Angular reduction in multiparticle matrix elements

A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of the spherical harmonics. For non-scalar couplings, the reduction gives Cartesian tensor forms for the spherical harmonic products, with tensors built from the physical vectors in the original expression. The reduction for arbitrary couplings is given in closed form, making it amenable to symbolic manipulation on a computer. The final expressions do not depend on a special choice of coordinate axes, nor do they contain azimuthal quantum number summations, nor do they have complex tensor terms for couplings to a scalar. Consequently, they are easily interpretable from the properties of the physical vectors they contain.Comment: This version contains added comments and typographical corrections to the original article. Now 27 pages, 0 figure

HAZMAT VI: The Evolution of Extreme Ultraviolet Radiation Emitted from Early M Star

Quantifying the evolution of stellar extreme ultraviolet (EUV, 100 -- 1000 $\overset{\circ}{A}$) emission is critical for assessing the evolution of planetary atmospheres and the habitability of M dwarf systems. Previous studies from the HAbitable Zones and M dwarf Activity across Time (HAZMAT) program showed the far- and near-UV (FUV, NUV) emission from M stars at various stages of a stellar lifetime through photometric measurements from the Galaxy Evolution Explorer (GALEX). The results revealed increased levels of short-wavelength emission that remain elevated for hundreds of millions of years. The trend for EUV flux as a function of age could not be determined empirically because absorption by the interstellar medium prevents access to the EUV wavelengths for the vast majority of stars. In this paper, we model the evolution of EUV flux from early M stars to address this observational gap. We present synthetic spectra spanning EUV to infrared wavelengths of 0.4 $\pm$ 0.05 M$_{\odot}$ stars at five distinct ages between 10 and 5000 Myr, computed with the PHOENIX atmosphere code and guided by the GALEX photometry. We model a range of EUV fluxes spanning two orders of magnitude, consistent with the observed spread in X-ray, FUV, and NUV flux at each epoch. Our results show that the stellar EUV emission from young M stars is 100 times stronger than field age M stars, and decreases as t$^{-1}$ after remaining constant for a few hundred million years. This decline stems from changes in the chromospheric temperature structure, which steadily shifts outward with time. Our models reconstruct the full spectrally and temporally resolved history of an M star's UV radiation, including the unobservable EUV radiation, which drives planetary atmospheric escape, directly impacting a planet's potential for habitability.Comment: 23 pages, 15 figures, accepted to Ap

Multiloop String-Like Formulas for QED

Multiloop gauge-theory amplitudes written in the Feynman-parameter representation are poised to take advantage of two important developments of the last decade: the spinor-helicity technique and the superstring reorganization. The former has been considered in a previous article; the latter will be elaborated in this paper. We show here how to write multiloop string-like formulas in the Feynman-parameter representation for any process in QED, including those involving other non-electromagnetic interactions. The general connection between the Feynman-parameter approach and the superstring/first-quantized approach is discussed. In the special case of a one-loop multi-photon amplitude, these formulas reduce to the ones obtained by the superstring and the first quantized methods. The string-like formulas exhibits a simple gauge structure which makes the Ward-Takahashi identity apparent, and enables the integration-by-parts technique of Bern and Kosower to be applied, so that gauge-invariant parts can be extracted diagram-by-diagram with the seagull vertex neglected.Comment: 25 pages in Plain Tex, plus four figures in a postscript file; McGill/92-5

General Solutions for Tunneling of Scalar Fields with Quartic Potentials in de Sitter Space

The tunneling rates for scalar fields with quartic potentials in de Sitter space in the limit of no gravitational back reaction are calculated numerically and the results are fitted by analytic formulae.Comment: (Contours in Figure 1 corrected, two-dimensional fitting coefficient corrected, references added.), 16 pages, KUNS 124

Multigluon tree amplitudes with a pair of massive fermions

We consider the calculation of n-point multigluon tree amplitudes with a pair of massive fermions in QCD. We give the explicit transformation rules of this kind of massive fermion-pair amplitudes with respect to different reference momenta and check the correctness of them by SUSY Ward identities. Using these rules and onshell BCFW recursion relation, we calculate the analytic results of several n-point multigluon amplitudes.Comment: 15page

Angular Correlations in Top Quark Pair Production and Decay at Hadron Colliders

We show how to observe sizable angular correlations between the decay products of the top quark and those of the anti-top quark in top quark pair production and decay at hadron colliders. These correlations result from the large asymmetry in the rate for producing like-spin versus unlike-spin top quark pairs provided the appropriate spin axes are used. The effects of new physics at production or decay on these correlations are briefly discussed.Comment: 34 pages, revtex, including 12 uuencoded postscript figure

Boundary Contributions Using Fermion Pair Deformation

Continuing the study of boundary BCFW recursion relation of tree level amplitudes initiated in \cite{Feng:2009ei}, we consider boundary contributions coming from fermion pair deformation. We present the general strategy for these boundary contributions and demonstrate calculations using two examples, i.e, the standard QCD and deformed QCD with anomalous magnetic momentum coupling. As a by-product, we have extended BCFW recursion relation to off-shell gluon current, where because off-shell gluon current is not gauge invariant, a new feature must be cooperated.Comment: 26 pages, 4 figure

Majorana Neutrinos and Gravitational Oscillation

We analyze the possibility of encountering resonant transitions of high energy Majorana neutrinos produced in Active Galactic Nuclei (AGN). We consider gravitational, electromagnetic and matter effects and show that the latter are ignorable. Resonant oscillations due to the gravitational interactions are shown to occur at energies in the PeV range for magnetic moments in the $10^{-17} \mu_B$ range. Coherent precession will dominate for larger magnetic moments. The alllowed regions for gravitational resonant transitions are obtained.Comment: 11 pages, 8 figures, Latex; requires revtex and epsf.tex submitted to Physical Review