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A formalism, covariant up to terms of 0 ( 1 /MQ ), is presented, which describes from the center-ofmass frame a (hydrogenlike) system consisting of a heavy quark ( Q ) and a light quark ( q ) . The effective interaction between them is characterized by a color Coulomb-like potential V = -c / r , a linear scalar potential S =br ( b > 01, and a Breit potential. The formalism is applied to B-and D-meson spectroscopy and to the calculation of the M1 widths lY3S1-'Soy ). Recoil effects on these widths are included through a boost (in the opposite direction to the photon momentum) on the final ( Q , q ) bound state wave function. By plotting the ratio R v n * =T(D*+-D+y )/lYD*'-Doy) as a function of the magnetic , -

Context. The protoMIRAX hard X-ray imaging telescope is a balloon-borne experiment developed as a pathfinder for the MIRAX satellite mission. The experiment consists essentially in a coded-aperture hard X-ray (30-200 keV) imager with a square array (13 × 13) of 2 mm-thick planar CZT detectors with a total area of 169 cm 2 . The total, fully-coded field-of-view is 21 • × 21 • and the angular resolution is 1 • 43 . Aims. The main objective of protoMIRAX is to carry out imaging spectroscopy of selected bright sources to demonstrate the performance of a prototype of the MIRAX hard X-ray imager. In this paper we describe the protoMIRAX instrument and all the subsystems of its balloon gondola, and we show simulated results of the instrument performance. Methods. Detailed background and imaging simulations were performed for protoMIRAX balloon flights. The 3σ sensitivity for the 30-200 keV range is ∼1.9 × 10 −5 photons cm −2 s −1 for an integration time of 8 h at an atmospheric depth of 2.7 g cm −2 and an average zenith angle of 30 • . We developed an attitude-control system for the balloon gondola and new data handling and ground systems that also include prototypes for the MIRAX satellite.Results. We present the results of Monte Carlo simulations of the camera response at balloon altitudes, showing the expected background level and the detailed sensitivity of protoMIRAX. We also present the results of imaging simulations of the Crab region. Conclusions. The results show that protoMIRAX is capable of making spectral and imaging observations of bright hard X-ray source fields. Furthermore, the balloon observations will carry out very important tests and demonstrations of MIRAX hardware and software in a near space environment.

We discuss the exclusive semileptonic decay B to De nu which is based on a relativistic approach to hadronic systems consisting of a heavy quark and a light quark (hydrogen-like mesons). The corresponding weak form factor at zero momentum transfer is calculated and f+(0)=0.55 obtained. From this and experimental data from B to De nu we determine mod Vcb mod .

Radial probability density function of a heavy quark-light quark (Q,q) system in the states S, P and D, is studied numerically. It is found that the maximum of this function at r = a 0 and the light quark energy (Eq) are related through Eq(, where l is the orbital angular momentum, Z = 0.446/ξ, and ξ is the strength of the color Coulomb potential. Phenomenology predicts that to difference of the hydrogen atom of QED, the "color atomic number" is such that Z ≤ 1. This can be thought of as due to an anti-screening effect from the gluons. The respective expectation value for the radial coordinate in these states is found to beThese results are valid for ξ in the range 0.446 < ξ < 0.646 and a light quark mass in the range 0 < m < 300 MeV. The above relations coincide with the maximum value of the slope of the Isgur-Wise at zero recoil point in the following way ξ (1)max = − 5 6 = − 1 − l 2 (l + 1) 2 ξ + l 4 (l + 1) 4 ξ 2 a 0 r .The relations found in the present work imply that ξ (1) = − 1 2 − Z 2 3 r 2 a 2 0 , from which we argue that the value of ξ (1) is very sensitive to the color Coulomb-like interaction U = −ξ/r.As is well known the radial probability density function ρ(r) = r 2 |ψ| 2 , associated to a hydrogen-like atom has a maximum located at r = n 2 a 0 , where a 0 is inversely proportional to the mass of the electron moving around the nucleus. a The respective expectation value for the radial coordinate is r = 1 2Z [3n 2 − l(l + 1)]a 0 . The "similarity" between the hydrogenlike atom and the heavy quark-light quark (Q,q) system, leads us naturally to ask if the radial probability density function, ρ(r) associated to a (Q,q) system behaves in a similar fashion to the function ρ(r) associated to the hydrogen atom of QED. In order to answer this question, we must note that the interaction present in a (Q,q) system, is more complicated than the * E-mail: manuel@servm.fc.uaem.mx a The number a 0 is known as the Bohr radius and its value is a 0 = 1/(mee 2 ) = 0.5Å = 2.5 × 10 −5 GeV −1 .2059 Mod. Phys. Lett. A 1999.14:2059-2072. Downloaded from www.worldscientific.com by UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN on 03/10/15. For personal use only.