arXiv subjects

E. W. N. Glover

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

At least 127 records · Page 7Linked to original sources

arXiv2002

Two-Loop QCD Helicity Amplitudes for $e^+e^- \to 3$~Jets

We compute the two-loop QCD helicity amplitudes for the process e^+e^- --> q bar{q} g. The amplitudes are extracted in a scheme-independent manner from the coefficients appearing in the general tensorial structure for this process. The tensor coefficients are derived from the Feynman graph amplitudes by means of projectors, within the conventional dimensional regularization scheme. The actual calculation of the loop integrals is then performed by reducing all of them to a small set of known master integrals. The infrared pole structure of the renormalized helicity amplitudes agrees with the prediction made by Catani using an infrared factorization formula. We use this formula to structure our results for the finite part into terms arising from the expansion of the pole coefficients and a genuine finite remainder, which is independent of the scheme used to define the helicity amplitudes. The analytic result for the finite parts of the amplitudes is expressed in terms of one- and two-dimensional harmonic polylogarithms.

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arXiv2002

The QCD/SM Working Group: Summary Report

This Report documents the results obtained by the Working Group on Quantum ChromoDynamics and the Standard Model for the Workshop ``Physics at TeV Colliders'', Les Houches, France, 21 May - 1 June 2001. The account of uncertainties in Parton Distribution Functions is reviewed. Progresses in the description of multiparton final states at Next-to-Leading Order and the extension of calculations for precision QCD observables beyond this order are summarized. Various issues concerning the relevance of resummation for observables at TeV colliders is examined. Improvements to algorithms of jet reconstruction are discussed and predictions for diphoton and photon pi-zero production at the LHC are made for kinematic variables of interest regarding searches for a Higgs boson decaying into two photons. Finally, several improvements implemented in Monte-Carlo event generators are documented.

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arXiv2002

Two-loop corrections to Light-by-Light scattering in Supersymmetric QED

We use an n-dimensional projection method to calculate helicity amplitudes for photon-photon scattering up to the two-loop level, for massless particles inside the loop. We confirm the recent standard model results found by Bern et al using another calculational method. We further apply the method to N=1 and N=2 supersymmetric QED. As predicted by the supersymmetric Ward identity, two of the independent amplitudes vanish. The remaining amplitude simplifies as the number of supersymmetries increases. For N=2 SUSY QED, only contributions of weight 4 remain.

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arXiv2002

Two-loop QED and QCD corrections to massless fermion-boson scattering

We present the NNLO QCD virtual corrections for qurak-antiquark -> gluon photon, quark-antiquark -> photon photon and the NNLO QED virtual corrections for electron positron -> photon photon and all processes related by crossing symmetry. We perform an explicit evaluation of the two-loop diagrams in conventional dimensional regularisation, and our results are renormalised in the MSbar scheme. The infrared pole structure of the amplitudes is in agreement with the prediction of Catani's general formalism for the singularities of two-loop amplitudes, while expressions for the finite remainder are given for all processes in terms of logarithms and polylogarithms that are real in the physical region.

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arXiv2002

The quark Regge trajectory at two loops

The hypothesis of the quark Reggeization is tested by taking the high-energy limit of the two-loop amplitude for quark-gluon scattering which was recently calculated. The limit is compatible with the Reggeization in the leading and the next-to-leading orders and allows the determination of the quark trajectory in the two-loop approximation. The trajectory is presented as an expansion in powers of (D-4) for the space-time dimension $D$ tending to the physical value D=4.

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arXiv2001

The Two-Loop QCD Matrix Element for $e^+e^- \to 3$ Jets

We compute the ${\cal O}(α_s^3)$ virtual QCD corrections to the $γ^*\to q\bar q g$ matrix element arising from the interference of the two-loop with the tree-level amplitude and from the self-interference of the one-loop amplitude. The calculation is performed by reducing all loop integrals appearing in the two-loop amplitude to a small set of known master integrals. Infrared and ultraviolet divergences are both regularized using conventional dimensional regularization, and the ultraviolet renormalization is performed in the $\bar{MS}$ scheme. The infrared pole structure of the matrix elements agrees with the prediction made by Catani using an infrared factorization formula. The analytic result for the finite terms of both matrix elements is expressed in terms of one- and two-dimensional harmonic polylogarithms.

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arXiv2001

Two-loop QCD corrections to gluon-gluon scattering

We present the O(alpha_s^4) virtual QCD corrections to gluon-gluon scattering due to the interference of tree and two-loop amplitudes. We work in conventional dimensional regularisation and give analytic expressions renormalised in the MSbar scheme. The structure of the infrared divergences agrees with that predicted by Catani while formulae for the finite remainder are given in terms of logarithms and polylogarithms that are real in the physical region. These results, together with those previously obtained for quark-quark and quark-gluon scattering, complete the two-loop matrix elements needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders.

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arXiv2001

The high energy limit of QCD at two loops

By taking the high-energy limit of the two-loop amplitudes for parton-parton scattering, we have tested the validity of Fadin-Lipatov's ansatz for parton-parton scattering in the high-energy limit. As expected, we have found that it holds at LL and NLL accuracy, and hence we have independently re-evaluated the two-loop Regge trajectory, finding full agreement with the previous results by Fadin and collaborators. We have found, though, that the universality implied by the ansatz is violated at the next-to-next-to-leading logarithmic level.

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arXiv2001

Overview of NNLO QCD corrections

We discuss the motivation for making predictions for jet cross sections at next-to-next-to-leading order. We describe the theoretical ingredients needed for such a calculation and briefly review the progress in the field.

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arXiv2001

Second order contributions to elastic large-angle Bhabha scattering

We derive the coefficient of the O(alpha^2 log(s/m_e^2)) fixed order contribution to elastic large-angle Bhabha scattering. We adapt the classification of infrared divergences, that was recently developed within dimensional regularization, and apply it to the regularization scheme with a massive photon and electron.

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arXiv2001

Resumming the Light Hemisphere Mass and Narrow Jet Broadening distributions in e^+e^- annihilation

We present predictions of two event shape distributions, the light hemisphere mass and the narrow jet broadening, to next-to-leading logarithmic order. We apply the coherent branching formalism to resum the leading O(alphas^n L^{2n-1}) and next-to-leading O(alphas^n L^{2n-2}) infrared logarithms to all orders in the coupling constant. We include the recently calculated non-logarithmic next-to-leading order contributions. Applying simple power corrections to the resummed result gives good agreement with the available data from LEP.

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arXiv2001

One-loop QCD corrections to gluon-gluon scattering at NNLO

We present the O(alphas^4) virtual QCD corrections to gluon-gluon scattering due to the self-interference of the one-loop amplitude. We give analytic expressions renormalised in the MSbar scheme and work in conventional dimensional regularisation. We write the structure of the infrared divergences from direct Feynman diagram evaluation in terms of the Catani formalism for infrared divergences. Formulae for the finite remainder are given in terms of logarithms that are real in the physical region. These results, together with those previously obtained for quark-quark and quark-gluon scattering complete the one-loop matrix elements for 2 to 2 processes needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders.

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arXiv2001

Two-loop QCD corrections to the scattering of massless distinct quarks

We present the two-loop virtual QCD corrections to the scattering of massless distinct quarks in conventional dimensional regularisation. The structure of the infrared divergences agrees with that predicted by Catani while expressions for the finite remainder are given for each of the s-, t- and u-channels in terms of polylogarithms. The results presented here form a vital part of the next-to-next-to-leading order contribution to inclusive jet production in hadron colliders and will play a crucial role in improving the theoretical prediction for jet cross sections in hadron-hadron collisions.

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arXiv2001

Two-loop QCD corrections to massless identical quark scattering

We present the two-loop virtual QCD corrections to the scattering of massless identical quarks, q qbar to q qbar, in conventional dimensional regularisation and using the MSbar scheme. The structure of the infrared divergences agrees with that predicted by Catani while expressions for the finite remainder are given for the q qbar to qbar q and the q q to q q (qbar qbar to qbar qbar) scattering processes in terms of polylogarithms. The results presented here form a vital part of the next-to-next-to-leading order contribution to inclusive jet production in hadron colliders and will play a crucial role in improving the theoretical prediction for jet cross sections in hadron-hadron collisions.

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arXiv2000

One-loop QCD corrections to quark scattering at NNLO

We present the O(as^4) virtual QCD corrections to unlike-quark and like-quark scattering due to the interference of one-loop amplitudes with one-loop amplitudes. The structure of the infrared divergences agrees with that predicted by Catani. The results are expressed in an analytic form so that the relevant expressions for crossed scattering processes can be obtained in a straightforward manner. The one-loop contributions presented here, together with the interference of tree with two-loop amplitudes given recently, complete the 2 to 2 virtual QCD corrections at NNLO for the massless quark scattering processes.

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arXiv2000

Progress towards 2 to 2 scattering at two-loops

We discuss the two-loop integrals necessary for evaluating massless 2 to 2 scattering amplitudes. As a test process, we consider the leading colour two-loop contribution to qqbar to q'qbar'. We show that for physical scattering processes the two Smirnov-Veretin planar box graphs I1 and I2 are accompanied by factors of 1/(D-4) thereby necessitating a knowledge of both I1 and I2 to O(epsilon). Using an alternative basis I1 and the irreducible numerator integral I3, the factors of 1/(D-4) disappear.

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arXiv2000

The two-loop scalar and tensor pentabox graph with light-like legs

We study the scalar and tensor integrals associated with the pentabox topology: the class of two-loop box integrals with seven propagators - five in one loop and three in the other. We focus on the case where the external legs are light-like and use integration-by-parts identities to express the scalar integral in terms of two master-topology integrals and present an explicit analytic expression for the pentabox scalar integral as a series expansion in ep = (4-D)/2. We also give an algorithm based on integration by parts for relating the generic tensor integrals to the same two master integrals and provide general formulae describing the master integrals in arbitrary dimension and with general powers of propagators.

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arXiv1999

Application of the negative-dimension approach to massless scalar box integrals

We study massless one-loop box integrals by treating the number of space-time dimensions D as a negative integer. We consider integrals with up to three kinematic scales (s, t and either zero or one off-shell legs) and with arbitrary powers of propagators. For box integrals with q kinematic scales (where q=2 or 3) we immediately obtain a representation of the graph in terms of a finite sum of generalised hypergeometric functions with q-1 variables, valid for general D. Because the power each propagator is raised to is treated as a parameter, these general expressions are useful in evaluating certain types of two-loop box integrals which are one-loop insertions to one-loop box graphs. We present general expressions for this particular class of two-loop graphs with one off-shell leg, and give explicit representations in terms of polylogarithms in the on-shell case.

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