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Costas G. Papadopoulos

Publications and source records attributed to Costas G. Papadopoulos.

At least 19 recordsLinked to original sources
arXiv2022

Two-loop non-planar hexa-box integrals with one massive leg

Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral representation of the master integrals in terms of Generalised Polylogarithms, when the alphabet contains non-factorisable square roots. The results are relevant to the study of NNLO QCD corrections for $W,Z$ and Higgs-boson production in association with two hadronic jets.

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arXiv2021

Multiscale pentagon integrals to all orders

We present analytical results for one-loop five-point master integrals with up to three off-shell legs. The method of canonical differential equations along with the Simplified Differential Equations approach is employed. All necessary boundary terms are given in closed form, resulting to solutions in terms of Goncharov Polylogarithms of arbitrary weight. Explicit results up to weight six will be presented.

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arXiv2021

$N^3LO$ calculations for $2 \to 2$ processes using Simplified Differential Equations

We present the computation of the massless three-loop ladder-box family with one external off-shell leg using the Simplified Differential Equations (SDE) approach. We also discuss the methods we used for finding a canonical differential equation for the two tennis-court families with one off-shell leg, and the application of the SDE approach on these two families.

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arXiv2020

Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg

We present analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg. The calculation is based on the Simplified Differential Equations approach. The results are relevant to the study of many $2\to 3$ scattering processes of interest at the LHC, especially for the leading-color $W+2$ jets production.

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arXiv2019

Internal Reduction method for computing Feynman Integrals

A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of non-planar five-point two-loop Master Integrals with one external off-shell particle, relevant for instance for $H+2$ jets production at the LHC, in both Euclidean and physical kinematical regions.

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arXiv2017

Simplified differential equations approach for Master Integrals

A simplified differential equations approach for Master Integrals is presented. It allows to express them, straightforwardly, in terms of Goncharov Polylogarithms. As a proof-of-concept of the proposed method, results at one and two loops are presented, including the massless one-loop pentagon with up to one off-shell leg at order epsilon.

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arXiv2017

Cuts of Feynman Integrals in Baikov representation

Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in $d$ dimensions. The information provided by these computations may be used to determine the class of functions needed to analytically express the full integrals.

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arXiv2016

The Pentabox Master Integrals with the Simplified Differential Equations approach

We present the calculation of massless two-loop Master Integrals relevant to five-point amplitudes with one off-shell external leg and derive the complete set of planar Master Integrals with five on-mass-shell legs, that contribute to many $2\to 3$ amplitudes of interest at the LHC, as for instance three jet production, $γ, V, H +2$ jets etc., based on the Simplified Differential Equations approach.

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arXiv2015

Two-loop Master Integrals with the Simplified Differential Equations approach

We calculate the complete set of two-loop Master Integrals with two off mass-shell legs with massless internal propagators, that contribute to amplitudes of diboson $V_1V_2$ production at the LHC. This is done with the Simplified Differential Equations approach to Master Integrals, which was recently proposed by one of the authors.

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arXiv2012

Counting to one: reducibility of one- and two-loop amplitudes at the integrand level

Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction methods proved to be very helpful, lowering the number of integrals that need to be actually calculated. Especially, the reduction at the integrand level technique, improves the speed and set-up of these calculations. In this article we demonstrate, by counting the numbers of tensor structures and independent coefficients, how to write such relations at the integrand level for one- and two-loop amplitudes. We clarify their connection to the so-called spurious terms at one loop and discuss their structure in the two-loop case. This method is also applicable to higher loops, and the results obtained apply to both planar and non-planar diagrams.

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arXiv2011

Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order

Results for next-to-leading order QCD corrections to the pp(p\bar{p}) -> t \bar{t} -> W^+W^- b\bar{b} -> e^{+} ν_{e} μ^{-} \barν_μ b \bar{b} +X processes with complete off-shell effects are presented for the first time. Double-, single- and non-resonant top contributions of the order {\cal{O}}(α_{s}^3 α^4) are consistently taken into account, which requires the introduction of a complex-mass scheme for unstable top quarks. Moreover, the intermediate W bosons are treated off-shell. Comparison to the narrow width approximation for top quarks, where non-factorizable corrections are not accounted for is performed. Besides the total cross section and its scale dependence, several differential distributions at the TeVatron run II and the LHC are given. In case of the TeVatron the forward-backward asymmetry of the top is recalculated afresh. With inclusive selection cuts, the forward-backward asymmetry amounts to A^{t}_{FB} = 0.051 +/- 0.0013. Furthermore, the corrections with respect to leading order are positive and of the order 2.3% for the TeVatron and 47% for the LHC. A study of the scale dependence of our NLO predictions indicates that the residual theoretical uncertainty due to higher order corrections is 8% for the TeVatron and 9% for the LHC.

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arXiv2009

Helac-Phegas: a generator for all parton level processes

The updated version of the Helac-Phegas event generator is presented. The matrix elements are calculated through Dyson-Schwinger recursive equations. Helac-Phegas generates parton-level events with all necessary information, in the most recent Les Houches Accord format, for the study of any process within the Standard Model in hadron and lepton colliders.

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arXiv2008

CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes

We present a program that implements the OPP reduction method to extract the coefficients of the one-loop scalar integrals from a user defined (sub)-amplitude or Feynman Diagram, as well as the rational terms coming from the 4-dimensional part of the numerator. The rational pieces coming from the epsilon-dimensional part of the numerator are treated as an external input, and can be computed with the help of dedicated tree-level like Feynman rules. Possible numerical instabilities are dealt with the help of arbitrary precision routines, that activate only when needed.

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arXiv2008

On the Rational Terms of the one-loop amplitudes

The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be derived by using appropriate Feynman rules within a tree-like computation. For the terms that originate from the reduction of the 4-dimensional part of the numerator, we present two different strategies and explicit algorithms to compute them.

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arXiv2007

Numerical Evaluation of Six-Photon Amplitudes

We apply the recently proposed amplitude reduction at the integrand level method, to the computation of the scattering process 2 photons -> 4 photons, including the case of a massive fermion loop. We also present several improvements of the method, including a general strategy to reconstruct the rational part of any one-loop amplitude and the treatment of vanishing Gram-determinants.

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arXiv2007

Multi-parton Cross Sections at Hadron Colliders

We present an alternative method to calculate cross sections for multi-parton scattering processes in the Standard Model at leading order. The helicity amplitudes are computed using recursion relations in the number of particles, based on Dyson-Schwinger equations whereas the summation over colour and helicity configurations is performed by Monte Carlo methods. The computational cost of our algorithm grows asymptotically as 3^n, where n is the number of particles involved in the process, as opposed to the n!-growth of the Feynman diagram approach. Typical results for the total cross section, differential distributions of invariant masses and transverse momenta of partons are presented and cross checked by explicit summation over colours.

hep-ph↗
arXiv2006

Reducing full one-loop amplitudes to scalar integrals at the integrand level

We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no information on the analytical structure of the amplitude is required, making our method appealing for an efficient numerical implementation

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