We use the BLM method to fix the renormalization scale of the QCD coupling in exclusive hadronic amplitudes such as the pion form factor and the photon-to-pion transition form factor at large momentum transfer. Renormalization-scheme-independent commensurate scale relations are established which connect the hard scattering subprocess amplitudes that control exclusive processes to other QCD observables such as the heavy quark potential and the electron-positron annihilation cross section. The commensurate scale relation connecting the heavy quark potential, as determined from lattice gauge theory, to the photon-to-pion transition form factor is in excellent agreement with γe → π 0 e data assuming that the pion distribution amplitude is close to its asymptotic form √ 3f π x(1 − x). We also reproduce the scaling and normalization of the γγ → π + π − data at large momentum transfer. Because the renormalization scale is small, we argue that the effective coupling is nearly constant, thus accounting for the nominal scaling behavior of the data. However, the normalization of the space-like pion form factor F π (Q 2 ) obtained from electroproduction experiments is somewhat higher than that predicted by the corresponding commensurate scale relation. This discrepancy may be due to systematic errors introduced by the extrapolation of the γ

TSIL is a library of utilities for the numerical calculation of dimensionally regularized two-loop self-energy integrals. A convenient basis for these functions is given by the integrals obtained at the end of O.V. Tarasov's recurrence relation algorithm. The program computes the values of all of these basis functions, for arbitrary input masses and external momentum. When analytical expressions in terms of polylogarithms are available, they are used. Otherwise, the evaluation proceeds by a Runge-Kutta integration of the coupled first-order differential equations for the basis integrals, using the external momentum invariant as the independent variable. The starting point of the integration is provided by known analytic expressions at (or near) zero external momentum. The code is written in C, and may be linked from C, C++, or Fortran. A Fortran interface is provided. We describe the structure and usage of the program, and provide a simple example application. We also compute two new cases analytically, and compare all of our notations and conventions for the two-loop self-energy integrals to those used by several other groups.Comment: 31 pages. Updated to reflect new functionality through v1.4 May 2016 and new information about use with C++. Source code and documentation are available at http://www.niu.edu/spmartin/TSIL or http://faculty.otterbein.edu/DRobertson/tsil

We calculate the mass of the Higgs boson in the Standard Model in terms of the underlying Lagrangian parameters at complete 2-loop order with leading 3-loop corrections. A computer program implementing the results is provided. The program also computes and minimizes the Standard Model effective potential in Landau gauge at 2-loop order with leading 3-loop corrections. Contents

Sequestration of carbon dioxide by steelmaking slag was studied in an atmospheric three-phase system containing industrial slag particles, water, and CO 2 gas. Batch-type reactors were used to measure the rate of aqueous alkaline leaching and slag particle carbonization independently. Four sizes of slag particles were tested for the Ca leaching rate in deionized water at a constant 7.5 pH in an argon atmosphere and for carbonate conversion with CO 2 bubbled through an aqueous suspension. Conversion data (fraction of Ca leached or converted to carbonate) were evaluated to determine the rate-limiting step based on the shrinking core model. For Ca leaching, the chemical reaction is the controlling mechanism during the initial period of time, which then switches to diffusion through the developed porous layer as the rate-limiting step. Carbonate conversion proceeded much slower than leaching conversion and was found to be limited by diffusion through the product calcium carbonate layer. The calculated value of diffusivity was found to be 5 · 10 -9 cm 2 /s, which decreased by an order of magnitude with increasing carbonization conversion as a result of changing density of the product layer. The experimental data fit the shrinking core model well after correction for the particle specific surface area.

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The problem of spontaneous symmetry breaking in scalar field theories quantized on the light cone is considered. Within the framework of "discretized" light-cone field theory, a constrained zero mode of the scalar field, which is necessary for obtaining a consistent dynamics, is responsible for supporting nonzero vacuum expectation values classically. This basic structure is shown to carry over to the quantum theory as well, and the consistency of the formalism is checked in an explicit perturbative calculation in ( 1 + 1 )-dimensional 44 theory.PACS number(s): ll.lO.Ef, 11.30.Q~

We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite basis integrals that are particularly convenient for expressing renormalized quantities. The basis integrals can be computed numerically by solving coupled first-order differential equations, using as boundary conditions the analytically known special cases that depend on only one mass scale. We provide the results necessary to carry this out, and introduce an implementation in the form of a public software package called 3VIL (3-loop Vacuum Integral Library), which efficiently computes the numerical values of the basis integrals for any specified masses. 3VIL is written in C, and can be linked from C, C++, or FORTRAN code. Contents

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