Factorization in Exclusive and Seminclusive Decays and Effective Theories for Massless Particles

We prove rigorously factorization in the seminclusive decay $B\to D^{(*)} + jet$ using the large energy effective theory. It is also shown that this effective theory is unable to consistently describe completely exclusive processes, such as the decay $B\to D^{(*)}+\pi(\rho)$, and therefore also related properties such as factorization. This is due to an oversimplification of transverse momentum dynamics. We present a variant of the large energy effective theory, i.e. a new effective theory for massless particles, which properly takes into account transverse momentum dynamics and is therefore the natural framework to study exclusive non-leptonic decays. Finally, it is shown that the collinear instability of the large energy effective theory disappears when seminclusive observables are considered.Comment: Latex file, 34 pages, no figures. There is a more detailed discussion about pinch singularities; some typos are correcte

Magnetic dipoles and electric currents

We discuss several similarities and differences between the concepts of electric and magnetic dipoles. We then consider the relation between the magnetic dipole and a current loop and show that in the limit of a pointlike circuit, their magnetic fields coincide. The presentation is accessible to undergraduate students with a knowledge of the basic ideas of classical electromagnetism.Comment: 7 pages, 1 figur