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

Mutually unbiased bases for the rotor degree of freedom

We consider the existence of a continuous set of mutually unbiased bases for the continuous and periodic degree of freedom that describes motion on a circle (rotor degree of freedom). By a singular mapping of the circle to the line, we find a first, but somewhat unsatisfactory, continuous set which does not relate to an underlying Heisenberg pair of complementary observables. Then, by a nonsingular mapping of the discrete angular momentum basis of the rotor onto the Fock basis for linear motion, we construct such a Heisenberg pair for the rotor and use it to obtain a second, fully satisfactory, set of mutually unbiased bases.Comment: 9 pages, 4 figure

Mutually unbiased bases in dimension six: The four most distant bases

We consider the average distance between four bases in dimension six. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in dimension six. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically-found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases.Comment: 10 pages, 2 figures, 1 tabl

Clavier DUCK : Utilisation d'un système de déduction de mots pour faciliter la saisie de texte sur écran tactile pour les non-voyants

International audienceTouch screens rapidly and significantly replace physical keyboards on mobile devices. Hence, text entry is now dependent on software (or virtual) keyboards that are widely used by sighted people, but raise accessibility issues for visually impaired users. These users rely on tactile exploration with vocal feedback of the whole screen for entering text, which is time consuming. We designed a software keyboard that aims reducing tactile exploration and speeding up text entry for VI users. It relies on the selection of the first letter of a word and rapid and inaccurate typing of the remaining letters. It then proposes a list of words having the same first letter and a similar total distance between letters. The evaluation with twelve VI users showed that this keyboard is very efficient for words larger than five characters. It also helps preventing certain typing errors.L'utilisation des écrans tactiles et en particulier les claviers logiciels est extrêmement compliquée pour les non-voyants qui manquent de repères physiques sur ce type d'appareil. Nous proposons dans cet article une solution clavier logicielle qui propose une liste de mots pouvant correspondre au mot recherché à partir de frappes approximatives des utilisateurs non-voyants. Cette technique évite ainsi à l'utilisateur d'explorer le clavier en permanence pour trouver précisément les caractères à saisir. Une première évaluation nous permet de montrer que notre système est efficace pour les mots de plus de quatre caractères. Il permet aussi d'éviter certains types d'erreur de frappe. Mots Clés Saisie de texte ; déficience visuelle ; écran tactile ; dispositifs mobiles ; clavier logiciel ; système déductif

Design of a Debridement Device Using Impinging Jets

Chronic wound care is a significant burden on the healthcare system, affecting an estimated three to six million Americans, manifesting as ulcers associated with restricted blood flow, diabetes mellitus, or pressure. Treatment is frequently unsuccessful, with only an estimated 25–50% of venous and diabetic ulcers closing after 20 weeks of treatment. Debridement, the removal of necrotic tissue and foreign materials from the wounds, is a crucial component in the chronic wound care. While there exist many debridement techniques, the search for new and more effective methods is ongoing. The existing methods of debridement include surgical, the industry gold standard, as well as the mechanical, autolytic, enzymatic, and hydrosurgery (VersaJet™). The VersaJet™ uses a single high-speed jet directed parallel to the wound surface to remove soft necrotic tissue. This paper presents the design of a debridement device that uses two narrow, high-speed impinging fluid jets to excise necrotic tissue. The handheld device can be used to remove strips of necrotic tissue of a predetermined width and depth and was tested on samples of simulated slough, the soft necrotic tissue, and eschar, the hard, scablike necrotic tissue. The preliminary tests indicate that the technique removes necrotic tissue quickly and with good control, suggesting that, with further development, the technique may provide a time-saving alternative to surgical debridement. Further testing, however, is required to ensure that the jets do not damage the surrounding healthy tissues and to quantitatively analyze the effectiveness of the technique relative to other debridement strategies

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

The structure of the atomic helium trimers: Halos and Efimov states

The Faddeev equations for the atomic helium-trimer systems are solved numerically with high accuracy both for the most sophisticated realistic potentials available and for simple phenomenological potentials. An efficient numerical procedure is described. The large-distance asymptotic behavior, crucial for weakly bound three-body systems, is described almost analytically for arbitrary potentials. The Efimov effect is especially considered. The geometric structures of the bound states are quantitatively investigated. The accuracy of the schematic models and previous computations is comparable, i.e. within 20% for the spatially extended states and within 40% for the smaller ^4He-trimer ground state.Comment: 32 pages containing 7 figures and 6 table

A Variational Approach to the Spinless Relativistic Coulomb Problem

By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some Coulomb-type interaction.Comment: 7 pages, HEPHY-PUB 606/9

Sum rules in the heavy quark limit of QCD

In the leading order of the heavy quark expansion, we propose a method within the OPE and the trace formalism, that allows to obtain, in a systematic way, Bjorken-like sum rules for the derivatives of the elastic Isgur-Wise function $\xi(w)$ in terms of corresponding Isgur-Wise functions of transitions to excited states. A key element is the consideration of the non-forward amplitude, as introduced by Uraltsev. A simplifying feature of our method is to consider currents aligned along the initial and final four-velocities. As an illustration, we give a very simple derivation of Bjorken and Uraltsev sum rules. On the other hand, we obtain a new class of sum rules that involve the products of IW functions at zero recoil and IW functions at any $w$. Special care is given to the needed derivation of the projector on the polarization tensors of particles of arbitrary integer spin. The new sum rules give further information on the slope $\rho^2 = - \xi '(1)$ and also on the curvature $\sigma^2 = \xi '' (1)$, and imply, modulo a very natural assumption, the inequality $\sigma^2 \geq {5\over 4} \rho^2$, and therefore the absolute bound $\sigma^2 \geq {15 \over 16}$.Comment: 64 pages, Late