Relation between Light Cone Distribution Amplitudes and Shape Function in B mesons

The Bakamjian-Thomas relativistic quark model provides a Poincar\'e representation of bound states with a fixed number of constituents and, in the heavy quark limit, form factors of currents satisfy covariance and Isgur-Wise scaling. We compute the Light Cone Distribution Amplitudes of $B$ mesons $\phi_{\pm}^B(\omega)$ as well as the Shape Function $S(\omega)$, that enters in the decay $B \to X_s \gamma$, that are also covariant in this class of models. The LCDA and the SF are related through the quark model wave function. The former satisfy, in the limit of vanishing constituent light quark mass, the integral relation given by QCD in the valence sector of Fock space. Using a gaussian wave function, the obtained $S(\omega)$ is identical to the so-called Roman Shape Function. From the parameters for the latter that fit the $B \to X_s\gamma$ spectrum we predict the behaviour of $\phi_{\pm}^B(\omega)$. We discuss the important role played by the constituent light quark mass. In particular, although $\phi_-^B(0) \not= 0$ for vanishing light quark mass, a non-vanishing mass implies the unfamiliar result $\phi_-^B (0) = 0$. Moreover, we incorporate the short distance behaviour of QCD to $\phi_+^B (\omega)$, which has sizeable effects at large $\omega$. We obtain the values for the parameters $\bar{\Lambda} \cong 0.35$ GeV and $\lambda_B^{-1} \cong 1.43$ GeV$^{-1}$. We compare with other theoretical approaches and illustrate the great variety of models found in the literature for the functions $\phi_{\pm}^B (\omega)$; hence the necessity of imposing further constraints as in the present paper. We briefly review also the different phenomena that are sensitive to the LCDA.Comment: 6 figure

Pion-Exchange and Fermi-Motion Effects on the Proton-Deuteron Drell-Yan Process

Within a nuclear model that the deuteron has NN and \pi NN components, we derive convolution formula for investigating the Drell-Yan process in proton-deuteron (pd) reactions. The contribution from the \pi NN component is expressed in terms of a pion momentum distribution that depends sensitively on the \pi NN form factor. With a \pi NN form factor determined by fitting the \pi N scattering data up to invariant mass W = 1.3 GeV, we find that the pion-exchange and nucleon Fermi-motion effects can change significantly the ratios between the proton-deuteron and proton-proton Drell-Yan cross sections, R_{pd/pp} = \sigma^{pd}/(2\sigma^{pp}), in the region where the partons emitted from the target deuteron are in the Bjorken x_2 > 0.4 region. The calculated ratios R_{pd/pp} at 800 GeV agree with the available data. Predictions at 120 GeV for analyzing the forthcoming data from Fermilab are presented.Comment: 27 pages, 10 figures. A couple of new numerical results are added. arXiv admin note: substantial text overlap with arXiv:1106.556

Design and development of a 5 kV isolated solid state switch

A unique microcircuit intended for use as a shorting switch for large extraterrestrial solar cell arrays is described. The packaging design for the 5 kV isolated hybrid switch is different from most hybrid microcircuits in that it utilizes a compartmentalized plastic case (a portion of which is encapsulated), is not hermetic, and is designed for high voltage operation

Electromagnetic meson form factor from a relativistic coupled-channel approach

Point-form relativistic quantum mechanics is used to derive an expression for the electromagnetic form factor of a pseudoscalar meson for space-like momentum transfers. The elastic scattering of an electron by a confined quark-antiquark pair is treated as a relativistic two-channel problem for the $q\bar{q}e$ and $q\bar{q}e\gamma$ states. With the approximation that the total velocity of the $q\bar{q}e$ system is conserved at (electromagnetic) interaction vertices this simplifies to an eigenvalue problem for a Bakamjian-Thomas type mass operator. After elimination of the $q\bar{q}e\gamma$ channel the electromagnetic meson current and form factor can be directly read off from the one-photon-exchange optical potential. By choosing the invariant mass of the electron-meson system large enough, cluster separability violations become negligible. An equivalence with the usual front-form expression, resulting from a spectator current in the $q^+=0$ reference frame, is established. The generalization of this multichannel approach to electroweak form factors for an arbitrary bound few-body system is quite obvious. By an appropriate extension of the Hilbert space this approach is also able to accommodate exchange-current effects.Comment: 30 pages, 5 figure

Two-Pion Exchange in Proton-Proton Scattering

The contribution of the box and crossed two-pion-exchange diagrams to proton-proton scattering at 90$^{\circ}_{c.m.}$ is calculated in the laboratory momentum range up to 12 GeV/c. Relativistic form factors related to the nucleon and pion size and representing the pion source distribution based on the quark structure of the hadronic core are included at each vertex of the pion-nucleon interaction. These form factors depend on the four-momenta of the exchanged pions and scattering nucleons. Feynman-diagram amplitudes calculated without form factors are checked against those derived from dispersion relations. In this comparison, one notices that a very short-range part of the crossed diagram, neglected in dispersion-relation calculations of the two-pion-exchange nucleon-nucleon potential, gives a sizable contribution. In the Feynman-diagram calculation with form factors the agreement with measured spin-separated cross sections, as well as amplitudes in the lower part of the energy range considered, is much better for pion-nucleon pseudo-vector vis \`a vis pseudo-scalar coupling. While strengths of the box and crossed diagrams are comparable for laboratory momenta below 2 GeV/c, the crossed diagram dominates for larger momenta, largely due to the kinematics of the crossed diagram allowing a smaller momentum transfer in the nucleon center of mass. An important contribution arises from the principal-value part of the integrals which is non-zero when form factors are included. It seems that the importance of the exchange of color singlets may extend higher in energy than expected

Quenching of the Deuteron in Flight

We investigate the Lorentz contraction of a deuteron in flight. Our starting point is the Blankenbecler-Sugar projection of the Bethe-Salpeter equation to a 3-dimensional quasi potential equation, wqhich we apply for the deuteron bound in an harmonic oscillator potential (for an analytical result) and by the Bonn NN potential for a more realistic estimate. We find substantial quenching with increasing external momenta and a significant modification of the high momentum spectrum of the deuteron.Comment: 11 pages, 4 figure

Spatial distributions in static heavy-light mesons: a comparison of quark models with lattice QCD

Lattice measurements of spatial distributions of the light quark bilinear densities in static mesons allow to test directly and in detail the wave functions of quark models. These distributions are gauge invariant quantities directly related to the spatial distribution of wave functions. We make a detailed comparison of the recent lattice QCD results with our own quark models, formulated previously for quite different purposes. We find a striking agreement not only between our two quark models, but also with the lattice QCD data for the ground state in an important range of distances up to about 4/GeV. Moreover the agreement extends to the L=1 states [j^P=(1/2)^+]. An explanation of several particular features completely at odds with the non-relativistic approximation is provided. A rather direct, somewhat unexpected and of course approximate relation between wave functions of certain quark models and QCD has been established.Comment: 40 pages, 5 figures (version published in PRD

Parametrization of Realistic Bethe-Salpeter Amplitude for the Deuteron

The parametrization of the realistic Bethe-Salpeter amplitude for the deuteron is given. Eight components of the amplitude in the Euclidean space are presented as an analytical fit to the numerical solution of the Bethe-Salpeter equation in the ladder approximation. An applicability of the parametrization to the observables of the deuteron is briefly discussed.Comment: LaTeX, 11 pages, 2 Postscript figures; Text of the Fortran program is available from the author by reques

Selectivity of the Nucleon Induced Deuteron Breakup and Relativistic Effects

Theoretical predictions for the nucleon induced deuteron breakup process based on solutions of the three-nucleon Faddeev equation including such relativistic features as the relativistic kinematics and boost effects are presented. Large changes of the breakup cross section in some complete configurations are found at higher energies. The predicted relativistic effects, which are mostly of dynamical origin, seem to be supported by existing data.Comment: 4 pages, 4 figure

Relativity and the low energy nd Ay puzzle

We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator. We find that for neutron laboratory energies above 20 MeV relativistic effects on Ay are negligible. For energies below 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by 2% and Wigner rotations lower it further up to 10 % increasing thus disagreement between data and theory. This indicates that three-nucleon forces must provide an even larger increase of the Ay maximum than expected up to now.Comment: 29 pages, 2 ps figure