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

Relativistic quantum theories and neutrino oscillations

Neutrino oscillations are examined under the broad requirements of Poincar\'e-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The goal of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable, and how many factors that are important in principle end up being negligible in practice.Comment: 21 pages, no figure

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

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

Zero Modes in Electromagnetic Form Factors of the Nucleon in a Light-Cone Diquark Model

We use a diquark model of the nucleon to calculate the electromagnetic form factors of the nucleon described as a scalar and axialvector diquark bound state. We provide an analysis of the zero-mode contribution in the diquark model. We find there are zero-mode contributions to the form factors arising from the instantaneous part of the quark propagator, which cannot be neglected compared with the valence contribution but can be removed by the choice of wave function. We also find that the charge and magnetic radii and magnetic moment of the proton can be reproduced, while the magnetic moment of the neutron is too small. The dipole shape of the form factors, $G^p_M(Q^2)/\mu_p$ and $G^n_M(Q^2)/\mu_n,$ can be reproduced. The ratio $\mu G^p_E/G^p_M$ decreases with $Q^2,$ but too fast.Comment: 22 pages, 6 pages, accepted by J.Phys.

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

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

Relativistic Structure of the Deuteron: 1.Electro-disintegration and y-scaling

Realistic solutions of the spinor-spinor Bethe-Salpeter equation for the deuteron with realistic interaction kernel including the exchange of pi, sigma, omega, rho, eta and delta mesons, are used to systematically investigate relativistic effects in inclusive quasi-elastic electron-deuteron scattering within the relativistic impulse approximation. Relativistic y-scaling is considered by generalising the non relativistic scaling function to the relativistic case, and it is shown that y-scaling does occur in the usual relativistic scaling variable resulting from the energy conservation in the instant form of dynamics. The present approach of y-scaling is fully covariant, with the deuteron being described by eight components, viz. the 3S_1^{++}, 3S_1^{--}, 3D_1^{++}, 3D_1^{--}, 3P_1^{+-}, 3P_1^{-+}, 1P_1^{+-}, 1P_1^{-+} waves. It is demonstrated that if the negative relative energy states 1P_1, 3P_1 are disregarded, the concept of covariant momentum distributions N(p_0,p), with p_0=M_D/2-\sqrt{p^2+m^2}, can be introduced, and that calculations of lectro-disintegration cross section in terms of these distributions agree within few percents with the exact calculations which include the 1P_1, 3P_1 states, provided the nucleon three momentum |p|\<= 1 GeV/c; in this momentum range, the asymptotic relativistic scaling function is shown to coincide with the longitudinal covariant momentum distribution.Comment: 32 LaTeX pages, 18 eps-figures. Final version to appear in Phys. Rev.

The Balian-Br\'ezin Method in Relativistic Quantum Mechanics

The method suggested by Balian and Br\'ezin for treating angular momentum reduction in the Faddeev equations is shown to be applicable to the relativistic three-body problem.Comment: 14 pages in LaTe

Light-front Ward-Takahashi Identity for Two-Fermion Systems

We propose a three-dimensional electromagnetic current operator within light-front dynamics that satisfies a light-front Ward-Takahashi identity for two-fermion systems. The light-front current operator is obtained by a quasi-potential reduction of the four-dimensional current operator and acts on the light-front valence component of bound or scattering states. A relation between the light-front valence wave function and the four-dimensional Bethe-Salpeter amplitude both for bound or scattering states is also derived, such that the matrix elements of the four-dimensional current operator can be fully recovered from the corresponding light-front ones. The light-front current operator can be perturbatively calculated through a quasi-potential expansion, and the divergence of the proposed current satisfies a Ward-Takahashi identity at any given order of the expansion. In the quasi-potential expansion the instantaneous terms of the fermion propagator are accounted for by the effective interaction and two-body currents. We exemplify our theoretical construction in the Yukawa model in the ladder approximation, investigating in detail the current operator at the lowest nontrivial order of the quasi-potential expansion of the Bethe-Salpeter equation. The explicit realization of the light-front form of the Ward-Takahashi identity is verified. We also show the relevance of instantaneous terms and of the pair contribution to the two-body current and the Ward-Takahashi identity.Comment: 48 pages, 3 figure