Jonathan L. Rosner

Quantum Mechanics with Applications to Quarkonium

Some methods of nonrelativistic quantum mechanics which are particularly useful for studying the variation of bound-state parameters with constituent mass and excitation energy are reviewed. These techniques rely upon elementary scaling arguments and on the semiclassical (WKB) approximation. They are of general interest, but are applied here to the study of bound systems of a heavy quark and antiquark. Properties of the interquark interaction are extracted from information about masses and loptonic widths of the ψ and Y families. It is shown how general methods can be applied to the determination of the electric charge of quarks and to the prediction of properties of new families.

Quarkonium Level Spacings

Motivated by the apparent equal spacing M (ϒ′) - M (ϒ) = M ψi) - M (ψ), we show that the potential for which quarkonium level spacings are independent of quark mass, in the nonrelativistic limit, is V ( r ) = C In ( r / r 0 ). We enumerate consequences of the logarithmic potential and present an alternative interpretation of the data.

Decays of B mesons to two light pseudoscalars

The decays [ital B][r arrow][ital PP], where [ital P] denotes a light pseudoscalar meson, are analyzed. Numerous triangle relations for amplitudes hold within flavor SU(3) symmetry, relating (for example) the decays [ital B][sup +][r arrow][pi][sup +][pi][sup 0], [pi][sup 0][ital K][sup +], and [pi][sup +][ital K][sup 0]. Such relations can improve the possibilities for learning about phases of the Cabibbo-Kobayashi-Maskawa (CKM) matrix and for early detection of [ital CP]-violating asymmetries. Within the context of a graphical analysis of decays, relations are analyzed among SU(3) amplitudes which hold if some graphs are neglected. These relations allow the determination of weak and strong phases from rate measurements alone. Estimates of SU(3) breaking are included.

Electroweak penguin diagrams and two-body B decays.

We discuss the role of electroweak penguin diagrams in {ital B} decays to two light pseudoscalar mesons. We confirm that the extraction of the weak phase {alpha} through the isospin analysis involving {ital B}{r_arrow}{pi}{pi} decays is largely unaffected by such operators. However, the methods proposed to obtain weak and strong phases by relating {ital B}{r_arrow}{pi}{pi}, {ital B}{r_arrow}{pi}{ital K}, and {ital B}{r_arrow}{ital K{bar K}} decays through flavor SU(3) will be invalidated if eletroweak penguin diagrams are large. We show that, although the introduction of electroweak penguin contributions introduces no new amplitudes of flavor SU(3), there are a number of ways to experimentally measure the size of such effects. Finally, using SU(3) amplitude relations we present a new way of measuring the weak angle {gamma} which holds even in the presence of electroweak penguin diagrams.

Charmless B ---> P P decays using flavor SU(3) symmetry

The decays of B mesons to a charmless vector (V ) and pseudoscalar (P) meson are analyzed within a framework of flavor SU(3) in which symmetry breaking is taken into account through ratios of decay constants in tree (T) amplitudes. The magnitudes and relative phases of tree and penguin amplitudes are extracted from data; the symmetry assumption is tested; and predictions are made for rates and CP asymmetries in as-yet-unseen decay modes. A key assumption for which we perform some tests and suggest others is a relation between penguin amplitudes in which the spectator quark is incorporated into either a pseudoscalar meson or a vector meson. Values of slightly restricting the range currently allowed by fits to other data are favored, but outside this range there remain acceptable solutions which cannot be excluded solely on the basis of present B → V P experiments.

Quarkonia and their transitions

Valuable data on quarkonia (the bound states of a heavy quark Q=c,b and the corresponding antiquark) have recently been provided by a variety of sources, mainly e{sup +}e{sup -} collisions, but also hadronic interactions. This permits a thorough updating of the experimental and theoretical status of electromagnetic and strong transitions in quarkonia. The QQ transitions to other QQ states are discussed, with some reference to processes involving QQ annihilation.

New bound on γ from B±→πK decays

Abstract A bound on the angle γ of the unitarity triangle is derived using experimental information on the CP-averaged branching ratios for the rare decays B ± → π ± K 0 and B ± → π 0 K ± . The theoretical description is cleaner than the Fleischer–Mannel analysis of the decays B ± → π ± K 0 and B 0 → π ∓ K ± in that the two decay rates differ only in a single isospin amplitude, which has a simple structure in the SU(3) limit. As a consequence, electroweak penguin contributions and strong rescattering effects can be taken into account in a model-independent way. The resulting bound excludes values of cos γ around ≈0.6 and is thus largely complementary to indirect constraints derived from a global analysis of the unitarity triangle.

Weak coupling phase from decays of charged B mesons to

The theory of [ital CP] violation based on phases in weak couplings in the Cabibbo-Kobayashi-Maskawa matrix requires the phase [gamma][equivalent to]Arg[ital V][sub [ital u][ital b]][sup *] (in a standard convention) to be nonzero. A measurement of [gamma] is proposed based on charged [ital B] meson decay rates to [pi][sup +][ital K][sup 0], [pi][sup 0][ital K][sup +], [pi][sup +][pi][sup 0], and the charge-conjugate states. The corresponding branching ratios are expected to be of the order of 10[sup [minus]5].

\pi

Abstract The divergent part of Z3−1 is found to be (Z 3 −1 )div= α0 2π 2 3 + α0 2π − 1 4 α0 2π 2 log M 2 m 2 to sixth order in the bare charge e0, in a model in which corrections to internal photon lines in the vacuum polarization tensor are neglected. The simplicity and sign of the sixth-order term are of interest in the program to make quantum electrodynamics a consistent finite theory.

K and

The decays of