Diffusion of Botulinum Toxins

Background: It is generally agreed that diffusion of botulinum toxin occurs, but the extent of the spread and its clinical importance are disputed. Many factors have been suggested to play a role but which have the most clinical relevance is a subject of much discussion. Methods: This review discusses the variables affecting diffusion, including protein composition and molecular size as well as injection factors (e.g., volume, dose, injection method). It also discusses data on diffusion from comparative studies in animal models and human clinical trials that illustrate differences between the available botulinum toxin products (onabotulinumtoxinA, abobotulinumtoxinA, incobotulinumtoxinA, and rimabotulinumtoxinB). Results: Neither molecular weight nor the presence of complexing proteins appears to affect diffusion; however, injection volume, concentration, and dose all play roles and are modifiable. Both animal and human studies show that botulinum toxin products are not interchangeable, and that some products are associated with greater diffusion and higher rates of diffusion-related adverse events than others. Discussion: Each of the botulinum toxins is a unique pharmacologic entity. A working knowledge of the different serotypes is essential to avoid unwanted diffusion-related adverse events. In addition, clinicians should be aware that the factors influencing diffusion may range from properties intrinsic to the drug to accurate muscle selection as well as dilution, volume, and dose injected

Optimal Renormalization Scale and Scheme for Exclusive Processes

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 $\gamma e \to \pi^0 e$ data assuming that the pion distribution amplitude is close to its asymptotic form $\sqrt{3}f_\pi x(1-x)$. We also reproduce the scaling and normalization of the $\gamma \gamma \to \pi^+ \pi^-$ 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 $F_\pi(Q^2)$ 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 $\gamma^* p \to \pi^+ n$ electroproduction data to the pion pole.Comment: 22 pages, Latex, 7 Latex figures. Several references added, discussion of scale fixing revised for clarity. Final version to appear in Phys. Rev.

Renormalization-Scale-Invariant PQCD Predictions for R_e+e- and the Bjorken Sum Rule at Next-to-Leading Order

We discuss application of the physical QCD effective charge $\alpha_V$, defined via the heavy-quark potential, in perturbative calculations at next-to-leading order. When coupled with the Brodsky-Lepage-Mackenzie prescription for fixing the renormalization scales, the resulting series are automatically and naturally scale and scheme independent, and represent unambiguous predictions of perturbative QCD. We consider in detail such commensurate scale relations for the $e^+e^-$ annihilation ratio $R_{e^+e^-}$ and the Bjorken sum rule. In both cases the improved predictions are in excellent agreement with experiment.Comment: 13 Latex pages with 5 figures; to be published in Physical Review

Scaling laws in hadronic processes and string theory

We propose a possible scheme for getting the known QCD scaling laws within string theory. In particular, we consider amplitudes for exclusive scattering of hadrons at large momentum transfer, hadronic form factors and distribution functions.Comment: 13 pages, 2 figures, a comment and a reference added, a final version to appear in Physical Review

Light-Cone Quantization of Gauge Fields

Light-cone quantization of gauge field theory is considered. With a careful treatment of the relevant degrees of freedom and where they must be initialized, the results obtained in equal-time quantization are recovered, in particular the Mandelstam-Leibbrandt form of the gauge field propagator. Some aspects of the ``discretized'' light-cone quantization of gauge fields are discussed.Comment: SMUHEP/93-20, 17 pages (one figure available separately from the authors). Plain TeX, all macros include

Nucleon Helicity in Pion Photoproduction

Pion-photoproduction data is examined to check for the nucleon-helicity conservation predicted by asymptotic QCD. The differential cross section shows agreement with constituent-counting rules, and polarization data is not in disagreement with conservation of nucleon helicity. However large uncertainties in the polarization measurements do not allow a conclusive statement. The helicity amplitudes from a partial-wave analysis are also examined for helicity conservation. While the amplitudes become small as $s$ increases, the $s$ dependence of the helicity-conserving amplitudes is similar to the dependence of the non-conserving amplitudes.Comment: plain tex, 6 pages, 8 figure

Vacuum Structure of Two-Dimensional Gauge Theories on the Light Front

We discuss the problem of vacuum structure in light-front field theory in the context of (1+1)-dimensional gauge theories. We begin by reviewing the known light-front solution of the Schwinger model, highlighting the issues that are relevant for reproducing the $\theta$-structure of the vacuum. The most important of these are the need to introduce degrees of freedom initialized on two different null planes, the proper incorporation of gauge field zero modes when periodicity conditions are used to regulate the infrared, and the importance of carefully regulating singular operator products in a gauge-invariant way. We then consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)$/Z_2$, which possesses nontrivial topology. In particular, there are two topological sectors and the physical vacuum state has a structure analogous to a $\theta$ vacuum. We formulate the model using periodicity conditions in $x^\pm$ for infrared regulation, and consider a solution in which the gauge field zero mode is treated as a constrained operator. We obtain the expected $Z_2$ vacuum structure, and verify that the discrete vacuum angle which enters has no effect on the spectrum of the theory. We then calculate the chiral condensate, which is sensitive to the vacuum structure. The result is nonzero, but inversely proportional to the periodicity length, a situation which is familiar from the Schwinger model. The origin of this behavior is discussed.Comment: 29 pages, uses RevTeX. Improved discussion of the physical subspace generally and the vacuum states in particular. Basic conclusions are unchanged, but some specific results are modifie

Photoproduction at collider energies: from RHIC and HERA to the LHC

We present the mini-proceedings of the workshop on ``Photoproduction at collider energies: from RHIC and HERA to the LHC'' held at the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*, Trento) from January 15 to 19, 2007. The workshop gathered both theorists and experimentalists to discuss the current status of investigations of high-energy photon-induced processes at different colliders (HERA, RHIC, and Tevatron) as well as preparations for extension of these studies at the LHC. The main physics topics covered were: (i) small-$x$ QCD in photoproduction studies with protons and in electromagnetic (aka. ultraperipheral) nucleus-nucleus collisions, (ii) hard diffraction physics at hadron colliders, and (iii) photon-photon collisions at very high energies: electroweak and beyond the Standard Model processes. These mini-proceedings consist of an introduction and short summaries of the talks presented at the meeting

Scale Setting in QCD and the Momentum Flow in Feynman Diagrams

We present a formalism to evaluate QCD diagrams with a single virtual gluon using a running coupling constant at the vertices. This method, which corresponds to an all-order resummation of certain terms in a perturbative series, provides a description of the momentum flow through the gluon propagator. It can be viewed as a generalization of the scale-setting prescription of Brodsky, Lepage and Mackenzie to all orders in perturbation theory. In particular, the approach can be used to investigate why in some cases the ``typical'' momenta in a loop diagram are different from the ``natural'' scale of the process. It offers an intuitive understanding of the appearance of infrared renormalons in perturbation theory and their connection to the rate of convergence of a perturbative series. Moreover, it allows one to separate short- and long-distance contributions by introducing a hard factorization scale. Several applications to one- and two-scale problems are discussed in detail.Comment: eqs.(51) and (83) corrected, minor typographic changes mad