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

Complete Six-Gluon Disk Amplitude in Superstring Theory

We evaluate all next-to-maximal helicity violating (NMHV) six-gluon amplitudes in type I open superstring theory in four dimensions, at the disk level, to all orders in alpha'. Although the computation utilizes supersymmetric Ward identities, the result holds for all compactifications, even for those that break supersymmetry and is completely model-independent. Together with the maximally helicity violating (MHV) amplitudes presented in the previous work, our results provide the complete six-gluon disk amplitude.Comment: 29 pages, harvmac, v2: Appendix B3 added, v3: Final version to appear in NP

Trends in the use of payment instruments in the United States

In 2003, for the first time, the number of electronic payments in the United States exceeded the number of check payments--a result of substantial growth in electronic payments (especially by debit card) and a decline in check payments. The shift toward electronic payments suggests that, as with other large economies, many payments formerly made by check are now being made with electronic payment instruments. As in past years, however, the value of checks far exceeded the value of commonly used electronic payments. ; Comparisons among groups of depository institutions of different types and sizes suggest that the distribution of payments of different types is linked in part to the types of customers those institutions tend to serve. For example, at credit unions, which generally serve individuals rather than businesses, checks accounted for a smaller proportion of account debits, and debit card payments and ATM withdrawals accounted for a larger proportion, than at institutions of other types. ; Overall, "on us" check payments, those for which the payer and payee used the same institution, declined slightly. The rate at which checks are returned also declined, while the rate of returned ACH payments--almost twice that of checks--increased, in part because of new types of ACH payments, including ACH transactions initiated with a check. ; Data gathered in 2004 also reveal some differences among geographic regions. Debit card use was substantially greater, and check use substantially lower, in the West than in other regions. In contrast, debit card use was considerably less common in the Northeast, and the decline in check payments since 2000 was less pronounced in that region. ; Indirect evidence--data on ATM withdrawals and cash back from debit card payments--suggests that cash remains a popular means of making payments. Industry data showing increases in ATMs and ATM transactions appear to reflect a shift toward greater use of ATMs and less use of checks to obtain cash, and do not necessarily indicate an increase in the use of cash.Payment systems ; Checks

Supersymmetry Relations and MHV Amplitudes in Superstring Theory

We discuss supersymmetric Ward identities relating various scattering amplitudes in type I open superstring theory. We show that at the disk level, the form of such relations remains exactly the same, to all orders in alpha', as in the low-energy effective field theory describing the alpha'-> 0 limit. This result holds in D=4 for all compactifications, even for those that break supersymmetry. We apply SUSY relations to the computations of N-gluon MHV superstring amplitudes, simplifying the existing results for N<7 and deriving a compact expression for N=7.Comment: 34 pages, harvmac; v2: 2 figs added; final version to appear in NP

Decay widths of lowest massive Regge excitations of open strings

With the advent of the LHC there is widespread interest in the discovery potential for physics beyond the standard model. In TeV-scale open string theory, the new physics can be manifest in the excitation and decay of new resonant structures, corresponding to Regge recurrences of standard model particles. An essential input for the prediction of invariant mass spectra of the decay products (which could serve to identify the resonance as a string excitation) are the partial and total widths of the decay products. We present a parameter-free calculation of these widths for the first Regge recurrence of the SU(3) gluon octet, of the U(1) gauge boson which accompanies gluons in D-brane constructions, and of the quark triplet.Comment: 12 pages revtex, 1 eps figur

An Evolutionary Game Theory Explanation of ARCH Effects

While ARCH/GARCH equations have been widely used to model financial market data, formal explanations for the sources of conditional volatility are scarce. This paper presents a model with the property that standard econometric tests detect ARCH/GARCH effects similar to those found in asset returns. We use evolutionary game theory to describe how agents endogenously switch among different forecasting strategies. The agents evaluate past forecast errors in the context of an optimizing model of asset pricing given heterogeneous agents. We show that the prospects for divergent expectations depend on the relative variances of fundamental and extraneous variables and on how aggressively agents are pursuing the optimal forecast. Divergent expectations are the driving force leading to the appearance of ARCH/GARCH in the data. JEL Classification: C22, C73, G12, D84 Keywords:ARCH, autoregressive conditional heteroskedasticity, evolutionary game theory, rational expectations

Ultraviolet C II and Si III Transit Spectroscopy and Modeling of the Evaporating Atmosphere of GJ436b

Hydrogen gas evaporating from the atmosphere of the hot-Neptune GJ436b absorbs over 50% of the stellar Ly$\alpha$ emission during transit. Given the planet's atmospheric composition and energy-limited escape rate, this hydrogen outflow is expected to entrain heavier atoms such as C and O. We searched for C and Si in the escaping atmosphere of GJ436b using far-ultraviolet HST COS G130M observations made during the planet's extended H I transit. These observations show no transit absorption in the C II 1334,1335 \AA\ and Si III 1206 \AA\ lines integrated over [-100, 100] km s$^{-1}$, imposing 95% (2$\sigma$) upper limits of 14% (C II) and 60% (Si III) depth on the transit of an opaque disk and 22% (C II) and 49% (Si III) depth on an extended, highly asymmetric transit similar to that of H I Ly$\alpha$. C$^+$ is likely present in the outflow according to a simulation we carried out using a spherically-symmetric, photochemical-hydrodynamical model. This simulation predicts a $\sim$2% transit over the integrated bandpass, consistent with the data. At line center, we predict the C II transit depth to be as high as 19%. Our model predicts a neutral hydrogen escape rate of $1.6\times10^{9}$ g s$^{-1}$ ($3.1\times10^{9}$ g s$^{-1}$ for all species) for an upper atmosphere composed of hydrogen and helium.Comment: 7 pages, 4 figures, 1 table; accepted to ApJ Letter