arXiv subjects

E. W. N. Glover

Publications and source records attributed to E. W. N. Glover.

At least 145 records · Page 8Linked to original sources

arXiv1999

Scalar One-Loop Integrals using the Negative-Dimension Approach

We study massive one-loop integrals by analytically continuing the Feynman integral to negative dimensions as advocated by Halliday and Ricotta and developed by Suzuki and Schmidt. We consider n-point one-loop integrals with arbitrary powers of propagators in general dimension D. For integrals with m mass scales and q external momentum scales, we construct a template solution valid for all n which allows us to obtain a representation of the graph in terms of a finite sum of generalised hypergeometric functions with m+q-1 variables. All solutions for all possible kinematic regions are given simultaneously, allowing the investigation of different ranges of variation of mass and momentum scales. As a first step, we develop the general framework and apply it to massive bubble and vertex integrals. Of course many of these integrals are well known and we show that the known results are recovered. To give a concrete new result, we present expressions for the general vertex integral with one off-shell leg and two internal masses in terms of hypergeometric functions of two variables that converge in the appropriate kinematic regions. The kinematic singularity structure of this graph is sufficiently complex to give insight into how the negative-dimension method operates and gives some hope that more complicated graphs can also be evaluated.

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arXiv1998

Four jet event shapes in electron-positron annihilation

We report next-to-leading order perturbative QCD predictions of 4 jet event shape variables for the process e+e- \to 4 jets obtained using the general purpose Monte Carlo EERAD2. This program is based on the known `squared' one loop matrix elements for the virtual γ^* \to 4 parton contribution and squared matrix elements for 5 parton production. To combine the two distinct final states numerically we present a hybrid of the commonly used subtraction and slicing schemes based on the colour antenna structure of the final state which can be readily applied to other processes. We have checked that the numerical results obtained with EERAD2 are consistent with next-to-leading order estimates of the distributions of previously determined four jet-like event variables. We also report the next-to-leading order scale independent coefficients for some previously uncalculated observables; the light hemisphere mass, narrow jet broadening, Aplanarity and the 4 jet transition variables with respect to the JADE and Geneva jet finding algorithms. For each of these observables, the next-to-leading order corrections calculated at the physical scale significantly increase the rate compared to leading order (the K factor is approximately 1.5 -- 2). With the exception of the 4 jet transition variables, the published DELPHI data lies well above the O(α_s^3) predictions. The renormalisation scale uncertainty is still large and in most cases the data prefers a scale significantly smaller than the physical scale. This situation is reminiscent of that for three jet shape variables, and should be improved by the inclusion of power corrections and resummation of large infrared logarithms.

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arXiv1998

Double Unresolved Approximations to Multiparton Scattering Amplitudes

We present approximations to tree level multiparton scattering amplitudes which are appropriate when two partons are unresolved. These approximations are required for the analytic isolation of infrared singularities of n+2 parton scattering processes contributing to the next-to-next-to-leading order corrections to n jet cross sections. In each case the colour ordered matrix elements factorise and yield a function containing the singular factors multiplying the n parton amplitudes. When the unresolved particles are not colour connected, the approximations are simple products of the familar eikonal and Altarelli-Parisi splitting functions used to describe single unresolved emission. However, when the unresolved particles are colour connected the factorisation is more complicated and we introduce new and general functions to describe the triple collinear and soft/collinear limits in addition to the known double soft gluon limits of Berends and Giele. As expected the triple collinear splitting functions obey an N=1 SUSY identity. To illustrate the use of these double unresolved approximations, we have examined the singular limits of the tree level matrix elements for e+e- to 5 partons when only three partons are resolved. When integrated over the unresolved regions of phase space, these expressions will be of use in evaluating the O(alpha_s^3) corrections to the three jet rate in electron positron annihilation.

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arXiv1998

The One-loop QCD Corrections for $γ^* to Q\bar Q q\bar q$

We calculate the one-loop QCD corrections for the decay of an off-shell vector boson with vector couplings into two pairs of quarks of equal or unequal flavours keeping all orders in the number of colours. These matrix elements are relevant for the calculation of the next-to-leading order ${\cal O}(α_s^3)$ corrections to four jet production in electron-positron annihilation, the production of a gauge boson accompanied by two jets in hadron-hadron collisions and three jet production in deep inelastic scattering. We use standard techniques for computing the interference of one-loop and tree level Feynman diagrams, but organise the results in terms of combinations of scalar loop integrals that are finite in the limit of vanishing Gram determinants and are therefore numerically stable.

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arXiv1998

The One-loop QCD Corrections for gamma^* to q qbar gg

We compute the one-loop QCD amplitudes for the decay of an off-shell vector boson with vector couplings into a quark-antiquark pair accompanied by two gluons keeping, for the first time, all orders in the number of colours. Together with previous work this completes the calculation of the necessary one-loop amplitudes needed for the calculation of the next-to-leading order O(alpha_s^3) corrections to four jet production in electron-positron annihilation, the production of a gauge boson accompanied by two jets in hadron-hadron collisions and three jet production in deep inelastic scattering.

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arXiv1998

Final state photon production at LEP

We present a detailed study of photon production in hadronic events in electron-positron annihilation at LEP energies. We show that estimates of the inclusive photon spectrum using the quark-to-photon fragmentation function determined using the ALEPH `photon' +~1 jet data agree well with the observations of the OPAL collaboration. This agreement shows that the photon fragmentation function determined in this way can be used for inclusive observables. We also compare next-to-leading order and beyond leading logarithm predictions obtained using the numerically resummed solutions of the fragmentation function evolution equation of Bourhis, Fontannaz and Guillet and Glück, Reya and Vogt with the data. Moreover, in order to check the general behaviour of the fragmentation function, we consider an analytic series expansion in the strong coupling. We find that the parameterizations are inaccurate at large $x$ values. While the OPAL data is in broad agreement with estimates based on any of these approaches, the ALEPH data prefers the resummed BFG parameterization. Finally, there is some ambiguity as to whether the fragmentation function is treated as ${\cal O}(α)$ or ${\cal O}(α/α_s)$. We show that at present this ambiguity affects mainly the prediction for the `photon' +~1 jet rate at large $z$.

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arXiv1998

Jet Physics: Theoretical Overview

I review the status of fixed order jet Monte Carlos and briefly discuss the prospects for next-to-next-to-leading order calculations. I present a general purpose next-to-leading order Monte Carlo program for four jet event shape observables in electron-positron annihilation and present some estimates of the light jet mass and narrow jet broadening distributions. Finally, I discuss an estimate of the strong coupling constant using the measured energy evolution of the average value of event shape variables such as thrust and heavy jet mass.

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arXiv1998

Determination of Lambda_QCD from the measured energy dependence of <1-Thrust>

We directly fit the experimentally measured energy dependence of the average value of 1-Thrust, <1-T>, over the e^+e^- centre-of-mass energy range Q=14 - 172 GeV to the QCD expectation obtained by integrating up the evolution equation for d<1-T>/dlog Q in terms of <1-T>. We fit for Lambda_QCD, uncalculated O(alpha_S^3) and higher perturbative corrections parameterized by the scheme invariant rho_2, and the parameter lambda which characterizes the magnitude of the leading 1/Q power corrections anticipated for <1-T>. A 3-parameter fit yields Lambda_QCD=245^{+20}_{-17} MeV, rho_2=-16\pm 11 and lambda=0.27^{+0.12}_{-0.10} GeV, equivalent to alpha_S(M_Z)=0.1194 \pm 0.0014. In this approach, there is no error associated with the choice of the renormalization scale mu.

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arXiv1998

A complete ${\cal O}(αα_s)$ calculation of the Photon + 1 Jet rate in $e^+e^-$ annihilation

We present a complete calculation of the photon +~1 jet rate in $e^+e^-$ annihilation up to ${\cal O}(αα_{s})$. Although formally of next-to-leading order in perturbation theory, this calculation contains several ingredients appropriate to a next-to-next-to-leading order calculation of jet observables. In particular, we describe a generalization of the commonly used phase space slicing method to isolate the singularities present when more than one particle is unresolved. Within this approach, we analytically evaluate the singularities associated with the following double unresolved regions; triple collinear, soft/collinear and double single collinear configurations as well as those from the collinear limit of virtual graphs. By comparing the results of our calculation with the existing data on the photon +~1 jet rate from the ALEPH Collaboration at CERN, we make a next-to-leading order determination of the process-independent non-perturbative quark-to-photon fragmentation function $D_{q \to γ}(z,μ_{F})$ at ${\cal O}(αα_{s})$. As a first application of this measurement allied with our improved perturbative calculation, we determine the dependence of the isolated photon +~1 jet cross section in a democratic clustering approach on the jet resolution parameter $\ycut$ at next-to-leading order. The next-to-leading order corrections to this observable are moderate but improve the agreement between theoretical prediction and experimental data.

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arXiv1998

One-Loop Tensor Integrals in Dimensional Regularisation

We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of $n$- and $(n-1)$-point scalar integrals that are finite in the limit of vanishing Gram determinant. These non-trivial combinations of dilogarithms, logarithms and constants are systematically obtained by either differentiating with respect to the external parameters - essentially yielding scalar integrals with Feynman parameters in the numerator - or by developing the scalar integral in $D=6-2\e$ or higher dimensions. As an explicit example, we develop the tensor integrals and associated scalar integral combinations for processes where the internal particles are massless and where up to five (four massless and one massive) external particles are involved. For more general processes, we present the equations needed for deriving the relevant combinations of scalar integrals.

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arXiv1997

Probabilistic Jet Algorithms

Conventional jet algorithms are based on a deterministic view of the underlying hard scattering process. Each outgoing parton from the hard scattering is associated with a hard, well separated jet. This approach is very successful because it allows quantitative predictions using lowest order perturbation theory. However, beyond leading order in the coupling constant, when quantum fluctuations are included, deterministic jet algorithms will become problematic precisely because they attempt to describe an inherently stochastic quantum process using deterministic, classical language. This demands a shift in the way we view jet algorithms. We make a first attempt at constructing more probabilistic jet algorithms that reflect the properties of the underlying hard scattering and explore the basic properties and problems of such an approach.

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arXiv1997

Radiative Corrections to the Photon + 1 Jet Rate at LEP

We present the results of a calculation of the rate for the annihilation of an $e^+e^-$ pair into a jet containing an energetic photon and a single further jet at order $αα_{s}$. By comparing these results with the existing data on the photon + 1 jet rate from the ALEPH Collaboration, we make a first determination of the process independent quark-to-photon fragmentation function $D_{q \to γ}(z,μ_{F})$ at order $αα_{s}$. We also compare our prediction for the inclusive photon energy spectrum with the recent OPAL measurement.

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arXiv1997

Report of the Working Group on `W Mass and QCD' (Phenomenology Workshop on LEP2 Physics, Oxford, April 1997)

The W Mass and QCD Working Group discussed a wide variety of topics relating to present and future measurements of M(W) at LEP2, including QCD backgrounds to W+W- production. Particular attention was focused on experimental issues concerning the direct reconstruction and threshold mass measurements, and on theoretical and experimental issues concerning the four jet final state. This report summarises the main conclusions.

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arXiv1997

What does the W transverse momentum distribution say about the W+1 jet/W+0 jet ratio?

We compute the W transverse momentum distribution at large transverse momentum at fixed next-to-leading order (i.e. O(alpha_s^2) and find good agreement with the preliminary measurements reported by D0. We find that the W transverse momentum distribution is typically significantly larger than the exclusive one-jet rate for a given value of p_T^W or E_T^jet, mainly because two or more jet events are excluded. As a consequence, we find that theoretically the W+1 jet to W+0 jet ratio R^10 is smaller than the analogous quantity defined in terms of p_T^W, R^W. This hierarchy is preserved under changes of renormalisation/factorisation scales, strong coupling constant and jet algorithm. However, this appears to be in contradiction with the preliminary experimental results which suggest R^10 > R^W.

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arXiv1997

Jet Investigations Using the Radial Moment

We define the radial moment, , for jets produced in hadron-hadron collisions. It can be used as a tool for studying, as a function of the jet transverse energy and pseudorapidity, radiation within the jet and the quality of a perturbative description of the jet shape. We also discuss how non-perturbative corrections to the jet transverse energy affect .

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arXiv1996

Can partons describe the CDF jet data?

The recent CDF single jet inclusive measurements at Fermilab are incorporated in a global next-to-leading order parton analysis of the available deep inelastic and related data. We find that it is impossible to achieve a simultaneous QCD description of both the CDF jet distribution for transverse energies $E_T > 200$~GeV and the deep inelastic structure function data for $x > 0.3$. However, the CDF data for $E_T < 200$~GeV and the deep inelastic data are adequately described provided that the QCD coupling $α_S(M_Z^2)$ is increased from its preferred deep inelastic value to $α_S (M_Z^2) \simeq 0.116 - 0.120$.

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arXiv1995

Recombination Methods for Jets in $p\pbar$ Collisions

A jet algorithm must specify how to (re-)combine different partons or towers into a single four-vector. Various recombination schemes have been used experimentally to examine the transverse energy profile of jets in hadron colliders. Generally, the data is insensitive to which scheme is used. However, we argue that the recombination scheme previously used by the \DO\ collaboration is expected to have large perturbative corrections and should not be used for the purposes of making a quantitative comparison with fixed-order perturbation theory.

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arXiv1995

Physics with jets in $p\bar p$ collisions

We discuss the possibilities for extracting information on the parton density functions and the strong coupling constant from one- and two-jet events at the Fermilab TEVATRON. First we study the inclusive two-jet triply differential cross section $d^3σ/dE_Tdη_1dη_2$. Different $η_1$ and $η_2$ pseudorapidity regions are directly related to the parton momentum fractions at leading order and the shape of the triply differential distribution at fixed transverse energy $E_T$ is a particularly powerful tool for constraining the parton distributions at small to moderate $x$ values. Second, we consider the one-jet inclusive transverse energy distribution where there is impressive agreement between theory and experiment over a wide range of transverse energy. By equating the next-to-leading order theoretical prediction for a given set of input parton densities with the published CDF data, the evolution of the strong coupling constant at scale $μ$ can be studied between $μ\sim 50~$GeV and $μ\sim 400~$GeV. This evolution is in agreement with QCD and corresponds to $α_s(M_Z)$ = 0.121 for the MRSA parameterisation.

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