Central Charge Anomalies in 2D Sigma Models with Twisted Mass

We discuss the central charge in supersymmetric ${\cal N}=2$ sigma models in two dimensions. The target space is a symmetric K\"ahler manifold, CP$(N-1)$ is an example. The U(1) isometries allow one to introduce twisted masses in the model. At the classical level the central charge contains Noether charges of the U(1) isometries and a topological charge which is an integral of a total derivative of the Killing potentials. At the quantum level the topological part of the central charge acquires anomalous terms. A bifermion term was found previously, using supersymmetry which relates it to the superconformal anomaly. We present a direct calculation of this term using a number of regularizations. We derive, for the first time, the bosonic part in the central charge anomaly. We construct the supermultiplet of all anomalies and present its superfield description. We also discuss a related issue of BPS solitons in the CP(1) model and present an explicit form for the curve of marginal stability.Comment: 30 pages, 1 figure, references adde

Sum Rules for Heavy Flavor Transitions in the SV Limit

We show how sum rules for the weak decays of heavy flavor hadrons can be derived as the moments of spectral distributions in the small velocity (SV) limit. This systematic approach allows us to determine corrections to these sum rules, to obtain new sum rules and it provides us with a transparent physical interpretation; it also opens a new perspective on the notion of the heavy quark mass. Applying these sum rules we derive a lower bound on the deviation of the exclusive form factor $F_{B->D^*}$ from unity at zero recoil; likewise we give a field-theoretical derivation of a previously formulated inequality between the expectation value for the kinetic energy operator of the heavy quark and for the chromomagnetic operator. We analyze how the known results on nonperturbative corrections must be understood when one takes into account the normalization point dependence of the low scale parameters. Relation between the field-theoretic derivation of the sum rules and the quantum-mechanical approach is elucidated.Comment: 72 pages, 5 figures (uuencoded ps files added using figures option), Revised version. Paper is considerably extended to include some new results. New section on quantum mechanical approach is adde

On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays

In previous papers we have pointed out that there exists a QCD analog of the phenomenological concept of the so called Fermi motion for the heavy quark inside a hadron. Here we show in a more detailed way how this comes about and we analyze the limitations of this concept. Non-perturbative as well as perturbative aspects are included. We emphasize both the similarities and the differences to the well-known treatment of deep inelastic lepton-nucleon scattering. We derive a model-independent {\em lower} bound on the kinetic energy of the heavy quark inside the hadron.Comment: 34 pages, Latex, 4 figures. Some clarifying comments and postscript files of figures are adde