We present complete calculations of the electromagnetic form factors of the $Ω^-$ in the spacelike region and in the timelike region. The four elastic form factors: electric charge ($G_{E0}$), magnetic dipole ($G_{M1}$), electric quadrupole ($G_{E2}$) and magnetic octupole ($G_{M3}$), are estimated within the covariant spectator quark model, in terms of the square momentum transfer $q^2$. The free parameters of the $Ω^-$ wave function, including a $S$-wave state and two independent $D$-wave states radial wave functions and the admixture coefficients are fixed by the comparison with the lattice…
We present results for the quasi-elastic weak production of $Λ$ and $Σ$ hyperons induced by $\barν$ scattering off nuclei, in the kinematical region of interest for accelerator neutrino experiments. We employ realistic hole spectral functions and we describe the propagation of the hyperons in the nuclear medium by means of a Monte Carlo cascade. The latter strongly modifies the kinematics and the relative production rates of the hyperons, leading to a non-vanishing $Σ^+$ cross section, to a sizable enhancement of the $Λ$ production and to a drastic reduction of the $Σ^0$ and $Σ^-$ distribution…
Using $e^+e^-$ annihilation data taken at the CESR collider with the CLEO-c detector, measurements of hyperon pair production cross sections and elastic and transition electromagnetic form factors have been made at the charmonium resonances: $ψ(2S)$, $\sqrt{s}=3.69$ GeV, $|Q^2|=13.6$ GeV$^2$, $\mathcal{L}=48$~pb$^{-1}$; $ψ(3770)$, $\sqrt{s}=3.77$ GeV, $|Q^2|=14.2$ GeV$^2$, $\mathcal{L}=805$~pb$^{-1}$; and $ψ(4170)$, $\sqrt{s}=4.17$ GeV, $|Q^2|=17.4$ GeV$^2$, $\mathcal{L}=586$~pb$^{-1}$. %High efficiency particle identification has resulted in good statistical precision in the results. Results …
We generalize a recent model-independent form factor parameterization derived from rigorous dispersion relations to include constraints from data in the timelike region. These constraints dictate the convergence properties of the parameterization and appear as sum rules on the parameters. We further develop a new parameterization that takes into account finiteness and asymptotic conditions on the form factor, and use it to fit to the elastic πelectromagnetic form factor. We find that the existing world sample of timelike data gives only loose bounds on the form factor in the spacelike region, …
Based on the recently measurements of the $e^{+} e^{-} \to Σ^{+} \barΣ^{-}$ and $e^{+} e^{-} \to Σ^{-} \barΣ^{+}$ processes, the electromagnetic form factors of the hyperon $Σ^+$ and $Σ^-$ in the timelike region are investigate by using the vector meson dominance model. We have included the contributions from the $ρ$, $ω$ and $ϕ$ mesons. The model parameters are determined with the BESIII experimental data on the timelike effective form factors $|G_{\rm eff}|$ of $Σ^{+}$ and $Σ^{-}$ for center-of-mass energy from 2.3864 to 3.02 GeV. Then, we analytically continue the electromagnetic form facto…
Motivated by the recent experimental measurements of differential cross sections of the $Σ^{-}p$ elastic scattering in the momentum range of $470$ to $850$ MeV$/c$ by the J-PARC E$40$ experiment, we extend our previous studies of $S=-1$ hyperon-nucleon interactions to relatively higher energies up to $900$ MeV$/c$ for both the coupled-channel $Λp\rightarrow(Λp, Σ^{+}n, Σ^{0}p)$, $Σ^{-}p\rightarrow(Λn, Σ^{0}n, Σ^{-}p)$ and single-channel $Σ^{+}p\rightarrowΣ^{+}p$ reactions. We show that although the leading order covariant chiral effective field theory is only constrained by the low energy data…
We investigate the electroweak form factors and semileptonic decay rates of mesons using the constituent quark model based on the light-front degrees of freedom. Our results demonstrate the broader applicability of light-front approach including the timelike region of exclusive processes.
The elastic $I=1$ $p$-wave $ππ$ scattering amplitude is calculated together with the isovector timelike pion form factor using lattice QCD with $N_{\rm f}=2+1$ dynamical quark flavors. Wilson clover ensembles generated by the Coordinated Lattice Simulations (CLS) initiative are employed at four lattice spacings down to $a = 0.05\,\mathrm{fm}$, several pion masses down to $m_π = 200\,\mathrm{MeV}$, and spatial volumes of extent $L = 3.1-5.5\,\mathrm{fm}$. The set of measurements on these ensembles, which is publicly available, enables an investigation of systematic errors due to the finite latt…
The recently evaluated two-pion contribution to the muon g-2 and the phase of the pion electromagnetic form factor in the elastic region, known from ππscattering by Fermi-Watson theorem, are exploited by analytic techniques for finding correlations between the coefficients of the Taylor expansion at t=0 and the values of the form factor at several points in the spacelike region. We do not use specific parametrizations and the results are fully independent of the unknown phase in the inelastic region. Using for instance, from recent determinations, <r^2_π> = (0.435 \pm 0.005) fm^2 and F(-1.6 Ge…
We study the nucleon electromagnetic form factors (EM FFs) using a recently developed method combining Chiral Effective Field Theory ($χ$EFT) and dispersion analysis. The spectral functions on the two-pion cut at $t > 4 M_π^2$ are constructed using the elastic unitarity relation and an $N/D$ representation. $χ$EFT is used to calculate the real functions $J_\pm^1 (t) = f_\pm^1(t)/F_π(t)$ (ratios of the complex $ππ\rightarrow N \bar N$ partial-wave amplitudes and the timelike pion FF), which are free of $ππ$ rescattering. Rescattering effects are included through the empirical timelike pion FF $…
We analyze the degree to which parity-violating (PV) electroexcitation of the $Δ(1232)$ resonance may be used to extract the weak neutral axial vector transition form factors. We find that the axial vector electroweak radiative corrections are large and theoretically uncertain, thereby modifying the nominal interpretation of the PV asymmetry in terms of the weak neutral form factors. We also show that, in contrast to the situation for elastic electron scattering, the axial $N\toΔ$ PV asymmetry does not vanish at the photon point as a consequence of a new term entering the radiative corrections…
We present a theoretical parametrization of the nucleon electromagnetic form factors (FFs) based on a combination of chiral effective field theory and dispersion analysis. The isovector spectral functions on the two-pion cut are computed using elastic unitarity, chiral pion-nucleon amplitudes, and timelike pion FF data. Higher-mass isovector and isoscalar t-channel states are described by effective poles, whose strength is fixed by sum rules (charges, radii). Excellent agreement with the spacelike proton and neutron FF data is achieved up to Q^2 \sim 1 GeV^2. Our parametrization provides prope…
We present a determination of the pion charge radius from high precision data on the pion vector form factor from both timelike and spacelike regions, using a novel formalism based on analyticity and unitarity. At low energies, instead of the poorly known modulus of the form factor, we use its phase, known with high accuracy from Roy equations for $ππ$ elastic scattering via the Fermi-Watson theorem. We use also the values of the modulus at several higher timelike energies, where the data from $e^+e^-$-annihilation and $τ$-decay are mutually consistent, as well as the most recent measurements …
We extend recently developed methods used for determining the electromagnetic charge radius and $a_μ^{ππ}$ to obtain a determination of the electromagnetic form factor of the pion, $F_π^V(t)$, in several significant kinematical regions, using a parametrization-free formalism based on analyticity and unitarity, and with the inclusion of precise inputs from both timelike and spacelike regions. On the unitarity cut, below the first inelastic threshold we use the precisely known phase of the form factor, known from $ππ$ elastic scattering via the Fermi-Watson theorem, and above the inelastic thres…
We propose a method for calculating the nucleon form factors (FFs) of $G$-parity-even operators by combining Chiral Effective Field Theory ($χ$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $t > 4 M_π^2$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $ππ\rightarrow N\bar N$ partial-wave amplitudes and the timelike pion FF. $χ$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $ππ$ rescattering in the $t$-channel ($N/…
A method of deriving bounds on the weak meson form factors, based on perturbative QCD, analyticity and unitarity, is generalized in order to fully exploit heavy quark spin symmetry in the ground state $(L=0)$ doublet of pseudoscalar $(B)$ and vector $(B^*)$ mesons. All the relevant form factors of these mesons are taken into account in the unitarity sum. They are treated as independent functions along the timelike axis, being related by spin symmetry only near the zero recoil point. Heavy quark vacuum polarisation up to three loops in perturbative QCD and the experimental cross sections $σ(e^+…
In the partonic (or light-front) description of relativistic systems the electromagnetic form factors are expressed in terms of frame-independent charge and magnetization densities in transverse space. This formulation allows one to identify the chiral components of nucleon structure as the peripheral densities at transverse distances b = O(M_pi^{-1}) and compute them in a parametrically controlled manner. A dispersion relation connects the large-distance behavior of the transverse charge and magnetization densities to the spectral functions of the Dirac and Pauli form factors near the two-pio…
