The Mass of the b Quark

We review the current status of determinations of the b-quark mass, m_b. We describe the theoretical tools required for determining m_b, with particular emphasis on effective field theories both in the continuum and on the lattice. We present several definitions of m_b and highlight their advantages and disadvantages. Finally, we discuss the determinations of m_b from b-bar b systems, b-flavored hadrons, and high-energy processes, with careful attention to the corresponding theoretical uncertainties.Comment: 54 pages, 5 figures. With permission from the Annual Review of Nuclear & Particle Science. Final version of this material is scheduled to appear in the Annual Review of Nuclear & Particle Science, Vol. 52, to be published in December 2002 by Annual Reviews (http://AnnualReviews.org

Localizing the Energy and Momentum of Linear Gravity

A framework is developed which quantifies the local exchange of energy and momentum between matter and the linearized gravitational field. We derive the unique gravitational energy-momentum tensor consistent with this description, and find that this tensor only exists in the harmonic gauge. Consequently, nearly all the gauge freedom of our framework is naturally and unavoidably removed. The gravitational energy-momentum tensor is then shown to have two exceptional properties: (a) it is gauge-invariant for gravitational plane-waves, (b) for arbitrary transverse-traceless fields, the energy-density is never negative, and the energy-flux is never spacelike. We analyse in detail the local gauge invariant energy-momentum transferred between the gravitational field and an infinitesimal point-source, and show that these invariants depend only on the transverse-traceless components of the field. As a result, we are led to a natural gauge-fixing program which at last renders the energy-momentum of the linear gravitational field completely unambiguous, and additionally ensures that gravitational energy is never negative nor flows faster than light. Finally, we calculate the energy-momentum content of gravitational plane-waves, the linearized Schwarzschild spacetime (extending to arbitrary static linear spacetimes) and the gravitational radiation outside two compact sources: a vibrating rod, and an equal-mass binary.Comment: 20 pages, 3 figures, published in Phys. Rev.