The Study of the Heisenberg-Euler Lagrangian and Some of its Applications

The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest, but also has a rich variety of diverse applications in astrophysics, nonlinear optics and elementary particle physics etc. We discuss the series representation of this Lagrangian and a few of its applications in this study. [In an appendix, we discuss issues related to the renormalization - and the renormalization-group invariance - of the Heisenberg-Euler Lagrangian and its two-loop generalization.]Comment: 12 pages, LaTeX; Proceedings of the MRST-2003 conference; talk given by S. R. Vallur

Age spreads in star forming regions?

Rotation periods and projected equatorial velocities of pre-main-sequence (PMS) stars in star forming regions can be combined to give projected stellar radii. Assuming random axial orientation, a Monte-Carlo model is used to illustrate that distributions of projected stellar radii are very sensitive to ages and age dispersions between 1 and 10 Myr which, unlike age estimates from conventional Hertzsprung-Russell diagrams, are relatively immune to uncertainties due to extinction, variability, distance etc. Application of the technique to the Orion Nebula cluster reveals radius spreads of a factor of 2--3 (FWHM) at a given effective temperature. Modelling this dispersion as an age spread suggests that PMS stars in the ONC have an age range larger than the mean cluster age, that could be reasonably described by the age distribution deduced from the Hertzsprung-Russell diagram. These radius/age spreads are certainly large enough to invalidate the assumption of coevality when considering the evolution of PMS properties (rotation, disks etc.) from one young cluster to another.Comment: To appear in "The Ages of Stars", E.E. Mamajek, D.R. Soderblom, R.F.G. Wyse (eds.), IAU Symposium 258, CU

Model-Independent Bounds on R(J/ψ)R(J/\psi)

We present a model-independent bound on $R(J/\psi) \! \equiv \! \mathcal{BR} (B_c^+ \rightarrow J/\psi \, \tau^+\nu_\tau)/ \mathcal{BR} (B_c^+ \rightarrow J/\psi \, \mu^+\nu_\mu)$. This bound is constructed by constraining the form factors through a combination of dispersive relations, heavy-quark relations at zero-recoil, and the limited existing determinations from lattice QCD. The resulting 95\% confidence-level bound, $0.20\leq R(J/\psi)\leq0.39$, agrees with the recent LHCb result at $1.3 \, \sigma$, and rules out some previously suggested model form factors.Comment: 19 pages, 4 figures, JHEP format, revised to match published versio