Form Factor Model Research Articles

Further remarks on isospin breaking in charmless semileptonicBdecays

We consider the isospin breaking corrections to charmless semileptonic decays of B mesons. Both, the recently measured branching ratios of exclusive decays by the CLEO Collaboration and the end-point reion of the inclusive lepton spectrum in form factor models, can be affected by these corrections. Isospin corrections can affect the determination of |V_ub| from exclusive semileptonic B decays at a level comparable to present statistical uncertainties.

Infinite momentum frame calculation of semileptonic heavyΛb→Λctransitions including HQET improvements

We calculate the transition form factors that occur in heavy $\Lambda$-type baryon semileptonic decays as e.g. in $\Lambda_{b} \to \Lambda_{c}^{+} + l^{-} + \bar{\nu}_{l} $. We use Bauer-Stech-Wirbel type infinite momentum frame wave functions for the heavy $\Lambda$-type baryons which we assume to consist of a heavy quark and a light spin-isospin zero diquark system. The form factors at $ q^{2} = 0 $ are calculated from the overlap integrals of the initial and final $\Lambda$-type baryon states. To leading order in the heavy mass scale the structure of the form factors agrees with the HQET predictions including the normalization at zero recoil. The leading order $\omega$-dependence of the form factors is extracted by scaling arguments. By comparing the model form factors with the HQET predictions at ${\cal O}(1/m_{Q})$ we obtain a consistent set of model form factors up to ${\cal O}(1/m_{Q})$. With our preferred choice of parameter values we find that the contribution of the non-leading form factor is practically negligible. We use our form factor predictions to compute rates, spectra and various asymmetry parameters for the semi-leptonic decay $\Lambda_{b} \to \Lambda_{c}^{+} + l^{-} + \bar{\nu}_{l} $.

$\omega NN$ vertex function and the $\gamma\pi\pi\pi$ anomaly

We show that the empirical ωNN form factor (cut-off 1400–C1500 MeV) can be understood as arising from a combination of a quark model form factor (typical cut-off 700–C800 MeV) and an anomalous form factor ∼ q 2 arising from the 3π-intermediate state. The anomaly contributes to the Dirac form factor F 1(q 2) with F 1(0) = 0, (and sizable), and to the Pauli form factor F 2(q 2) with F 2(0) ≠ 0. The resulting tensor coupling F2(0) is sensitive to the cut-off of the pion momenta in the two-loop integrals and turns out to be small for values around 1 GeV. The quark model ωNN tensor coupling F 2(0) vanishes for point-like quarks. The anomaly, however, contributes a non-vanishing tensor coupling which can be seen to effectively enhance the vector coupling in NN models which do not include a tensor coupling.

Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting

Analysis and modeling of small-angle scattering data from systems consisting of colloidal particles or polymers in solution are discussed. The analysis requires application of least-squares methods, and the basic principles of linear and non-linear leastsquares methods are summarized with emphasis on applications in the analysis of small-angle scattering data. These include indirect Fourier transformation, square-root deconvolution, size distribution determinations, and modeling. The inclusion of corrections for instrumental smearing effects is also discussed. The most common analytical expressions for model form factors and structure factors are summarized. An example of analysis of small-angle neutron and X-ray scattering data from block copolymer micelles is given.

Electroproduction of hyperons

We present some estimates for the reaction ep → e′ Σ +. At small scattering angles, the differential cross section is completely determined by the experimental data for the radiative decay Σ + → pγ. For kinematical values typical of the proposed parity experiment at MAMI, we find a suppression factor of about 5 · 10 −15 as compared to elastic electron scattering. On the basis of conservative models for the transition form factors, this ratio might increase by about a factor of 20 at backward angles. Even higher values could be expected if the presently unknown convection currents should turn out to be large. Due to the parity violation involved in this process, we also expect a large asymmetry for polarized electrons.

Erratum: Nonleptonic weak decays of charmed baryons [Phys. Rev.D 46, 1042 (1992)

Weak current-induced baryonic form factors at zero recoil are evaluated in the rest frame of the heavy parent baryon using the nonrelativistic quark model. Contrary to previous similar work in the literature, our quark model results do satisfy the constraints imposed by heavy quark symmetry for heavy-heavy baryon transitions at the symmetric point $v\cdot v'=1$ and are in agreement with the predictions of the heavy quark effective theory for antitriplet-antitriplet heavy baryon form factors at zero recoil evaluated to order $1/m_Q$. Furthermore, the quark model approach has the merit that it is applicable to any heavy-heavy and heavy-light baryonic transitions at maximum $q^2$. Assuming a dipole $q^2$ behavior, we have applied the quark model form factors to nonleptonic, semileptonic and weak radiative decays of the heavy baryons. It is emphasized that the flavor suppression factor occurring in many heavy-light baryonic transitions, which is unfortunately overlooked in most literature, is very crucial towards an agreement between theory and experiment for the semileptonic decay $\Lambda_c\to\Lambda e^+\nu_e$. Predictions for the decay modes $\b,~\Lambda_c \to p\phi,~\Lambda_b\to\Lambda\gamma$, $\Xi_b\to\Xi\gamma$, and for the semileptonic decays of $\Lambda_b,~\Xi_{b,c}$ and $\Omega_b$ are presented. }

Extended vector meson dominance model for the baryon octet electromagnetic form factors.

An unresolved issue in the present understanding of nucleon structure is the effect of hidden strangeness on electromagnetic observables such as ${\mathit{G}}_{\mathit{E}}^{\mathit{n}}$(${\mathit{q}}^{2}$). Previously, we have shown that ${\mathit{G}}_{\mathit{E}}^{\mathit{n}}$(${\mathit{q}}^{2}$) is sensitive to small \ensuremath{\varphi}NN couplings. A complementary approach for understanding effects due to strangeness content and the Okubo-Zweig-Iizuka (OZI) rule is to investigate the electromagnetic structure of hyperons. We apply Sakurai's universality limit of the SU(3${)}_{\mathit{F}}$ symmetry relations and a prescription based on the OZI rule to calculate the electromagnetic form factors of the baryon octet states (p,n,\ensuremath{\Lambda},${\mathrm{\ensuremath{\Sigma}}}^{+}$,${\mathrm{\ensuremath{\Sigma}}}^{0}$,${\mathrm{\ensuremath{\Sigma}}}^{\mathrm{\ensuremath{-}}}$,${\mathrm{\ensuremath{\Xi}}}^{0}$,${\mathrm{\ensuremath{\Xi}}}^{\mathrm{\ensuremath{-}}}$) within the framework of an extended vector meson dominance model. To provide additional motivation for experimental investigation, we discuss the possibility of extracting the ratio ${\mathit{G}}_{\mathit{M}}^{\mathrm{\ensuremath{\Lambda}}}$(${\mathit{q}}^{2}$)/${\mathit{G}}_{\mathit{M}}^{\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Lambda}}}$(${\mathit{q}}^{2}$) from the \ensuremath{\Lambda}/\ensuremath{\Sigma} polarization ratio in kaon electroproduction experiments. \textcopyright{} 1996 The American Physical Society.

Nonfactorization and color-suppressedB →ψ(ψ′)+K(K*) decays

Using $N_c=3$ value of the parameter $a_2=0.09$ but including a modest nonfactorized amplitude, we show that it is possible to understand all data, including polarization, for color-suppressed $B\to\psi(\psi(2S))+K(K^*) $ decays in all commonly used models of form factors. We show that for $B\to\psi +K$ decay one can define an effective $ a_2$, which is process-dependent and, in general, complex; but it is not possible to define an effective $a_2$ for $B\to\psi +K^* $ decay. We also explain why nonfactorized amplitudes do not play a significant role in color-favored B decays.

1/M corrections to baryonic form factors in the quark model.

Weak current-induced baryonic form factors at zero recoil are evaluated in the rest frame of the heavy parent baryon using the nonrelativistic quark model. Contrary to previous similar work in the literature, our quark model results do satisfy the constraints imposed by heavy quark symmetry for heavy-heavy baryon transitions at the symmetric point v\ensuremath{\cdot}v\ensuremath{'}=1 and are in agreement with the predictions of the heavy quark effective theory for antitriplet-antitriplet heavy baryon form factors at zero recoil evaluated to order 1/${\mathit{m}}_{\mathit{Q}}$. Furthermore, the quark model approach has the merit that it is applicable to any heavy-heavy and heavy-light baryonic transitions at maximum ${\mathit{q}}^{2}$. Assuming a dipole ${\mathit{q}}^{2}$ behavior, we have applied the quark model form factors to nonleptonic, semileptonic, and weak radiative decays of the heavy baryons. It is emphasized that the flavor suppression factor occurring in many heavy-light baryonic transitions, which is unfortunately overlooked in most literature, is very crucial towards an agreement between theory and experiment for the semileptonic decay ${\mathrm{\ensuremath{\Lambda}}}_{\mathit{c}}$\ensuremath{\rightarrow}\ensuremath{\Lambda}${\mathit{e}}^{+}$${\ensuremath{\nu}}_{\mathit{e}}$. Predictions for the decay modes ${\mathrm{\ensuremath{\Lambda}}}_{\mathit{b}}$\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\Lambda}, ${\mathrm{\ensuremath{\Lambda}}}_{\mathit{c}}$\ensuremath{\rightarrow}p\ensuremath{\varphi}, ${\mathrm{\ensuremath{\Lambda}}}_{\mathit{b}}$\ensuremath{\rightarrow}\ensuremath{\Lambda}\ensuremath{\gamma}, ${\mathrm{\ensuremath{\Xi}}}_{\mathit{b}}$\ensuremath{\rightarrow}\ensuremath{\Xi}\ensuremath{\gamma}, and for the semileptonic decays of ${\mathrm{\ensuremath{\Lambda}}}_{\mathit{b}}$, ${\mathrm{\ensuremath{\Xi}}}_{\mathit{b},}$c, and ${\mathrm{\ensuremath{\Omega}}}_{\mathit{b}}$ are presented. \textcopyright{} 1996 The American Physical Society.

Covariant quark model of form factors in the heavy mass limit

We show that quark models of current matrix-elements based on the Bakamjian-Thomas construction of relativistic states with a fixed number of particles, plus the addivity assumption, are covariant in the heavy-quark limit and satisfies the full set of heavy-quark symmetry relations discovered by Isgur and Wise. We find the lower bound of ϱ 2 in such models to be 3 4 for ground state mesons, independently of any parameter. Another welcome property of these models is that in the infinite momentum limit, the wave functions vanish outside the domain 0 ≤ x ≤1

Model-independent constraints on the Isgur-Wise function and the Upsilon BB-bar couplings.

Model-independent constraints on the Isgur-Wise function and its derivatives, based on analyticity, unitarity, and perturbative QCD expansion for the polarization function in the spacelike region, are derived using a duality theorem in functional optimization. In particular, we obtan the allowed domain for the slope and the convexity of this function at zero recoil, using as input various information about the \ensuremath{\Upsilon} poles below the BB\ifmmode\bar\else\textasciimacron\fi{} threshold. The results are of interest for testing specific models of the heavy meson form factors and the extraction of the matrix element ${\mathit{V}}_{\mathit{c}\mathit{b}}$ from experimental data on exclusive semiliptonic decays of the B mesons.

Nuclear binding effects in relativistic Coulomb sum rules.

We extend the formulation of relativistic Coulomb sum rules to account for the average effects of nuclear binding on the initial and final states of ejected nucleons. Relativistic interactions are included by using a Dirac representation adapted from a vector-scalar field theory. The scalar field reduces the effective nucleon mass $M^*$ and increases the relativistic effects of recoil and Fermi motion. We consider two models for the off-shell behavior of the nuclear electromagnetic current, and demonstrate that the sum rule is accurate for applications to data over the interesting range of $M^*$ and three momentum $q$. We further indicate that the form of the sum rule is sufficiently general to accommodate a broad class of off-shell form factor models.

Testing factorization in color-suppressed b-flavor decays with the B--> eta c+K(K*) modes.

The discrepancy recently observed between B\ensuremath{\rightarrow}J/\ensuremath{\psi}+K(${\mathit{K}}^{\mathrm{*}}$) data and commonly used hadronic form factor models might be due to a breakdown of the factorization assumption. By showing that the B\ensuremath{\rightarrow}${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$+K(${\mathit{K}}^{\mathrm{*}}$) rates can be calculated without using any particular form factor model, we propose a test of the factorization hypothesis. This test is free of possible uncertainties caused by W-exchange graph contributions. If factorization holds, the measurable ratio \ensuremath{\Gamma}(B\ensuremath{\rightarrow}${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$+${\mathit{K}}^{\mathrm{*}}$)/\ensuremath{\Gamma}(B\ensuremath{\rightarrow}${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$+K) is predicted to be in the range from 0.18 to 0.95 when the CLEO II data on B\ensuremath{\rightarrow}J/\ensuremath{\psi}+K(${\mathit{K}}^{\mathrm{*}}$) are used.

A study of the reactions 14C(→d, d′) 14C and 14C(→d, p) 15C at 16.0 MeV

Cross-section and vector-analyzing-power measurements for 14C(d, d′) and 14C(d, p) reactions have been carried out for E d = 16 MeV. The inelastic-scattering data have been analyzed using the DWBA with a collective and a microscopic model form-factor and also by using the coupled-channels formalism with a vibrational model form-factor. It is observed that while the cross-section angular-distribution data for the two 2 + states at E x = 7.012 and 8.318 MeV are very similar, the corresponding vector analyzing powers are quite different. The results of the analyses indicate that the distinctive characteristics probably arise from the difference in the relative importance of the proton and neutron components in the transition amplitude. The 3 − state at E x = 6.728 MeV is identified as predominantly a 1p-3h state. Although the deformation parameters are relatively large, the single-particle structure aspects play a more dominant role than channel-coupling effects in populating the inelastic states. The transfer reaction data have been analyzed using the DWBA for bound and unbound states. The importance of two-step processes has been investigated via coupled-reaction-channels calculations. The g.s. and the states with excitation energies 0.770, 3.103 and 4.78 MeV in 15C are populated primarily by a one-step process with a small two-step contribution in the case of the 3.103 MeV state. The 4.22 MeV state is populated predominantly by two-step processes. The 4.78 and the 5.83 MeV states have been identified as 1p-2h and 3p-4h, 3/2 + state, respectively, in an earlier report. There is close similarity in the level structures and reaction mechanisms between the states of 15C and 17O populated via the (d, p) reaction.

Tensor polarization in elastic electron-deuteron scattering in the momentum transfer range 3.8

The tensor polarization of the recoil deuteron in elastic electron-deuteron scattering has been measured at the Bates Linear Accelerator Center at three values of four-momentum transfer [ital Q]=3.78, 4.22, and 4.62 fm[sup [minus]1], corresponding to incident electron energies of 653, 755, and 853 MeV. The scattered electrons and the recoil deuterons were detected in coincidence. The recoil deuterons were transported to a liquid hydrogen target to undergo a second scattering. The angular distribution of the [ital [rvec d]]-[ital p] scattering was measured using a polarimeter. The polarimeter was calibrated in an auxiliary experiment using a polarized deuteron beam at the Laboratoire National Saturne. A Monte Carlo procedure was used to generate interpolated calibration data because the energy spread in the deuteron energies in the Bates experiment spanned the range of deuteron energies in the calibration experiment. The extracted values of [ital t][sub 20] are compared to predictions of different theoretical models of the electromagnetic form factors of the deuteron: nonrelativistic and relativistic nucleon-meson dynamics, Skyrme model, quark models, and perturbative quantum chromodynamics. Along with the world data the structure functions [ital A]([ital Q]) and [ital B]([ital Q]) are used to separate the charge monopole and charge quadrupole form factors ofmore » the deuteron. A node in the charge monopole form factor is observed at [ital Q]=4.39[plus minus]0.16 fm[sup [minus]1].« less

Electromagnetic structure of a-hyperon at the scattering of high-energetic λ-hyperons on atomic electrons

A scattering of high-energetic λ-hyperons on atomic electrons is investigated theoretically in order to inspire experimentalists to measure λ-hyperon electromagnetic form factors in spacelike region by that process. In the one-photon exchange approximation a differential cross-section as a function of a special scaling variablez for the λe- → λe- process in the laboratory system of a rest electron is derived for the first time. By using a recently proposed unitary and analytic VMD model of the A-hyperon electromagnetic form factors a behaviour of the λe-→ λe- differential cross-section as a function ofz is predicted for energies of initial λe- → → λe--hyperons to be 100 GeV, 200 GeV, 500 GeV and 1000 GeV.

Determination of the b-->c handedness using nonleptonic Lambda c decays.

We consider possibilities to determine the handedness of $b\ensuremath{\rightarrow}c$ current transitions using semileptonic baryonic ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}$ transitions. We propose to analyze the longitudinal polarization of the daughter baryon ${\ensuremath{\Lambda}}_{c}$ by using momentum-spin correlation measurements in the for n of forward-backward (FB) asymmetry measures involving its nonleptonic decay products. We use an explicit form factor model to determine the longitudinal polarization of ${\ensuremath{\Lambda}}_{c}$ in the semileptonic decay ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}+{l}^{\ensuremath{-}}+{\overline{\ensuremath{\nu}}}_{l}$. The mean longitudinal polarization of ${\ensuremath{\Lambda}}_{c}$ is negative (positive) for left-chiral (right-chiral) $b\ensuremath{\rightarrow}c$ current transitions. The frame-dependent longitudinal polarization of ${\ensuremath{\Lambda}}_{c}$ is large (\ensuremath{\cong} 80%) in the ${\ensuremath{\Lambda}}_{b}$ rest frame and somewhat smaller (30%-40%) in the lab frame when the ${\ensuremath{\Lambda}}_{b}'\mathrm{s}$ are produced on the ${Z}^{0}$ peak. We suggest to use nonleptonic decay modes of ${\ensuremath{\Lambda}}_{c}$ to analyze its polarization and thereby to determine the chirality of the $b\ensuremath{\rightarrow}c$ transition. Since ${\ensuremath{\Lambda}}_{b}'\mathrm{s}$ produced on the ${Z}^{0}$ are expected to be polarized we discuss issues of the polarization transfer in ${\ensuremath{\Lambda}}_{b}\ensuremath{\rightarrow}{\ensuremath{\Lambda}}_{c}$ transitions. We also investigate the ${p}_{\ensuremath{\perp}}$- and $p$-cut sensitivity of our predictions for the polarization of ${\ensuremath{\Lambda}}_{c}$.

Quark model form factors for heavy-quark effective theory

We show how both the spectroscopy of heavy-light hadrons and the slope of the Isgur-Wise function can be simultaneously fitted when Heavy Quark Effective Theory is matched onto dynamical quark models, including careful treatment of Wigner rotations. Working consistently to order ν 2 and using the parameters from hadron spectroscopy as input, we determine the slope parameter ϱ for s-wave transitions to be 1.19 ± 0.03. This agrees with the empirical value for b → c transitions.

Bootstrap quark model and electromagnetic nucleon form factors

The approximate solutions of relativistic three-quark equations are found in the framework of the dispersion relations technique. The mass values of the lowest baryons (JP=1+/2, 3+/2) are obtained. The behaviours of the nucleon electromagnetic form factors at small and intermediate momentum transferQ2<1.5GeV2 are determined.

Spin dependent spectral function of 3He and the asymmetry in the process 3H

The asymmetry for quasielastic inclusive scattering of polarized electrons by polarized $^{3}\mathrm{He}$ has been computed for the first time in terms of a spin dependent spectral function obtained from a realistic three-body wave function without using the closure approximation. It is shown that a proper choice of kinematics minimizes the proton contribution to the asymmetry, which therefore becomes very sensitive to different models of the electromagnetic form factors of the neutron. The calculated asymmetry qualitatively agrees with the available experimental data.