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C. Oleari

Publications and source records attributed to C. Oleari.

49 records · Page 3Linked to original sources
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.

hep-ph↗
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

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs

The class of the two-loop massless crossed boxes, with light-like external legs, is the final unresolved issue in the program of computing the scattering amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order. In this paper, we describe an algorithm for the tensor reduction of such diagrams. After connecting tensor integrals to scalar ones with arbitrary powers of propagators in higher dimensions, we derive recurrence relations from integration-by-parts and Lorentz-invariance identities, that allow us to write the scalar integrals as a combination of two master crossed boxes plus simpler-topology diagrams. We derive the system of differential equations that the two master integrals satisfy using two different methods, and we use one of these equations to express the second master integral as a function of the first one, already known in the literature. We then give the analytic expansion of the second master integral as a function of epsilon=(4-D)/2, where D is the space-time dimension, up to order O(epsilon^0).

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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.

hep-ph↗
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.

hep-ph↗
arXiv1999

A Phenomenological Study of Heavy-Quark Fragmentation Functions in e+e- Annihilation

We consider the computation of D and B fragmentation functions in e+e- annihilation. We compare the results of fitting present data using the next-to-leading-logarithmic resummed approach, versus the O(alpha_s^2) fixed-order calculation, including also mass-suppressed effects. We also propose a method for merging the fixed-order calculation with the resummed approach.

hep-ph↗
arXiv1999

Sudakov Resummation Effects in Prompt-Photon Hadroproduction

We compute the effects of soft-gluon resummation, at the next-to-leading-logarithmic level, in the fixed-target hadroproduction cross section for prompt photons. We find in general that the corrections to the fixed next-to-leading-order results are large for large renormalization scales, and small for small scales. This leads to a significant reduction of the scale dependence of the results for most experimental configurations of interest. We compare our results to the recent measurements by the E706 and UA6 collaborations.

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arXiv1997

On the Fragmentation Function for Heavy Quarks in e+e- collisions

We use a recent O(alpha_s^2) calculation of the differential cross section for the production of heavy quarks in e+e- annihilation to compute a few moments of the heavy quark single-inclusive production cross section. We verify that, contrary to some recent claims, the leading and next-to-leading logarithmic terms in this cross section are correctly given by the standard NLO fragmentation function formalism for heavy quark production.

hep-ph↗
arXiv1997

Next-to-Leading-Order Corrections to Momentum Correlations in $Z^0 \to b\bar{b}$

We recently completed a calculation of the process $e^+e^- \to Q\bar{Q}+X$, where Q is a heavy quark, at order $O(α_s^2)$. As a first application of this calculation we compute the momentum correlations of $b\bar{b}$ pairs at next-to-leading-order. This quantity is interesting since it may affect the determination of $R_b$ as measured in $Z^0$ decays. We find that the next-to-leading corrections are of moderate size, thus confirming the conclusions that can be drawn from the leading-order calculation.

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