Continuous Electron Beam Accelerator Facility

We present the predictions of the ISGW2 model, an update of the ISGW quark model for semileptonic meson decays. The updated model incorporates a number of features which should make it more reliable, including the constraints imposed by heavy quark symmetry, hyperfine distortions of wave functions, and form factors with more realistic high recoil behaviors.

It has recently been shown that hadrons containing a single heavy quark exhibit a new flavor-spin symmetry of QCD. We discuss the implications of this symmetry for the masses and strong decay widths of such hadrons.

A comprehensive phenomenological analysis of a two Higgs doublet model, with flavor-changing scalar currents at the tree level, called model III, is presented. Constraints from existing experimental information especially on $\ensuremath{\Delta}F=2$ processes are systematically incorporated. Constraints emerging from rare $B$ decays, $Z\ensuremath{\rightarrow}b\overline{b}$, and the $\ensuremath{\rho}$ parameter are also examined. Experimental implications for ${e}^{+}{e}^{\ensuremath{-}}({\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})\ensuremath{\rightarrow}t\overline{c}+\overline{t}c$, $t\ensuremath{\rightarrow}c\ensuremath{\gamma}(Z,g), {D}^{0}\ensuremath{-}{\overline{D}}^{0}$, and ${B}_{s}^{0}\ensuremath{-}{\overline{B}}_{s}^{0}$ oscillations, and for ${e}^{+}{e}^{\ensuremath{-}}(Z)\ensuremath{\rightarrow}b\overline{s}+\overline{b}s$ are investigated and experimental effort towards these is stressed. We also emphasize the importance of clarifying the experimental issues pertaining to $Z\ensuremath{\rightarrow}b\overline{b}$.

We have measured the ratio $\frac{{g}_{1}^{p}}{{F}_{1}^{p}}$ over the range $0.029<x<0.8$ and $1.3<{Q}^{2}<10$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ using deep-inelastic scattering of polarized electrons from polarized ammonia. An evaluation of the integral $\ensuremath{\int}{0}^{1}{g}_{1}^{p}(x, {Q}^{2})\mathrm{dx}$ at fixed ${Q}^{2}=3$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ yields 0.127\ifmmode\pm\else\textpm\fi{}0.004(stat)\ifmmode\pm\else\textpm\fi{}0.010(syst), in agreement with previous experiments, but well below the Ellis-Jaffe sum rule prediction of 0.160\ifmmode\pm\else\textpm\fi{}0.006. In the quark-parton model, this implies $\ensuremath{\Delta}q=0.27\ifmmode\pm\else\textpm\fi{}0.10$.

We examine the decays of nonstrange baryons to the final states \ensuremath{\Delta}\ensuremath{\pi}, N\ensuremath{\rho}, N\ensuremath{\eta}, N\ensuremath{\eta}', N\ensuremath{\omega}, N1/${2}^{+}$(1440)\ensuremath{\pi}, and \ensuremath{\Delta}3/${2}^{+}$(1600)\ensuremath{\pi}, in a relativized pair-creation ${(}^{3}$${\mathit{P}}_{0}$) model which has been developed in a previous study of the N\ensuremath{\pi} decays of the same baryon states. As it is our goal to provide a guide for the possible discovery of new baryon states at CEBAF and elsewhere, we examine the decays of resonances which have already been seen in the partial-wave analyses, along with those of states which are predicted by the quark model but which remain undiscovered. The level of agreement between our calculation and the available widths from the partial-wave analyses is encouraging.

I develop a diagrammatic method for calculating chiral logarithms in the quenched approximation. While not rigorous, the method is based on physically reasonable assumptions, which can be tested by numerical simulations. The main results are that, at leading order in the chiral expansion, (a) there are no chiral logarithms in quenched ${f}_{\ensuremath{\pi}},\mathrm{for} {m}_{u}={m}_{d}$ (b) the chiral logarithms in ${B}_{K}$ and related kaon $B$ parameters are, for ${m}_{d}={m}_{s}$, the same in the quenched approximation as in the full theory, and (c) for ${m}_{\ensuremath{\pi}}$ and the condensate there are extra chiral logarithms due to loops containing the ${\ensuremath{\eta}}^{\ensuremath{'}}$, which lead to a peculiar nonanalytic dependence of these quantities on the bare quark mass. Following the work of Gasser and Leutwyler, I discuss how there is a predictable finite volume dependence associated with each chiral logarithm. I compare the resulting predictions with numerical results: for most quantities the expected volume dependence is smaller than the errors, but for ${B}_{V}$ and ${B}_{A}$ there is an observed dependence which is consistent with the predictions.

We report on a high-statistics measurement of the deuteron spin structure function ${g}_{1}^{d}$ at a beam energy of 29 GeV in the kinematic range $0.029<x<0.8$ and $1<{Q}^{2}<10$ (GeV $/c$${)}^{2}$. The integral ${\ensuremath{\gamma}}_{1}^{d}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\int}{1}^{}{g}_{1}^{d}\mathrm{dx}$ evaluated at fixed ${Q}^{2}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ (GeV $/c$${)}^{2}$ gives $0.042\ifmmode\pm\else\textpm\fi{}0.003(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.004(\mathrm{syst})$. Combining this result with our earlier measurement of ${g}_{1}^{p}$, we find ${\ensuremath{\gamma}}_{1}^{p}\ensuremath{-}{\ensuremath{\gamma}}_{1}^{n}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.163\ifmmode\pm\else\textpm\fi{}0.010(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.016(\mathrm{syst})$, which agrees with the prediction of the Bjorken sum rule with $O({\ensuremath{\alpha}}_{s}^{3})$ corrections, ${\ensuremath{\gamma}}_{1}^{p}\ensuremath{-}{\ensuremath{\gamma}}_{1}^{n}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.171\ifmmode\pm\else\textpm\fi{}0.008$. We find the quark contribution to the proton helicity to be $\ensuremath{\Delta}q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.30\ifmmode\pm\else\textpm\fi{}0.06$.

Photoproduction amplitudes for the nonstrange baryons are calculated in a quark model with an electromagnetic transition operator containing relativistic corrections, and relativized-quark-model wave functions. A one-parameter fit to the photocouplings shows significant improvements over models using the nonrelativistic transition operator or nonrelativistic wave functions. Helicity asymmetries and other ratios in the electroproduction of some low-lying resonances are also predicted.

Nucleon-nucleon data below 300-MeV laboratory energy are described by a manifestly covariant wave equation in which one of the intermediate nucleons is restricted to its mass shell. Antisymmetrization of the kernel yields an equation in which the two nucleons are treated in an exactly symmetric manner, and in which all amplitudes satisfy the Pauli principle exactly. The kernel is modeled by the sum of one boson exchanges, and four models, all of which fit the data very well (${\mathrm{\ensuremath{\chi}}}^{2}$\ensuremath{\simeq}3 per data point) are discussed. Two models require the exchange of only the \ensuremath{\pi}, \ensuremath{\sigma}, \ensuremath{\rho}, and \ensuremath{\omega}, but also require an admixture of ${\ensuremath{\gamma}}^{5}$ coupling for the pion, while two other models restrict the pion coupling to pure ${\ensuremath{\gamma}}^{5}$${\ensuremath{\gamma}}^{\mathrm{\ensuremath{\mu}}}$, but require the exchange of six mesons, including the \ensuremath{\eta}, and a light scalar-isovector meson referred to as ${\mathrm{\ensuremath{\sigma}}}_{1}$. Deuteron wave functions resulting from these models are obtained. The singularities and relativistic effects which are a part of this approach are discussed, and a complete development of the theory is presented.

The relation between the nucleon-nucleon interaction and exchange currents needed for current conservation are derived for the Bethe-Salpeter formalism, and for the approach in which the spectator particle is restricted to its mass shell. For both approaches, it is shown how to achieve current conservation for a completely general isospin dependent, energy dependent interaction with arbitrary phenomenological electromagnetic form factors for the nucleon and mesons, and with strong form factors at the meson-nucleon vertices. Contrary to what has often been stated in the literature, the development shows that current conservation places no restrictions on the use of different electromagnetic form factors for mesons and nucleons, and that phenomenological meson-nucleon form factors can be introduced in a way which is consistent with current conservation. The longitudinal part of the exchange current is uniquely determined by current conservation, and for the common case of an interaction that only depends on the invariant momentum transfer variable an explicit expression for this longitudinal exchange current is given. The transverse part, which contains all electromagnetic form factors, is unconstrained by current conservation.

Current matrix elements and observables for electro- and photo-excitation of baryons from the nucleon are studied in a light-front framework. Relativistic effects are estimated by comparison to a nonrelativistic model, where we use simple basis states to represent the baryon wave functions. Sizeable relativistic effects are found for certain transitions, for example, to radial excitations such as that conventionally used to describe the Roper resonance. A systematic study shows that the violation of rotational covariance of the baryon transition matrix elements stemming from the use of one-body currents is generally small.

Motivated by the present interest in the heavy quark effective theory, we use the spectator equation to treat the mesonic bound states of heavy quarks. The kernel we use is based on scalar confining and vector Coulomb potentials. Wave functions are treated to leading order and energies to order 1/${\mathit{m}}_{\mathit{Q}}$ in the heavy-light systems, and order 1/${\mathit{m}}_{\mathit{Q}}^{2}$ in heavy-heavy systems. Our results are in reasonable agreement with experimental measurements. We estimate two of the parameters of the heavy quark effective theory, and propose further calculations that may be undertaken in the future.

It has recently been shown that hadrons containing a single heavy quark exhibit a new flavor-spin symmetry of QCD. We exploit this symmetry to obtain model-independent predictions for the 14 form factors in weak decays from the ground-state pseudoscalar meson ${P}_{{Q}_{i}}$ of a heavy quark ${Q}_{i}$ to the low-lying positive-parity excited states of a heavy quark ${Q}_{j}$ in terms of two universal functions of momentum transfer. These predictions are of interest in the study of $\overline{B}\ensuremath{\rightarrow}{D}_{2}^{*}(2460), {D}_{1}(2420), {D}_{1}(\ensuremath{\sim}2360), \mathrm{and} {D}_{0}^{*}(\ensuremath{\sim}2360)$ semileptonic decays. We also discuss the connection between these results and the slope of the function $\ensuremath{\xi}$ (which determines the $\overline{B}\ensuremath{\rightarrow}D$ and $\overline{B}\ensuremath{\rightarrow}{D}^{*}$ transition form factors) given by a heavy-quark sum rule suggested by Bjorken.

The QCD-sum-rule calculation of the pion wave function by Chernyak and Zhitnitsky (CZ) implicitly assumes that the correlation length of vacuum fluctuations is large compared to the typical hadronic scale $\ensuremath{\sim}\frac{1}{{m}_{\ensuremath{\rho}}}$, so that one can substitute the original nonlocal objects such as $〈\overline{q}(0)q(z)〉$ by constant $〈\overline{q}(0)q〉$-type values. We outline a formalism enabling one to work directly with the nonlocal condensates, and construct a modified sum rule for the moments $〈{\ensuremath{\xi}}^{N}〉$ of the pion wave function. The results are rather sensitive to the value of the parameter ${\ensuremath{\lambda}}_{q}^{2}=\frac{〈\overline{q}{D}^{2}q〉}{〈\overline{q}q〉}$ specifying the average virtuality of the vacuum quarks. Varying it from the most popular value ${\ensuremath{\lambda}}_{q}^{2}=0.4$ Ge${\mathrm{V}}^{2}$ up to the value ${\ensuremath{\lambda}}_{q}^{2}=1.2$ Ge${\mathrm{V}}^{2}$ suggested by the instanton-liquid model, we obtain $〈{\ensuremath{\xi}}^{2}〉=0.25\ensuremath{-}0.20$, to be compared to the CZ value $〈{\ensuremath{\xi}}^{2}〉=0.43$ obtained with ${\ensuremath{\lambda}}_{q}^{2}=0$.

We calculate the $N\ensuremath{\pi}$ decay amplitudes of baryon resonances in a semirelativistic version of the $^{3}P_{0}$ model of hadron decays. We use relativized wave functions for the baryons and mesons, and include an intuitive modification of the usual $^{3}P_{0}$ model. Our results are in reasonable agreement with the reported amplitudes for all known nonstrange resonances, and confirm a proposed solution to the mystery of the "missing" states.

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.

The elastic electromagnetic form factors for the deuteron are calculated in the context of a one-boson-exchange model using the Gross or Spectator equation. The formalism is manifestly covariant and gauge invariant, and provides a very good representation of the data.

Inclusive electron-scattering measurements of \ensuremath{\Delta} electroexcitation in nuclei are reported. Electrons with energies of 0.96, 1.1, 1.3, and 1.5 GeV were scattered from $^{1}\mathrm{H}$, $^{4}\mathrm{He}$, C Fe, and W at 37.5\ifmmode^\circ\else\textdegree\fi{}, corresponding to ${Q}^{2}$=0.20--0.52 (GeV/c${)}^{2}$ at the \ensuremath{\Delta} peak. The centroid of the \ensuremath{\Delta}-region cross-section peak is above that for the free nucleon and it shifts to higher invariant mass as ${Q}^{2}$ increases. The A dependence in the dip region and ratios of nuclear to nucleon integrated cross sections indicate that at these ${Q}^{2}$ values there is little specifically nuclear, e.g., quasideuteron, background contribution.

Pion nucleon scattering up to 600 MeV laboratory kinetic energy is described by a manifestly covariant wave equation in which the pion is restricted to its mass shell. The kernel of the equation includes nucleon (N), Roper (${\mathit{N}}^{\mathrm{*}}$), delta (\ensuremath{\Delta}), and ${\mathit{D}}_{13}$ poles, with their corresponding crossed pole terms approximated by contact interactions, and contact \ensuremath{\sigma}- and \ensuremath{\rho}-like exchange terms. The \ensuremath{\pi}NN vertex is treated as a mixture of ${\ensuremath{\gamma}}^{5}$ and ${\ensuremath{\gamma}}^{\mathrm{\ensuremath{\mu}}}$${\ensuremath{\gamma}}^{5}$ coupling, with a mixing parameter \ensuremath{\lambda} chosen so that the dressed nucleon pole will be unshifted by the interaction. Chiral symmetry is maintained at threshold. The resonance contributions are fully unitarized by the equation, with their widths determined by the dynamics included in the model. The \ensuremath{\Delta} and ${\mathit{D}}_{13}$ are treated as pure spin 3/2 particles, with no spin 1/2 amplitude in the S channel. The complete development of this model, which gives a very good fit to all the data up to 600 MeV, is presented.

We introduce a new model of mesons as quark-antiquark bound states. The model is covariant, confining, and chirally symmetric. Our equations give an analytic solution for a zero-mass pseudoscalar bound state in the case of exact chiral symmetry, and also reduce to the familiar, highly successful nonrelativistic linear potential models in the limit of heavy-quark mass and lightly bound systems. In this fashion we are constructing a unified description of all the mesons from the $\ensuremath{\pi}$ through the $\ensuremath{\Upsilon}$. Numerical solutions for other cases are also presented.