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

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

Space-like and time-like pion electromagnetic form factor and Fock state components within the Light-Front dynamics

The simultaneous investigation of the pion electromagnetic form factor in the space- and time-like regions within a light-front model allows one to address the issue of non-valence components of the pion and photon wave functions. Our relativistic approach is based on a microscopic vector meson dominance (VMD) model for the dressed vertex where a photon decays in a quark-antiquark pair, and on a simple parametrization for the emission or absorption of a pion by a quark. The results show an excellent agreement in the space like region up to -10 $(GeV/c)^2$, while in time-like region the model produces reasonable results up to 10 $(GeV/c)^2$.Comment: 74 pages, 11 figures, use revtex

Rotational covariance and light-front current matrix elements

Light-front current matrix elements for elastic scattering from hadrons with spin~1 or greater must satisfy a nontrivial constraint associated with the requirement of rotational covariance for the current operator. Using a model $\rho$ meson as a prototype for hadronic quark models, this constraint and its implications are studied at both low and high momentum transfers. In the kinematic region appropriate for asymptotic QCD, helicity rules, together with the rotational covariance condition, yield an additional relation between the light-front current matrix elements.Comment: 16 pages, [no number

The Rotation Average in Lightcone Time-Ordered Perturbation Theory

We present a rotation average of the two-body scattering amplitude in the lightcone time($\tau$)-ordered perturbation theory. Using a rotation average procedure, we show that the contribution of individual time-ordered diagram can be quantified in a Lorentz invariant way. The number of time-ordered diagrams can also be reduced by half if the masses of two bodies are same. In the numerical example of $\phi^{3}$ theory, we find that the higher Fock-state contribution is quite small in the lightcone quantization.Comment: 25 pages, REVTeX, epsf.sty, 69 eps file

Basis States for Relativistic, Dynamically-Entangled Particles

In several recent papers on entanglement in relativistic quantum systems and relativistic Bell's inequalities, relativistic Bell-type two-particle states have been constructed in analogy to non-relativistic states. These constructions do not have the form suggested by relativistic invariance of the dynamics. Two relativistic formulations of Bell-type states are shown for massive particles, one using the standard Wigner spin basis and one using the helicity basis. The construction hinges on the use of Clebsch-Gordan coefficients of the Poincar\'e group to reduce the direct product of two unitary irreducible representations (UIRs) into a direct sum of UIRs.Comment: 19 pages, three tables, revte

On algebraic models of relativistic scattering

In this paper we develop an algebraic technique for building relativistic models in the framework of direct-interaction theories. The interacting mass operator M in the Bakamjian-Thomas construction is related to a quadratic Casimir operator C of a non-compact group G. As a consequence, the S matrix can be gained from an intertwining relation between Weyl-equivalent representations of G. The method is illustrated by explicit application to a model with SO(3,1) dynamical symmetry.Comment: 10 pages, to appear in J. Phys. A : Math. Theo

Baryon Current Matrix Elements in a Light-Front Framework

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 wavefunctions. Sizeable relativistic effects are found for certain transitions, for example, to radial excitations such as that conventionally used to describe to 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.Comment: 32 pages, LaTeX, 10 postscript figures, uses epsf.sty; figures uuencoded with uufiles (or available by request in .ps or hardcopy form