Bottom quark electroproduction in variable flavor number schemes

Two variable flavor number schemes are used to describe bottom quark production in deep inelastic electron-proton scattering. In these schemes the coefficient functions are derived from mass factorization of the heavy quark coefficient functions presented in a fixed flavor number scheme. Also one has to construct a parton density set with five light flavors (u,d,s,c,b) out of a set which only contains four light flavors (u,d,s,c). In order $\alpha_s^2$ the two sets are discontinuous at $\mu=m_b$ which follows from mass factorization of the heavy quark coefficient functions when it is carried out in the ${\bar {\rm MS}}$-scheme. Both variable flavor number schemes give almost identical predictions for the bottom structure functions $F_{2,b}$ and $F_{L,b}$. Also they both agree well with the corresponding results based on fixed order four-flavor perturbation theory over a wide range in $x$ and $Q^2$.Comment: Latex with seventeen PostScript figure

Evaluation and validation of Damage Assessment Tracking Criteria models within the sector of UK automotive remanufacturing

This paper details the specific aims and purposes of the Damage Assessment Tracking Criteria; a series of evaluation tools designed to aid in remanufacturing inspection operations. The background and justification of this model, which is detailed in a separate work, identifies ill definition and an over reliance on opinion as barriers to effective inspection activities. Analysis of this issue led to the building of the Damage Assessment Tracking Criteria; a 4-model foundation that aims to provide a more comprehensive and more structured approach to the inspection stages of the typical remanufacturing process. Through expert opinion this model was evaluated multiple times. One review was used to gauge the level of idea communication within an academic situation, this was followed up by external industrial reviews of the model by those most likely to utilise it during industry practice. After extensive feedback and modification the final model assessment was carried out with an expert panel that were instructed to be as critical as possible with the model in order to ensure that its evaluation was as robust as possible. The results of these reviews were all on the positive side of the scale. Multiple statements regarding the potential value and suitability of each model aspect and justification for their use was presented in the format of an evaluation form which was used by those involved to present their findings and feedback. Negative feedback was addressed and successful modification yielding more positive results in the next evaluation was achieved. Though walking the line between specificity and generic was noted to be the most difficult factor to consider when developing the models, the final findings of the evaluation show that significant value was perceived by those operating within industry. The potential benefits of customised variants of the models is acknowledged by all parties as a possible future avenue of research

Comparison between variable flavor number schemes for charm quark electroproduction

Where appropriate, the abbreviation 'VFNS' is replaced by 'CSN' to indicate the scheme using massive heavy quark coefficient functions proposed in this paper. The text below Eq. (2.13) and between Eqs. (2.33) and (2.36) has been considerably changed.Comment: 64 pages, LaTeX, 16 Postscript figure

Order \alpha_s^2 Contributions to charm production in charged-current deep-inelastic lepton-hadron scattering

The most important part of the order $\alpha_s^2$ corrections to the charm component of the charged-current structure functions $F_2(x,Q^2)$ and $F_3(x,Q^2)$ have been calculated. This calculation is based on the asymptotic form of the heavy-quark coefficient functions corresponding to the higher order corrections to the W-boson-gluon fusion process. These coefficient functions which are in principle only valid for $Q^2 \gg m^2$ can be also used to estimate the order $\alpha_s^2$ contributions at lower $Q^2$ values provided $x < 0.1$. It turns out that the above corrections are appreciable in the large $Q^2$-region and they explain the discrepancy found for the structure functions between the fixed-flavour scheme (FFS) and the variable-flavour-number scheme (VFNS). These corrections also hamper the extraction of the strange-quark density from the data obtained for the charged-current and the electromagnetic-current processes.Comment: 45 pages LaTeX, 17 Postscript Figure

A scalar invariant and the local geometry of a class of static spacetimes

The scalar invariant, I, constructed from the "square" of the first covariant derivative of the curvature tensor is used to probe the local geometry of static spacetimes which are also Einstein spaces. We obtain an explicit form of this invariant, exploiting the local warp-product structure of a 4-dimensional static spacetime, $~^{(3)}\Sigma \times_{f} \reals$, where $^{(3)}\Sigma$ is the Riemannian hypersurface orthogonal to a timelike Killing vector field with norm given by a positive function, $f$ on $^{(3)}\Sigma$. For a static spacetime which is an Einstein space, it is shown that the locally measurable scalar, I, contains a term which vanishes if and only if $^{(3)}\Sigma$ is conformally flat; also, the vanishing of this term implies (a) $~^{(3)}\Sigma$ is locally foliated by level surfaces of $f$, $^{(2)}S$, which are totally umbilic spaces of constant curvature, and (b) $^{(3)}\Sigma$ is locally a warp-product space. Futhermore, if $^{(3)}\Sigma$ is conformally flat it follows that every non-trivial static solution of the vacuum Einstein equation with a cosmological constant, is either Nariai-type or Kottler-type - the classes of spacetimes relevant to quantum aspects of gravity.Comment: LaTeX, 13 pages, JHEP3.cls; The paper is completely rewritten with a new title and introduction as well as additional results and reference

Spin glass transition in a magnetic field: a renormalization group study

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order epsilon = 6-d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.

Definition and Calculation of Bottom Quark Cross-Sections in Deep-inelastic Scattering at HERA and Determination of their Uncertainties

The uncertainties involved in the calculation of bottom quark cross-sections in deep-inelastic scattering at HERA are studied in different phase space regions. Besides the inclusive bottom quark cross-section, definitions closer to the detector acceptance requiring at least one high energetic muon from the semi-leptonic \bquark decay or a jet with high transverse energy are investigated. For each case the uncertainties due to the choice of the renormalisation and factorisation scale as well as the \bquark mass are estimated in the perturbative NLO QCD calculation and furthermore uncertainties in the fragmenation of the bottom quark to a B-meson and in its semi-leptonic decay are discussed

Next-to-Leading Order Cross Sections for Tagged Reactions

We extend the phase space slicing method of Giele, Glover and Kosower for performing next-to-leading order jet cross section calculations in two important ways: we show how to include fragmentation functions and how to include massive particles. These extensions allow the application of this method to not just jet cross sections but also to cross sections in which a particular final state particle, including a $D$ or $B$-meson, is tagged.Comment: 36 pages, Latex Small corrections to text. To appear in Phys. Rev.

The Planetary Nebula Luminosity Function at the Dawn of Gaia

The [O III] 5007 Planetary Nebula Luminosity Function (PNLF) is an excellent extragalactic standard candle. In theory, the PNLF method should not work at all, since the luminosities of the brightest planetary nebulae (PNe) should be highly sensitive to the age of their host stellar population. Yet the method appears robust, as it consistently produces < 10% distances to galaxies of all Hubble types, from the earliest ellipticals to the latest-type spirals and irregulars. It is therefore uniquely suited for cross-checking the results of other techniques and finding small offsets between the Population I and Population II distance ladders. We review the calibration of the method and show that the zero points provided by Cepheids and the Tip of the Red Giant Branch are in excellent agreement. We then compare the results of the PNLF with those from Surface Brightness Fluctuation measurements, and show that, although both techniques agree in a relative sense, the latter method yields distances that are ~15% larger than those from the PNLF. We trace this discrepancy back to the calibration galaxies and argue that, due to a small systematic error associated with internal reddening, the true distance scale likely falls between the extremes of the two methods. We also demonstrate how PNLF measurements in the early-type galaxies that have hosted Type Ia supernovae can help calibrate the SN Ia maximum magnitude-rate of decline relation. Finally, we discuss how the results from space missions such as Kepler and Gaia can help our understanding of the PNLF phenomenon and improve our knowledge of the physics of local planetary nebulae.Comment: 12 pages, invited review at the conference "The Fundamental Cosmic Distance Scale: State of the Art and Gaia Perspective", to appear in Astrophysics and Space Scienc

Globular cluster luminosity function as distance indicator

Globular clusters are among the first objects used to establish the distance scale of the Universe. In the 1970-ies it has been recognized that the differential magnitude distribution of old globular clusters is very similar in different galaxies presenting a peak at M_V ~ -7.5. This peak magnitude of the so-called Globular Cluster Luminosity Function has been then established as a secondary distance indicator. The intrinsic accuracy of the method has been estimated to be of the order of ~0.2 mag, competitive with other distance determination methods. Lately the study of the Globular Cluster Systems has been used more as a tool for galaxy formation and evolution, and less so for distance determinations. Nevertheless, the collection of homogeneous and large datasets with the ACS on board HST presented new insights on the usefulness of the Globular Cluster Luminosity Function as distance indicator. I discuss here recent results based on observational and theoretical studies, which show that this distance indicator depends on complex physics of the cluster formation and dynamical evolution, and thus can have dependencies on Hubble type, environment and dynamical history of the host galaxy. While the corrections are often relatively small, they can amount to important systematic differences that make the Globular Cluster Luminosity Function a less accurate distance indicator with respect to some other standard candles.Comment: Accepted for publication in Astrophysics and Space Science. Review paper based on the invited talk at the conference "The Fundamental Cosmic Distance Scale: State of the Art and Gaia Perspective", Naples, May 2011. (13 pages, 8 figures