A note on the power divergence in lattice calculations of ΔI=1/2\Delta I = 1/2 K→ππK\to\pi\pi amplitudes at MK=MπM_{K}=M_{\pi}

In this note, we clarify a point concerning the power divergence in lattice calculations of $\Delta I = 1/2$ $K\to\pi\pi$ decay amplitudes. There have been worries that this divergence might show up in the Minkowski amplitudes at $M_{K}=M_{\pi}$ with all the mesons at rest. Here we demonstrate, via an explicit calculation in leading-order Chiral Perturbation Theory, that the power divergence is absent at the above kinematic point, as predicted by CPS symmetry.Comment: 5 pages, 2 figure

Finite-Volume Two-Pion Amplitudes in the I=0 Channel

We perform a calculation in one-loop chiral perturbation theory of the two-pion matrix elements and correlation functions of an I=0 scalar operator, in finite and infinite volumes for both full and quenched QCD. We show that major difficulties arise in the quenched theory due to the lack of unitarity. Similar problems are expected for quenched lattice calculations of $K \to \pi \pi$ amplitudes with $\Delta I=1/2$. Our results raise the important question of whether it is consistent to study $K\to\pi\pi$ amplitudes beyond leading order in chiral perturbation theory in quenched or partially quenched QCD.Comment: Version to appear on Phys. Lett. B, with only very minor and stylistic change

Biostimulation of Immobilized Microbes in a Fixed-Bed Bioreactor towards Hydrocarbon-Contaminated Water Remediation Using Compost Tea and Egg Shell Powder

The need to satisfy the ever increasing petroleum demand coupled with the availability of enough crude oil reserves to meet demand for several decades to come makes petroleum contamination a globally important subject. Bioremediation has emerged as an efficient treatment option for the remediation of organic contaminants including petroleum owing to the failure of physico-chemical treatment options to address petroleum contamination. The current study targeted the application of compost tea (CT) and egg shell powder (ESP) solution at various levels as nutrient amendments/bio-stimulants for hydrocarbon-eating microbes attached to support media surfaces in a fixed-bed bioreactor system. CT and ESP were characterized to be rich in essential nutrients including N, P, K, Ca, Mg, Na and C. CT and ESP application at four levels each recorded appreciable boosts in microbial numbers and TPH removal across applied levels. CT application recorded 23.49±2.20 to 29.36±0.79 % boost in TPH removal and 17.03±3.01 to 61.07±2.26 % boost in microbial mass. Boosts in TPH removal assumed the order 3200 ml 1600 ml 800 ml 400 ml. ESP application similarly recorded 27.56±2.62 to 29.57±0.90 % boost in TPH removal and 17.50±1.60 to 24.43±2.05 % boost in microbial mass. Recorded TPH removal boosts assumed the trend 20 g/l 10 g/ l 2.5 g/l 5 g/l

Chiral Perturbation Theory and Nucleon Polarizabilities

Compton scattering offers in principle an intriguing new window on nucleon structure. Existing experiments and future programs are discussed and the state of theoretical understanding of such measurements is explored.Comment: 15 page standard Latex file---invited talk at Chiral Dynamics Workshop, Mainz, Germany---typos correcte

Energy Loss of a Heavy Quark Produced in a Finite Size Medium

We study the medium-induced energy loss $-\Delta E_0(L_p)$ suffered by a heavy quark produced at initial time in a quark-gluon plasma, and escaping the plasma after travelling the distance $L_p$. The heavy quark is treated classically, and within the same framework $-\Delta E_0(L_p)$ consistently includes: the loss from standard collisional processes, initial bremsstrahlung due to the sudden acceleration of the quark, and transition radiation. The radiative loss {\it induced by rescatterings} $-\Delta E_{rad}(L_p)$ is not included in our study. For a ultrarelativistic heavy quark with momentum p \gsim 10 {\rm GeV}, and for a finite plasma with L_p \lsim 5 {\rm fm}, the loss $-\Delta E_0(L_p)$ is strongly suppressed compared to the stationary collisional contribution $-\Delta E_{coll}(L_p) \propto L_p$. Our results support that $-\Delta E_{rad}$ is the dominant contribution to the heavy quark energy loss (at least for L_p \lsim 5 {\rm fm}), as indeed assumed in most of jet-quenching analyses. However they might raise some question concerning the RHIC data on large $p_{\perp}$ electron spectra.Comment: 18 pages, 3 figures. New version clarified and simplified. A critical discussion added in section 2, and previous sections 3 and 4 have been merged together. Main results are unchange

Burkhardt-Cottingham sum rule and forward spin polarizabilities in Heavy Baryon Chiral Perturbation Theory

We study spin-dependent sum rules for forward virtual Compton scattering(VVCS) off the nucleon in heavy baryon chiral perturbation theory at order $O(p^4)$. We show how these sum rules can be evaluated from low energy expansions (in the virtual photon energy) of the forward VVCS amplitudes. We study in particular the Burkhardt -Cottingham sum rule in HBChPT and higher terms in the low energy expansion, which can be related to the generalized forward spin polarizabilities of the nucleon. The dependence of these observables on the photon virtuality $Q^2$ can be accessed, at small and intermediate $Q^2$ values, from existing and forthcoming data at Jefferson Lab.Comment: 16 pages,4 fig

Black holes in which the electrostatic or scalar equation is solvable in closed form

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically symmetric geometries with a non-degenerated horizon in which the static scalar equation can be solved in closed form. We give the explicit results in 6 dimensions. We determine moreover the expressions of the electrostatic potential and of the static scalar field for a point source in the extremal Reissner-Nordstrom black holes in higher dimensions.Comment: 20 pages, no figur

Retardation Effect for Collisional Energy Loss of Hard Partons Produced in a QGP

We study the collisional energy loss suffered by an energetic parton travelling the distance L in a high temperature quark-gluon plasma and initially produced in the medium. We find that the medium-induced collisional loss -Delta E(L) is strongly suppressed compared to previous estimates which assumed the collisional energy loss rate -dE/dx to be constant. The large L linear asymptotic behaviour of -Delta E(L) sets in only after a quite large retardation time. The suppression of -Delta E(L) is partly due to the fact that gluon bremsstrahlung arising from the initial acceleration of the energetic parton is reduced in the medium compared to vacuum. The latter radiation spectrum is sensitive to the plasmon modes of the quark-gluon plasma and has a rich angular structure.Comment: 19 pages, 4 figures. Substantial changes have been made in version 2, especially in section 3. In particular, in section 3.2 the dependence on a spurious ultraviolet cut-off has been removed. As a consequence numerical results are quantitatively modified, but the retardation effect is qualitatively unchanged. The physical origin of the largeness of the retardation time is also emphasized, and two Appendices have been adde

Finite volume corrections to the electromagnetic current of the nucleon

We compute corrections to both the isovector anomalous magnetic moment and the isovector electromagnetic current of the nucleon to $O(p^3)$ in the framework of covariant two-flavor Baryon Chiral Perturbation Theory. We then apply these corrections to lattice data for the anomalous magnetic moment from the LHPC, RBC & UKQCD and QCDSF collaborations