T. Paul — Page 3 | Search arXiv

arXiv1997

Radiative Tau Lepton Pair Production as a Probe of Anomalous Electromagnetic Couplings of the Tau

We calculate the squared matrix element for the process e+ e- --> tau+ tau- gamma allowing for anomalous magnetic and electric dipole moments at the tau tau gamma vertex. No interferences are neglected and no approximations of light fermion masses are made. We show that anomalous moments affect not only the cross section, but also the shape of the photon energy and angular distributions. We also demonstrate that in the case of the anomalous magnetic dipole moment, the contribution from interference involving Standard Model and anomalous amplitudes is significant compared to the contribution from anomalous amplitudes alone. A program to perform the calculation is available and it may be employed as a Monte Carlo generator.

hep-ph↗

arXiv1994

Legendrian Distributions with Applications to Poincaré Series

Let $X$ be a compact Kahler manifold and $L\to X$ a quantizing holomorphic Hermitian line bundle. To immersed Lagrangian submanifolds $Λ$ of $X$ satisfying a Bohr-Sommerfeld condition we associate sequences $\{ |Λ, k\rangle \}_{k=1}^\infty$, where $\forall k$ $|Λ, k\rangle$ is a holomorphic section of $L^{\otimes k}$. The terms in each sequence concentrate on $Λ$, and a sequence itself has a symbol which is a half-form, $σ$, on $Λ$. We prove estimates, as $k\to\infty$, of the norm squares $\langle Λ, k|Λ, k\rangle$ in terms of $\int_Λσ\overlineσ$. More generally, we show that if $Λ_1$ and $Λ_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting cleanly, the inner products $\langleΛ_1, k|Λ_2, k\rangle$ have an asymptotic expansion as $k\to\infty$, the leading coefficient being an integral over the intersection $Λ_1\capΛ_2$. Our construction is a quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove that the Poincaré series on hyperbolic surfaces are a particular case, and therefore obtain estimates of their norms and inner products.

hep-th↗