Direct Production of Tripartite Pump-Signal-Idler Entanglement in the Above-Threshold Optical Parametric Oscillator

We calculate the quantum correlations existing among the three output fields (pump, signal, and idler) of a triply resonant non-degenerate Optical Parametric Oscillator operating above threshold. By applying the standard criteria [P. van Loock and A. Furusawa, Phys. Rev. A 67, 052315 (2003)], we show that strong tripartite continuous-variable entanglement is present in this well-known and simple system. Furthermore, since the entanglement is generated directly from a nonlinear process, the three entangled fields can have very different frequencies, opening the way for multicolored quantum information networks.Comment: 4 pages, 3 figure

Non-Perturbative Renormalisation of Composite Operators

It is shown that the renormalisation constants of two quark operators can be accurately determined (to a precision of a few per-cent using 18 gluon configurations) using Chiral Ward identities. A method for computing renormalisation constants of generic composite operators without the use of lattice perturbation theory is proposed.Comment: 3 pages, uuencoded compressed postscript file, to appear in the Proceedings of the International Symposium on Lattice Field Theory, Dallas, Texas, 12-17 October 1993, Southampton Preprint 93/94-0

Electromagnetic corrections to leptonic decay rates of charged pseudoscalar mesons: finite-volume effects

In Carrasco et al. we have recently proposed a method to calculate $O(e^2)$ electromagnetic corrections to leptonic decay widths of pseudoscalar mesons. The method is based on the observation that the infrared divergent contributions (that appear at intermediate stages of the calculation and that cancel in physical quantities thanks to the Bloch-Nordsieck mechanism) are universal, i.e. depend on the charge and the mass of the meson but not on its internal structure. In this talk we perform a detailed analysis of the finite-volume effects associated with our method. In particular we show that also the leading $1/L$ finite-volume effects are universal and perform an analytical calculation of the finite-volume leptonic decay rate for a point-like meson

Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD

We demonstrate that the leading and next-to-leading finite-volume effects in the evaluation of leptonic decay widths of pseudoscalar mesons at $O(\alpha)$ are universal, i.e. they are independent of the structure of the meson. This is analogous to a similar result for the spectrum but with some fundamental differences, most notably the presence of infrared divergences in decay amplitudes. The leading non-universal, structure-dependent terms are of $O(1/L^2)$ (compared to the $O(1/L^3)$ leading non-universal corrections in the spectrum). We calculate the universal finite-volume effects, which requires an extension of previously developed techniques to include a dependence on an external three-momentum (in our case, the momentum of the final state lepton). The result can be included in the strategy proposed in Ref.\,\cite{Carrasco:2015xwa} for using lattice simulations to compute the decay widths at $O(\alpha)$, with the remaining finite-volume effects starting at order $O(1/L^2)$. The methods developed in this paper can be generalised to other decay processes, most notably to semileptonic decays, and hence open the possibility of a new era in precision flavour physics

The Kaon BB-parameter with Wilson Fermions

We calculate the kaon $B$-parameter in quenched lattice QCD at $\beta=6.0$ using Wilson fermions at $\kappa=0.154$ and $0.155$. We use two kinds of non-local (``smeared'') sources for quark propagators to calculate the matrix elements between states of definite momentum. The use of smeared sources yields results with much smaller errors than obtained in previous calculations with Wilson fermions. By combining results for $\vec p =(0,0,0)$ and $\vec p =(0,0,1)$, we show that one can carry out the non-perturbative subtraction necessary to remove the dominant lattice artifacts induced by the chiral symmetry breaking term in the Wilson action. Our final results are in good agreement with those obtained using staggered fermions. We also present results for $B$-parameters of the $\Delta I = 3/2$ part of the electromagnetic penguin operators, and preliminary results for \bk\ in the presence of two flavors of dynamical quarks.Comment: 39 pages, including 9 PS figures (LA UR-91-3522

Relaxation times of kinetically constrained spin models with glassy dynamics

We analyze the density and size dependence of the relaxation time $\tau$ for kinetically constrained spin systems. These have been proposed as models for strong or fragile glasses and for systems undergoing jamming transitions. For the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any density $\rho<1$ and for the Knight model below the critical density at which the glass transition occurs, we show that the persistence and the spin-spin time auto-correlation functions decay exponentially. This excludes the stretched exponential relaxation which was derived by numerical simulations. For FA2f in $d\geq 2$, we also prove a super-Arrhenius scaling of the form $\exp(1/(1-\rho))\leq \tau\leq\exp(1/(1-\rho)^2)$. For FA1f in $d$=$1,2$ we rigorously prove the power law scalings recently derived in \cite{JMS} while in $d\geq 3$ we obtain upper and lower bounds consistent with findings therein. Our results are based on a novel multi-scale approach which allows to analyze $\tau$ in presence of kinetic constraints and to connect time-scales and dynamical heterogeneities. The techniques are flexible enough to allow a variety of constraints and can also be applied to conservative stochastic lattice gases in presence of kinetic constraints.Comment: 4 page

Leading isospin-breaking corrections to pion, kaon and charmed-meson masses with Twisted-Mass fermions

We present a lattice computation of the isospin-breaking corrections to pseudoscalar meson masses using the gauge configurations produced by the European Twisted Mass collaboration with $N_f = 2 + 1 + 1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082$ and $0.089$ fm) with pion masses in the range $M_\pi \simeq 210 - 450$ MeV. The strange and charm quark masses are tuned at their physical values. We adopt the RM123 method based on the combined expansion of the path integral in powers of the $d$- and $u$-quark mass difference ($\widehat{m}_d - \widehat{m}_u$) and of the electromagnetic coupling $\alpha_{em}$. Within the quenched QED approximation, which neglects the effects of the sea-quark charges, and after the extrapolations to the physical pion mass and to the continuum and infinite volume limits, we provide results for the pion, kaon and (for the first time) charmed-meson mass splittings, for the prescription-dependent parameters $\epsilon_{\pi^0}$, \epsilon_\gamma(\overline{MS}, 2~\mbox{GeV}), \epsilon_{K^0}(\overline{MS}, 2~\mbox{GeV}), related to the violations of the Dashen's theorem, and for the light quark mass difference (\widehat{m}_d - \widehat{m}_u)(\overline{MS}, 2~\mbox{GeV}).Comment: 47 pages, 20 figures, 4 tables; comments on QED and QCD splitting prescriptions added; version to appear in PR

Evolution of the fine-structure constant in runaway dilaton models

We study the detailed evolution of the fine-structure constant $\alpha$ in the string-inspired runaway dilaton class of models of Damour, Piazza and Veneziano. We provide constraints on this scenario using the most recent $\alpha$ measurements and discuss ways to distinguish it from alternative models for varying $\alpha$. For model parameters which saturate bounds from current observations, the redshift drift signal can differ considerably from that of the canonical $\Lambda$CDM paradigm at high redshifts. Measurements of this signal by the forthcoming European Extremely Large Telescope (E-ELT), together with more sensitive $\alpha$ measurements, will thus dramatically constrain these scenarios.Comment: 11 pages, 4 figure