Forward Elastic Scattering of Light on Light, \gamma+\gamma\to\gamma+\gamma

The forward elastic scattering of light on light, {\em i.e.,} the reaction $\gamma+\gamma \to \gamma+\gamma$ in the forward direction, is analyzed utilizing real analytic amplitudes. We calculate $\rho_{\gamma \gamma}$, the ratio of the real to the imaginary portion of the forward scattering amplitude, by fitting the total $\gamma \gamma$ cross section data in the high energy region $5 GeV \le \sqrt s \le 130$ GeV, assuming a cross section that rises asymptotically as $\ln^2 s$. We then compare $\rho_{\gamma\gamma}$ to $\rho_{nn}$, the ratio of the even portions of the $pp$ and \pbar p forward scattering amplitudes, as well as to $\rho_{\gamma p}$, the $\rho$ value for Compton scattering. Within errors, we find that the three $\rho$-values in the c.m.s. energy region $5 GeV \le \sqrt s \le 130$ GeV are the same, as predicted by a factorization theorem of Block and Kadailov.Comment: 5 pages, Latex2e, 2 postscript figures, uses epsfig.st

Decoupling the coupled DGLAP evolution equations: an analytic solution to pQCD

Using Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we decouple the solutions for the singlet structure function $F_s(x,Q^2)$ and $G(x,Q^2)$ of the two leading-order coupled singlet DGLAP equations, allowing us to write fully decoupled solutions: F_s(x,Q^2)={\cal F}_s(F_{s0}(x), G_0(x)), G(x,Q^2)={\cal G}(F_{s0}(x), G_0(x)). Here ${\cal F}_s$ and $\cal G$ are known functions---found using the DGLAP splitting functions---of the functions $F_{s0}(x) \equiv F_s(x,Q_0^2)$ and $G_{0}(x) \equiv G(x,Q_0^2)$, the chosen starting functions at the virtuality $Q_0^2$. As a proof of method, we compare our numerical results from the above equations with the published MSTW LO gluon and singlet $F_s$ distributions, starting from their initial values at $Q_0^2=1 GeV^2$. Our method completely decouples the two LO distributions, at the same time guaranteeing that both distributions satisfy the singlet coupled DGLAP equations. It furnishes us with a new tool for readily obtaining the effects of the starting functions (independently) on the gluon and singlet structure functions, as functions of both $Q^2$ and $Q_0^2$. In addition, it can also be used for non-singlet distributions, thus allowing one to solve analytically for individual quark and gluon distributions values at a given $x$ and $Q^2$, with typical numerical accuracies of about 1 part in $10^5$, rather than having to evolve numerically coupled integral-differential equations on a two-dimensional grid in $x, Q^2$, as is currently done.Comment: 6 pages, 2 figure

Necessity and Opportunity Entrepreneurs and their Duration in Self-employment: Evidence from German Micro Data

Using data from the German Socio-Economic Panel Study (GSOEP), we analyze whether necessity entrepreneurs differ from opportunity entrepreneurs in terms of self-employment duration. Using univariate statistics, we find that opportunity entrepreneurs remain in self-employment longer than necessity entrepreneurs. However, after controlling for the entrepreneurs’ education in the professional area where they start their venture, this effect is no longer significant. We therefore conclude that the difference observed is not an original effect but rather is due to selection. We then go on to discuss the implications of our findings for entrepreneurship-policy making, and give suggestions to improve governmental start-up programs

On Factorization, Quark Counting, and Vector Dominance

Using an eikonal structure for the scattering amplitude, Block and Kaidalov have derived factorization theorems for nucleon-nucleon, $\gamma p$ and $\gamma\gamma$ scattering at high energies, using only some very general assumptions. We present here an analysis giving experimental confirmation for factorization of cross sections, nuclear slope parameters B and $\rho$-values (ratio of real to imaginary portion of forward scattering amplitudes), showing that: i) the three factorization theorems hold, ii) the additive quark model holds to ~1%, and iii) vector dominance holds to better than ~4%.Comment: Latex2e, 11 pages, 6 postscript figures, uses epsfig.sty. Version to be published in Eur. Phys. Jour.