Brushed-Off Testimony

In line with years of tradition, soldiers young and old come together at the local pub or hall to swap war stories of time in the trenches. For the forensic clinician, the trenches represent the hard-fought battles during expert testimony. As it turns out, our pub was a social gathering at the 2012 meeting of the American Psychology Law Society in San Juan, Puerto Rico. The University of Alabama Psychology Law Program hosted a social gathering for its faculty, graduate students, alumni, and friends to come together and share stories and camaraderie. It was in this setting that we launched into a spirited discussion of similar experiences testifying in rural county courts

Application of the Principle of Maximum Conformality to Top-Pair Production

A major contribution to the uncertainty of finite-order perturbative QCD predictions is the perceived ambiguity in setting the renormalization scale $\mu_r$. For example, by using the conventional way of setting $\mu_r \in [m_t/2,2m_t]$, one obtains the total $t \bar{t}$ production cross-section $\sigma_{t \bar{t}}$ with the uncertainty \Delta \sigma_{t \bar{t}}/\sigma_{t \bar{t}}\sim ({}^{+3%}_{-4%}) at the Tevatron and LHC even for the present NNLO level. The Principle of Maximum Conformality (PMC) eliminates the renormalization scale ambiguity in precision tests of Abelian QED and non-Abelian QCD theories. In this paper we apply PMC scale-setting to predict the $t \bar t$ cross-section $\sigma_{t\bar{t}}$ at the Tevatron and LHC colliders. It is found that $\sigma_{t\bar{t}}$ remains almost unchanged by varying $\mu^{\rm init}_r$ within the region of $[m_t/4,4m_t]$. The convergence of the expansion series is greatly improved. For the $(q\bar{q})$-channel, which is dominant at the Tevatron, its NLO PMC scale is much smaller than the top-quark mass in the small $x$-region, and thus its NLO cross-section is increased by about a factor of two. In the case of the $(gg)$-channel, which is dominant at the LHC, its NLO PMC scale slightly increases with the subprocess collision energy $\sqrt{s}$, but it is still smaller than $m_t$ for $\sqrt{s}\lesssim 1$ TeV, and the resulting NLO cross-section is increased by $\sim 20$. As a result, a larger $\sigma_{t\bar{t}}$ is obtained in comparison to the conventional scale-setting method, which agrees well with the present Tevatron and LHC data. More explicitly, by setting $m_t=172.9\pm 1.1$ GeV, we predict $\sigma_{\rm Tevatron,\;1.96\,TeV} = 7.626^{+0.265}_{-0.257}$ pb, $\sigma_{\rm LHC,\;7\,TeV} = 171.8^{+5.8}_{-5.6}$ pb and $\sigma_{\rm LHC,\;14\,TeV} = 941.3^{+28.4}_{-26.5}$ pb. [full abstract can be found in the paper.]Comment: 15 pages, 11 figures, 5 tables. Fig.(9) is correcte

Light-Front Holography: A First Approximation to QCD

Starting from the Hamiltonian equation of motion in QCD, we identify an invariant light-front coordinate $\zeta$ which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single variable light-front Schrodinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-$J$ modes on anti-de Sitter (AdS) space.Comment: 4 pages. The limits of validity of the model are further discussed. To appear in Physical Review Letter

Essence of the vacuum quark condensate

We show that the chiral-limit vacuum quark condensate is qualitatively equivalent to the pseudoscalar meson leptonic decay constant in the sense that they are both obtained as the chiral-limit value of well-defined gauge-invariant hadron-to-vacuum transition amplitudes that possess a spectral representation in terms of the current-quark mass. Thus, whereas it might sometimes be convenient to imagine otherwise, neither is essentially a constant mass-scale that fills all spacetime. This means, in particular, that the quark condensate can be understood as a property of hadrons themselves, which is expressed, for example, in their Bethe-Salpeter or light-front wavefunctions.Comment: 5 pages, 1 figur

High Energy Photon-Photon and Electron-Photon Collisions

The advent of a next linear $e^\pm e^-$ collider and back-scatterd laser beams will allow the study of a vast array of high energy processes of the Standard Model through the fusion of real and virtual photons and other gauge bosons. As examples, I discuss virtual photon scattering $\gamma^* \gamma^* \to X$ in the region dominated by BFKL hard Pomeron exchange and report the predicted cross sections at present and future $e^\pm e^-$ colliders. I also discuss exclusive $\gamma \gamma$ reactions in QCD as a measure of hadron distribution amplitudes and a new method for measuring the anomalous magnetic and quadrupole moments of the $W$ and $Z$ gauge bosons to high precision in polarized electron-photon collisions.Comment: LaTex, 12 page

Scale Setting Using the Extended Renormalization Group and the Principle of Maximum Conformality: the QCD Coupling Constant at Four Loops

A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The extended renormalization group equations, which express the invariance of physical observables under both the renormalization scale- and scheme-parameter transformations, provide a convenient way for estimating the scale- and scheme-dependence of the physical process. In this paper, we present a solution for the scale-equation of the extended renormalization group equations at the four-loop level. Using the principle of maximum conformality (PMC) / Brodsky-Lepage-Mackenzie (BLM) scale-setting method, all non-conformal $\{\beta_i\}$ terms in the perturbative expansion series can be summed into the running coupling, and the resulting scale-fixed predictions are independent of the renormalization scheme. Different schemes lead to different effective PMC/BLM scales, but the final results are scheme independent. Conversely, from the requirement of scheme independence, one not only can obtain scheme-independent commensurate scale relations among different observables, but also determine the scale displacements among the PMC/BLM scales which are derived under different schemes. In principle, the PMC/BLM scales can be fixed order-by-order, and as a useful reference, we present a systematic and scheme-independent procedure for setting PMC/BLM scales up to NNLO. An explicit application for determining the scale setting of $R_{e^{+}e^-}(Q)$ up to four loops is presented. By using the world average $\alpha^{\bar{MS}}_s(M_Z) =0.1184 \pm 0.0007$, we obtain the asymptotic scale for the 't Hooft associated with the $\bar{MS}$ scheme, $\Lambda^{'tH}_{\bar{MS}}= 245^{+9}_{-10}$ MeV, and the asymptotic scale for the conventional $\bar{MS}$ scheme, $\Lambda_{\bar{MS}}= 213^{+19}_{-8}$ MeV.Comment: 9 pages, no figures. The formulas in the Appendix are correcte

Self-Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale

In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariance - reflectivity, symmetry, and transitivity. Using the PMC, all non-conformal $\{\beta^{\cal R}_i\}$-terms (${\cal R}$ stands for an arbitrary renormalization scheme) in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance. [...More in the text...]Comment: 15 pages, 4 figures. References updated. To be published in Phys.Rev.

Light-Front Quantization and AdS/QCD: An Overview

We give an overview of the light-front holographic approach to strongly coupled QCD, whereby a confining gauge theory, quantized on the light front, is mapped to a higher-dimensional anti de Sitter (AdS) space. The framework is guided by the AdS/CFT correspondence incorporating a gravitational background asymptotic to AdS space which encodes the salient properties of QCD, such as the ultraviolet conformal limit at the AdS boundary at $z \to 0$, as well as modifications of the geometry in the large $z$ infrared region to describe confinement and linear Regge behavior. There are two equivalent procedures for deriving the AdS/QCD equations of motion: one can start from the Hamiltonian equation of motion in physical space time by studying the off-shell dynamics of the bound state wavefunctions as a function of the invariant mass of the constituents. To a first semiclassical approximation, where quantum loops and quark masses are not included, this leads to a light-front Hamiltonian equation which describes the bound state dynamics of light hadrons in terms of an invariant impact variable $\zeta$ which measures the separation of the partons within the hadron at equal light-front time. Alternatively, one can start from the gravity side by studying the propagation of hadronic modes in a fixed effective gravitational background. Both approaches are equivalent in the semiclassical approximation. This allows us to identify the holographic variable $z$ in AdS space with the impact variable $\zeta$. Light-front holography thus allows a precise mapping of transition amplitudes from AdS to physical space-time. The internal structure of hadrons is explicitly introduced and the angular momentum of the constituents plays a key role.Comment: Invited talk presented by GdT at the XIV School of Particles and Fields, Morelia, Mexico, November 8-12, 201

An Examination of Website Advice to Avoid Jury Duty

The use of a jury in legal proceedings can be traced as far back as the participatory democracies that emerged in Greece in the sixth century BC, although it was not until the signing of the Magna Carta that the right to a trial by a jury of one’s peers emerged.1 In the United States, the Sixth and Seventh Amendments of the U.S. Constitution expressly provide this right in both criminal and civil proceedings.2 Furthermore, these amendments provide individuals with the right to a trial before an impartial jury.3 This right intends to serve as a safeguard against unfair treatment during a trial, providing a system of checks and balances to pursue the goal that justice remains at the heart of the legal system. A jury is intended to serve as a cross-section of the community, as it is drawn from and purports to represent the collective community conscience and common sense when resolving disagreements.4 Despite this rich constitutional history and community context, many residents of the United States actively seek to avoid jury service when they are called, for reasons we discuss further below. Some individuals search the Internet for information about how to avoid participating in jury service. As trial judges are tasked with oversight that spans the entire process of impanelment through voir dire, this study sought to provide a contextual background to assist the judiciary in easily recognizing and assessing potential jury avoidance. In the current study, the investigators examined advice offered by popular websites about how reluctant jurors may attempt to be excused from jury service

Structure Functions are not Parton Probabilities

The common view that structure functions measured in deep inelastic lepton scattering are determined by the probability of finding quarks and gluons in the target is not correct in gauge theory. We show that gluon exchange between the fast, outgoing partons and target spectators, which is usually assumed to be an irrelevant gauge artifact, affects the leading twist structure functions in a profound way. This observation removes the apparent contradiction between the projectile (eikonal) and target (parton model) views of diffractive and small x_{Bjorken} phenomena. The diffractive scattering of the fast outgoing quarks on spectators in the target causes shadowing in the DIS cross section. Thus the depletion of the nuclear structure functions is not intrinsic to the wave function of the nucleus, but is a coherent effect arising from the destructive interference of diffractive channels induced by final state interactions. This is consistent with the Glauber-Gribov interpretation of shadowing as a rescattering effect.Comment: 35 pages, 8 figures. Discussion of physical consequences of final state interactions amplified. Material on light-cone gauge choices adde