Search

We present results for five reactions, Lambda(b) -> J/psi K(-)p, Lambda(b) -> J/psi eta Lambda, Lambda(b) -> J/psi pi(-)p, Lambda(b) -> J/psi K-0 Lambda and Xi(-)(b) -> J/psi K-Lambda, where combining information from the meson baryon interaction, using the chiral unitary approach, and predictions made for molecular states of hidden charm, with or without strangeness, we can evaluate invariant mass distributions for the light meson baryon states, and for those of J/psi p or J/psi Lambda. We show that with the present available information, in all of these reactions one finds peaks where the pentaquark states show up. In the Lambda(b) -> J/psi K(-)p, and Lambda(b) -> J/psi pi(-)p reactions we show that the results obtained from our study are compatible with present experimental observations. (C) 2016 Elsevier B.V. All rights reserved.

In this paper, we discuss reactions involving charmed baryons to explore their unique features. A well known phenomenon, the separation of the two internal motions of the ρ and λ types of a three-quark system is revisited. First we discuss the mass spectrum of low lying excitations as function of the heavy quark mass, smoothly connecting the S U ( 3 ) and heavy quark limits. The properties of these modes can be tested in the production and decay reactions of the baryons. For production, we consider a one step process which excites dominantly λ modes. We find abundant production rates for some of the excited states. For decay, we study a pion emission process which provides a clean tool to test the structure of heavy quark systems due to the well controlled low energy dynamics of pions and quarks. Both production and decay of charmed baryons are issues for future experiments at J-PARC.

The S-wave ΛΛ and NΞ interactions are studied on the basis of the (2+1)-flavor lattice QCD simulations close to the physical point ( m π ≃ 146 MeV and m K ≃ 525 MeV ). Lattice QCD potentials in four different spin-isospin channels are extracted by using the coupled-channel HAL QCD method and are parametrized by analytic functions to calculate the scattering phase shifts. The ΛΛ interaction at low energies shows only a weak attraction, which does not provide a bound or resonant dihyperon. The NΞ interaction in the spin-singlet and isospin-singlet channel is most attractive and lead the NΞ system near unitarity. Relevance to the strangeness = −2 hypernuclei as well as to two-baryon correlations in proton-proton, proton-nucleus and nucleus-nucleus collisions is also discussed.

We predict glueball/oddball resonances lying on the pomeron/odderon trajectories. A simple new form of the trajectories, with threshold and asymptotic behaviour required by analyticity and unitarity, is proposed. The parameters of these (pomeron and odderon) trajectories are fitted to the data on high-energy elastic proton-proton scattering. The fitted trajectories are extrapolated to the resonance region to predict masses and widths of glueballs and oddballs. The (pomeron and odderon) trajectories may be used to calculate processes of central exclusive diffraction (CED)., Comment: 37 pages, 15 figures, 5 tables

It is argued that the very first signatures of the approach to the black disk asymptotical limit in hadron collisions may be observed in the differential cross section of elastic scattering. The exponentially decreasing with the angle (or $\sqrt {|t|}$) regime beyond the diffraction peak will become replaced by an oscillatory behavior or by the power-like falloff. Some estimates of energies where this can happen are presented., Comment: 8 pages, some corrections and refs added

We review recent work concerning the $\bar{K}N$ interaction and Faddeev equations with chiral dynamics which allow us to look at the $\bar{K}NN$ from a different perspective and pay attention to problems that have been posed in previous studies on the subject. We show results which provide extra experimental evidence on the existence of two $\Lambda(1405)$ states. We then show the findings of a recent approach to Faddeev equations using chiral unitary dynamics, where an explicit cancellation of the two body off shell amplitude with three body forces stemming from the same chiral Lagrangians takes place. This removal of the unphysical off shell part of the amplitudes is most welcome and renders the approach unambiguous, showing that only on shell two body amplitudes need to be used. With this information in mind we use an approximation to the Faddeev equations within the fixed center approximation to study the $\bar{K}NN$ system, providing answers within this approximation to questions that have been brought before and evaluating binding energies and widths of this three body system. As a novelty with respect to recent work on the topic we find a bound state of the system with spin S=1, like a bound state of $\bar{K}$-deuteron, less bound that the one of S=0, where all recent efforts have been devoted. The width is relatively large in this case, suggesting problems in a possible experimental observation., Comment: 18 pages, 7 figures, one misprint corrected, Nuclear Physics A in press

An almost model-independent parametrization for the ratio of the total cross section to the elastic slope, as function of the center of mass energy, is introduced. The analytical result is based on the approximate relation of this quantity with the ratio $R$ of the elastic to total cross section and empirical fits to the $R$ data from proton-proton scattering above 10 GeV, under the conditions of asymptotic unitarity and the black-disk limit. This parametrization may be useful in studies of extensive air showers and the determination of the proton-proton total cross section from proton-air production cross section in cosmic-ray experiments., 15 pages, 4 figures, v4: few typos corrected, final version to be published in Nucl. Phys. A

We present and apply a novel scheme for studying photon- and pion-nucleon scattering beyond the threshold region. Partial-wave amplitudes for the $\gamma\, N$ and $\pi N$ states are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. Based on the chiral Lagrangian we recover the empirical s- and p-wave amplitudes up to energies $\sqrt{s}\simeq 1300$ MeV in terms of the parameters relevant at order $Q^3$., Comment: 76 pages, 23 figures, one additional figure, Tables 4,5 and Figure 4 are corrected, a few references and comments are added. The role of higher partial waves in pion photoproduction is clarified

Currently, the most restrictive test of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is anchored by nuclear beta decay. Precise measurements of the ft -values for superallowed beta transitions between analog 0 + states are used to determine G V , the vector coupling constant; this, in turn, yields V u d , the up-down element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. When the value for V u d obtained from the latest survey of world data is combined with V u s and V u b , the other top-row elements, it leads to the most demanding test available of the unitarity of that matrix. Important ingredients required in the extraction of V u d from experiment are calculated radiative corrections as well as corrections to account for the isospin symmetry breaking that occurs between the analog parent and daughter states of each superallowed transition. The latter are well supported by comparison with experiment. The current value for the unitarity sum is 0.99995(61), a result that is in remarkable agreement with Standard Model expectations.

The structure of baryon resonance in coupled-channel meson-baryon scattering is studied from the viewpoint of chiral dynamics. The meson-baryon scattering amplitude can be successfully described together with the properties of the resonance in the scattering, by implementing the unitarity condition for the amplitude whose low energy structure is constrained by chiral theorem. Recently, there have been a major progress in the study of the structure of the resonance in chiral dynamics. We review the methods to clarify the structure of the resonance by focusing on the Lambda(1405) resonance., Comment: 6 pages, talk give at 4th International Symposium on Symmetries in Subatomic Physics (SSP2009), June 2-5, 2009, National Taiwan University, Taipei

We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d=4-epsilon spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E=E_(LDA)(1+c_s (3N)^(-2/3)), where E_(LDA) is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find c_s=1.68, which is significantly larger than the result for non-interacting fermions, c_s=0.5., 17 pages, final version, Nuclear Physics A, in press

Considering analyticity, unitarity and an influence of coupled channels, experimental data on the isovector P -wave of ππ scattering was analyzed to study ρ -like mesons below 1900 MeV. The analysis indicates that in the energy range 1200–1900 MeV, there are possibly four ρ -like mesons: ρ ( 1250 ) , ρ ( 1450 ) , ρ ( 1600 ) , and ρ ( 1900 ) . The obtained P -wave ππ -scattering length ( a 1 1 = 33.9 ± 2.02 [ 10 −3 m π + −3 ] ) matches most to that calculated in the local Nambu–Jona-Lasinio model.

We discuss the lightest scalar resonances, $f_0(600)$, $\kappa(800)$, $a_0(980)$ and $f_0(980)$ in the extended Nambu Jona-Lasinio model. We find that the model parameters can be tuned, but unnaturally, to accommodate for those scalars except the $f_0(980)$. We also discuss problems encountered in the K Matrix unitarization approximation by using $N_c$ counting technique., Comment: 23 pages 3 eps figures, To appear in Nucl. Phys. A

I give a brief overview of recent theoretical developments within perturbative QCD concerning the high–energy dynamics in the vicinity of the unitarity limit. I focus on the physical implications of these developments for deep inelastic scattering at small x .

In previous works we have compared the pion-pion scattering amplitude obtained from Chiral Perturbation Theory (ChPT) at one- and two-loop approximations with those obtained from dispersion relation formalism. The two approaches yield the same analytical structure to the amplitude at both approximation levels, while the unitarization procedure that uses dispersion relation integrals provides a more economic method than ChPT. This work give the tools for extending the use of the formalism in order to compute further unitarity corrections to partial waves.

pi(+)pi(-) transitions of heavy quarkonia, especially the Y(3S) -> Y(1S) pi(+)pi(-) decay process, are revisited. In the framework of the Chiral Unitary Theory (ChUT), the S wave pi pi final state interaction (FSI) is included. It is found that when an additional intermediate state with J(P) = 1(+) and I = 1 is introduced, not only the pi pi invariant mass spectrum and the cos theta(*)(pi) distribution in the Y(3S) -> Y(1S)pi(+)pi(-) process can simultaneously be well explained, but also a consistent description for other bottomonia pi(+)pi(-) transitions can be obtained. As a consequence, the mass and the width of the intermediate state are predicted. From the quark content analysis, this state should be a bbqq state. (c) 2005 Elsevier B.V. All rights reserved.

The known resonance parameters of the Λ and Σ hyperons were determined almost entirely from energy-dependent partial-wave analyses of K ¯ N scattering data. Some of these analyses attempted to obtain a consistent set of parameters for reactions involving different final states ( K ¯ N , πΛ , πΣ ), but unitarity was not enforced and various features (e.g., backgrounds) were not treated consistently. Now that K − p → neutrals data are beginning to be published by the Crystal Ball Collaboration, it is timely to take a fresh look at the strangeness −1 hyperons. First results are presented for a new unitary, multichannel description of several K ¯ N reactions.

The study of superallowed nuclear β -decay currently provides the most precise and convincing confirmation of the conservation of the vector current (CVC) and is a key component of the most demanding available test of the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, a basic pillar of the Electroweak Standard Model. The status of these fundamental studies is summarized and recent work described.

At the highest possible precisions, atomic-mass measurements can be used to perform fundamental studies. Examples for such studies are a check of the conserved-vector-current (CVC) hypothesis and the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, both postulates of the Standard Model. The comparative half-lives Ft of superallowed β decays constitute the nuclear-physics access to these tests. The Q value of the β decay of 74 Rb, one of the three experimentally accessible parameters that enter into the Ft values, has been measured with the ISOLTRAP experiment at ISOLDE/CERN. The ultimate mass precision requirement and the way to achieve it are outlined.

The decays η , η ′→ π + π − γ are investigated within an approach that combines one-loop chiral perturbation theory with a coupled channel Bethe–Salpeter equation which satisfies unitarity constraints and generates vector mesons dynamically from composite states of two pseudoscalar mesons. It is furthermore shown that the inclusion of the η ′ as a dynamical degree of freedom does not renormalize the Wess–Zumino–Witten term.

We discuss the recent developments in theory and experiment that bear on our understanding of three-body recombination at ultracold temperatures. Some of these predictions include the fourth-power dependence of the three-body rate on the two-body scattering lenght a , the appearance of quantum mechanical shape resonance and Feshbach resonances, and the existence of destructive interference minima at large positive scattering lenghts. At very large scattering lenghts, however, the a 4 dependence of the recombination rate eventually will exceed the unitarity limit. We propose in this paper a simple way to correct this problem, permitting an approximate extension of previous predictions to slightly higher energies above the three-body fragmentation threshold. A preliminary comparison is carried out with a very recent experiment by Grimm and coworkers, showing reasonable agreement.

A new unitarization approach incorporated with chiral symmetry is established and applied to study the πK elastic scatterings. We demonstrate that the κ resonance exists, if the scattering length parameter in the I =1/2, J =0 channel does not deviate much from its value predicted by chiral perturbation theory. The mass and width of the κ resonance is found to be M κ =594±79 MeV, Γ κ =724±332 MeV, obtained by fitting the LASS data up to 1430 MeV. Better determination to the pole parameters is possible if the chiral predictions on scattering lengths are taken into account.

In this paper the semi-classical approach to the solution of non-linear evolution equation is developed. We found the solution in the entire kinematic region to the non-linear evolution equation that governs the dynamics in the high parton density QCD. The large impact parameter ($b_t$) behavior of the solution is discussed as well as the way how to include the non-perturbative QCD corrections in this region of $b_t$. The geometrical scaling behavior and other properties of the solution in the saturation (Color Glass Condensate) kinematic domain are analyzed. We obtain the asymptotic behavior for the physical observables and found the unitarity bounds for them., Comment: 41 pp. 19 figures in eps files

We have established a new convergent scheme to treat analytically nucleon–nucleon interactions from a chiral effective field theory. The Kaplan–Savage–Wise (KSW) amplitudes are resummed to fulfill the unitarity or right-hand cut to all orders below pion production threshold. This is achieved by matching order by order in the KSW power counting the general expression of a partial wave with resummed unitarity cut, with the inverses of the KSW amplitudes. As a result, a new convergent and systematic KSW expansion is derived for an on-shell interacting kernel R in terms of which the partial waves are computed. The agreement with data for the S-waves is fairly good up to laboratory energies around 350 MeV and clearly improves and reestablishes the phenomenological success of the KSW amplitudes when treated within this scheme.

In a recent work on low energy pion-nucleon scattering, instead of using chiral perturbation theory (ChPT) amplitude, we started from a pion-nucleon {\it soft-pion} result and used elastic unitarity directly as a dynamical constraint to construct first-order unitarity corrected amplitudes. The resulting amplitudes are crossing symmetric but, as the ChPT ones, satisfy only approximate unitarity relation. In the present work, we reconsider our approach and we apply the inverse amplitude method (IAM) in order to access the energy resonance region. We present the resulting S- and P-wave phase shifts that are shown to be in qualitative agreement with experimental data., 6 pages, 3 figures

A model is developed for the hadronic interaction in the two-nucleon system above pion threshold which is based on meson, nucleon and $\Delta$ degrees of freedom and which includes full meson retardation in the exchange operators. For technical reasons, the model allows maximal one meson to be present explicitly. Thus the Hilbert space contains besides $NN$ and $N\Delta$ also configurations consisting of two nucleons and one meson. For this reason, only two- and three-body unitarity is obeyed, and the model is suited for reactions in the two nucleon sector only, where one pion is produced or absorbed. Starting from a realistic pure nucleonic retarded potential, which had to be renormalized because of the additional $\pi$ and $\Delta$ degrees of freedom, a reasonable fit to experimental $NN$-scattering data could be achieved., Comment: 30 pages revtex including 17 figures, outline of model and discussion shortened, typos corrected

We have studied the invariant mass distributions of the ππ and KK systems for invariant masses up to 1.2 GeV from the J/Ψ→φππ(KK) decays. The approach exploits the connection between these processes and the ππ and KK strange and nonstrange scalar form factors by considering the φ meson as a spectator. The calculated scalar form factors are then matched with the ones from next-to-leading-order chiral perturbation theory, including the calculation of the the KK scalar form factors. Final state interactions in the J/Ψ→φππ(KK) processes are taken into account as rescattering effects in the system of the two pseudoscalar mesons. A very good agreement with the experimental data from DM2 and MARK-III is achieved. Furthermore, making use of SU(3) symmetry, the S-wave contribution to the π+π− event distribution in the J/Ψ→ωπ+π− reaction is also given and the data up to energies of about 0.7 GeV are reproduced. These decays of the J/Ψ to a vector and a pair of pseudoscalars turn out to be very sensitive to OZI-violating physics which we parameterize in terms of a direct OZI-violation parameter and the chiral perturbation theory low-energy constants L4r and L6r. These constants all come out very different from zero, lending further credit to the statement that the OZI rule is subjected to large corrections in the scalar 0++ channel.

We present a new chiral expansion scheme for the nucleon-nucleon scattering amplitude which preserves unitarity exactly. Our effective field theory builds on the power counting rules for 2-nucleon reducible diagrams proposed in \cite{lutz}. We evaluate the leading order terms of the isospin one scattering amplitude and elaborate in detail on the $^1S_0$ phase shift. Our chiral description of the $^1S_0$-phase shift does compete in quality with modern phenomenological nucleon-nucleon potentials. We describe elastic and inelastic scattering quantitatively up to laboratory energies of $E_{\rm lab} \simeq 600$ MeV., Comment: 89 pages, 5 figures, submitted to Nucl. Phys. A (substantially revised version)

Possible strong Van der Waals interaction between hadrons is searched in the P-wave amplitude of the π-π scattering by removing the cut of the two-pion exchange spectrum as well as the unitarity cut.

The π0π0 mass spectra and angular distributions around K K - threshold and at 1.5 GeV in p p (at rest) → 3π 0 in the Crystal Barrel experiment are reanalyzed by applying the new method, which is consistent with unitarity of S-matrix and expressed directly by resonance parameters. The effects of light σ-meson production are clearly seen to improve the fit with σ, in comparing with the fit without σ.

A lambda-nucleon effective interaction for lambda hypernuclei is derived in the unitary-model-operator approach. Numerical calculation is performed for Λ17O, using the hyperon-nucleon interactions of the Nijmegen soft-core including the '97-models, Julich A and B. The single-particle energies of lambda in the O s 1 2 , o p 3 2 , O p 1 2 and the partial-wave contributions to the potential energy of lambda in the O s 1 2 state are calculated.

A method is present to unitarize a low energy pion–nucleon scattering amplitude. Starting from a soft-pion result, we have used unitarity directly as a dynamical constraint and constructed amplitudes from their first-order discontinuities. There is no commitment to the existence of resonances, but they can be derived from the general structure of the model. Working with two parameters we determine low energy πN amplitudes. We have fixed the two parameters of the model by fitting the experimental P 33 phase shifts near 90°. Five S - and P -wave phase shifts are then shown to agree qualitatively with experimental data.

A Lorentz covariant representation of the NN t -matrix has been obtaained over the energy range from 150 to 500 MeV by solving the integral equation that connects the t -matrix with the K -matrix. The K -matrix is expanded in a complete set of on-shell Lorentz invariant amplitudes represented phenomenologically by isoscalar and isovector “meson” exchanges. The real part of the K -matrix is fit over the energy range from 150 to 500 MeV using coupling strengths that are allowed to vary quadratically with energy. Above the pion production threshold at T lab = 280 MeV, the real K -matrix is supplemented by an imaginary part with linear energy dependence. The K -matrix parameters are fit to thesmost recent (January 1999) Arndt amplitudes [R.A. Arndt, D. Roper, VPI and SU Scattering Analysis Interactive Dial-in Program and Data Base]. Direct and exchange contributions to the K -matrix are handled explicitly in the formalism. The resulting t -matrix satisfies elastic unitary below the pion production threshold and contains non-local terms that are not present in direct Love-Franey parameterizations of the t -matrix. Results are given for the NN amplitudes and compared with both the Arndt amplitudes and amplitudes obtained from a direct fit of the t -matrix [O.V. Maxwell, Nucl. Phys. A 600 (1996) 509]. Results are also given for a selected set of np and pp observables.

Superallowed {beta}-decays are a sensitive probe of the fundamental aspects of the weak interaction. Such decays are used to stringently test the CVC hypothesis, deduce a precise value of the weak vector coupling constant, test the unitarity of the CKM matrix and look for deviation from the V-A structure for the weak interaction. The ability to efficiently capture and store short-lived superallowed beta-emitters in ion traps will help to elucidate discrepancies in the most precise unitarity test of the CKM matrix and tighten the present limits on interactions outside the standard V-A form.

A new operator for pion photo- and electroproduction has been developed for nuclear applications at photon equivalent energies up to 1 GeV. The model contains Born terms, vector mesons and nucleon resonances ($P_{33}(1232)$, $P_{11}(1440)$, $D_{13}(1520)$, $S_{11}(1535)$, $F_{15}(1680)$, and $D_{33}(1700)$). The resonance contributions are included taking into account unitarity to provide the correct phases of the pion photoproduction multipoles. The $Q^2$ dependence of electromagnetic resonance vertices is described with appropriate form factors in the electromagnetic helicity amplitudes. Within this model we have obtained good agreement with the experimental data for pion photo- and electroproduction on the nucleon for both differential cross sections and polarization observables. The model can be used as a starting point to predict and analyze forthcoming data., 32 pages LaTeX including 23 postscript figures (a few misprints have been corrected)

We present a computationally reliable and accurate method for solving the Gribov-Lipatov-Altarelli-Parisi equations at next to leading order, both in the non-singlet and in the singlet case. It requires solving numerically the renormalization group equations for the anomalous dimensions of composite operators in the complex plane, and finally performing an inverse Mellin transformation. In this way the group property of renormalization is exactly preserved, i.e. performing two successive scale transformations coincides exactly with a direct one making parton distributions independent of the integration path used to connect two different scales. This is relevant when large scale differences are involved and makes upward or downward evolution fully equivalent. Thus, it becomes possible to evolve the known parton distributions and leading twist contributions to the structure functions from Q2 = mb2 to the lowest possible scale imposed by positivity and unitarity.

The semiclassical approach, successfully applied in the past to the inelastic, inclusive electron scattering off nuclei, is extended to the treatment of exclusive processes. The final states interaction is accounted for in the mean field approximation, respecting the Pauli principle. The impact on the exclusive cross section of the shape of the potential binding the nucleons into the nucleus and of the distortion of the outgoing nucleon wave are explored. The exclusive scattering is found to be quite sensitive to the mean field final states interaction, unlike the inclusive one. Indeed we verify that the latter is not affected, as implied by unitarity, by the distortion of the outgoing nucleon wave except for the effect of relativity, which is modest in the range of momenta up to about 500 MeV/c. Furthermore, depending upon the correlations between the directions of the outgoing and of the initial nucleon, the exclusive cross-section turns out to be remarkably sensitive to the shape of the potential binding the nucleons. These correlations also critically affect the domain in the missing energy-- missing momentum plane where the exclusive process occurs., Comment: 39 pages, latex, including 9 figures (fig.ps)

Nonperturbative polaron variational methods are applied, within the so-called particle or worldline representation of relativistic field theory, to study scattering in the context of the scalar Wick - Cutkosky model. Important features of the variational calculation are that it is a controlled approximation scheme valid for arbitrary coupling strengths, the Green functions have all the cuts and poles expected for the exact result at any order in perturbation theory and that the variational parameters are simultaneously sensitive to the infrared as well as the ultraviolet behaviour of the theory. We generalize the previously used quadratic trial action by allowing more freedom for off-shell propagation without a change in the on-shell variational equations and evaluate the scattering amplitude at first order in the variational scheme. Particular attention is paid to the $s$-channel scattering near threshold because here non-perturbative effects can be large. We check the unitarity of a our numerical calculation and find it greatly improved compared to perturbation theory and to the zeroth order variational results.

The analysis of ππ scattering phase shifts near threshold has been performed. The average S- and P-ππ phase shifts have been determined by fitting all of the available experimental data for 5 charge reaction channels. The application of the Roy equations allows one to obtain self-consistent ππ scattering partial amplitudes. The calculated amplitudes are in agreement with the experimentally obtained phase shifts and satisfy the analyticity, unitarity and crossing conditions for a restricted range of S-wave scattering lengths 0.205 < a00 < 0.270, −0.048 < a02 < −0.016 in inverse pion mass units.

Dispersion relations allow for a coherent description of the nucleon electromagnetic form factors measured over a large range of momentum transfer, $Q^2 \simeq 0 \ldots 35$ GeV$^2$. Including constraints from unitarity and perturbative QCD, we present a novel parametrisation of the absorptive parts of the various isoscalar and isovector nucleon form factors. Using the current world data, we obtain results for the electromagnetic form factors, nucleon radii and meson couplings. We stress the importance of measurements at large momentum transfer to test the predictions of perturbative QCD., 33 pp, RevTEX or plain LaTeX, 7 figures (in ffig.uu)

A fully relativistic, gauge invariant and unitary pion photoproduction model is constructed including π, ϱ, ω, N and Δ degrees of freedom. The model is compared in detail to pion photoproduction observables in view of several sets of high-quality data that were obtained through the Δ resonance region in recent years. Starting from the relativistic model, a non-relativistic model mean ffor calculations in the nuclear medium is derived. The non-relativistic model is constructed to satisfy unitarity and is applied to both charged and neutral pion photoproduction with the same parameter set.

If super-allowed Fermi beta-decay is to be consistent with the conserved vector current and with unitarity of the Cabibbo-Kobayashi-Maskawa matrix it is necessary to understand a mismatch, as between the parent and daughter members of the isotriplets involved, that is worth several tenths of a percent in the transition rates. Present theoretical estimates of this mismatch fall short of what is needed by a factor of order 2 or more. It has been suggested that this shortfall is due to inadequate allowance for the effects of the spectator nucleons, but the present study shows that such effects are worth only a few hundredths of one percent.

Numerical calculations of the nuclear-mismatch correction δ C for superallowed 0 + →0 + beta decays are made from formulae previously developed using the formalism of R-matrix theory. The present values of δ C are considerably smaller than those obtained in previous calculations, and lead to ft -values that are not consistent with either the CVC hypothesis or unitarity of the KM mixing matrix.