Retention capacity of random surfaces

We introduce a "water retention" model for liquids captured on a random surface with open boundaries, and investigate it for both continuous and discrete surface heights 0, 1, ... n-1, on a square lattice with a square boundary. The model is found to have several intriguing features, including a non-monotonic dependence of the retention on the number of levels in the discrete case: for many n, the retention is counterintuitively greater than that of an n+1-level system. The behavior is explained using percolation theory, by mapping it to a 2-level system with variable probability. Results in 1-dimension are also found.Comment: 5 page

Decay of pseudoscalars into lepton pairs and large-Nc QCD

The counterterm combination that describes the decay of pseudoscalar mesons into charged lepton pairs at lowest order in chiral perturbation theory is considered within the framework of QCD in the limit of a large number of colours Nc. When further restricted to the lowest meson dominance approximation to large-Nc QCD, our results agree well with the available experimental data.Comment: 5 pages, 2 figure

Pion-Pion Phase-Shifts and the Value of Quark-Antiquark Condensate in the Chiral Limit

We use low energy pion-pion phase-shifts in order to make distinction between the alternatives for the value of the quark-antiquark condensate $B_0$ in the chiral limit. We will consider the amplitude up to and including ${\cal O}(p^4)$ contributions within the Standard and Generalized Chiral Perturbation Theory frameworks. They are unitarized by means of Pad\'e approximants in order to fit experimental phase-shifts in the resonance region. As the best fits correspond to $\alpha = \beta = 1$, we conclude that pion-pion phase-shift analysis favors the standard ChPT scenario, which assumes just one, large leading order parameter $_{_0}$.Comment: 5 pages, 3 figures and 1 tabl

pi-N charge exchange and pi(+)-pi(0) scattering at low energies

pi-N and pi-pi interactions near threshold are uniquely sensitive to the chiral symmetry breaking part of the strong interaction. The pi-N sigma-term value with its implications for nucleon quark structure and the recent controversy concerning the size of the scalar quark condensate have renewed the experimental interest in these two fundamental systems. We report new differential cross sections for the reaction $pi^-p \to \pi^0n$ at 27.5 MeV pion incident kinetic energy, measured between $\theta_{CM} = 0^\circ$ and $55^\circ$. Our results are in excellent agreement with the existing comprehensive pi-N phase shift analysis. We also report on a Chew-Low analysis of exclusive $\pi^+ p \to \pi^+\pi^0p$ data at 260 MeV pion incident energy.Comment: Talk given by D. Pocanic at QULEN97, Osaka, 20-23 May 1997; 4 pages, 2 PostScript figures, writen in LaTeX 2e, uses packages "epsfig" and "espcrc1

Contributions of order O(mquark2){\cal O}(m_{\rm quark}^2) to Kℓ3K_{\ell 3} form factors and unitarity of the CKM matrix

The form factors for the $K_{\ell 3}$ semileptonic decay are computed to order $O(p^4)$ in generalized chiral perturbation theory. The main difference with the standard $O(p^4)$ expressions consists in contributions quadratic in quark masses, which are described by a single divergence-free low-energy constant, $A_3$. A new simultaneous analysis is presented for the CKM matrix element $V_{us}$, the ratio $F_K/F_{\pi}$, $K_{\ell 3}$ decay rates and the scalar form factor slope $\lambda_0$. This framework easily accommodates the precise value for $V_{ud}$ deduced from superallowed nuclear $\beta$-decays

Performance of Geant4 in simulating semiconductor particle detector response in the energy range below 1 MeV

Geant4 simulations play a crucial role in the analysis and interpretation of experiments providing low energy precision tests of the Standard Model. This paper focuses on the accuracy of the description of the electron processes in the energy range between 100 and 1000 keV. The effect of the different simulation parameters and multiple scattering models on the backscattering coefficients is investigated. Simulations of the response of HPGe and passivated implanted planar Si detectors to \beta{} particles are compared to experimental results. An overall good agreement is found between Geant4 simulations and experimental data

Thin-disk laser pump schemes for large number of passes and moderate pump source quality

Novel thin-disk laser pump layouts are proposed yielding an increased number of passes for a given pump module size and pump source quality. These novel layouts result from a general scheme which bases on merging two simpler pump optics arrangements. Some peculiar examples can be realized by adapting standard commercially available pump optics simply by intro ducing an additional mirror-pair. More pump passes yield better efficiency, opening the way for usage of active materials with low absorption. In a standard multi-pass pump design, scaling of the number of beam passes brings ab out an increase of the overall size of the optical arrangement or an increase of the pump source quality requirements. Such increases are minimized in our scheme, making them eligible for industrial applicationsComment: 16 pages, 9 figure

The anomalous dimension of the composite operator A^2 in the Landau gauge

The local composite operator A^2 is analysed in pure Yang-Mills theory in the Landau gauge within the algebraic renormalization. It is proven that the anomalous dimension of A^2 is not an independent parameter, being expressed as a linear combination of the gauge beta function and of the anomalous dimension of the gauge fields.Comment: 12 pages, LaTeX2e, final version to appear in Phys. Lett.

Contribution of higher meson resonances to the electromagnetic π\pi-meson mass difference

Modifications of the DGMLY relation for calculation of electromagnetic $\pi$-meson mass difference based on the Chiral Symmetry Restoration phenomenon at high energies as well as the Operator Product Expansion of quark densities for vector ($\rho$) and axial-vector ($a_1$) meson fields difference are proposed. In the calculations higher meson resonances in vector and axial-vector channels are taken into account. It is shown that the inclusion of the first $\rho$ and $a_1$ radial excitations improves the results for electromagnetic $\pi$-meson mass difference as compared with the previous ones. Estimations on the electromagnetic $\rho$ and $a_1$-meson decay constants and the constant $L_{10}$ of effective chiral Lagrangian are obtained from the generalized Weinberg sum rules.Comment: Latex2e, 10 pages, submitted to Yad. Phy