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Vittorio Del Duca

Publications and source records attributed to Vittorio Del Duca.

At least 55 records · Page 3Linked to original sources
arXiv2013

Beyond Reggeization for two- and three-loop QCD amplitudes

The high-energy factorization of gauge theory scattering amplitudes in terms of universal impact factors and a Reggeized exchange in the $t$-channel, corresponding to a Regge pole in the angular momentum plane, is know to conflict with the structure of soft anomalous dimensions starting at the two-loop level. We explore the implications of this violation of factorization for two- and three-loop QCD amplitudes: first we propose criteria to organize the amplitudes into factorizing and non-factorizing terms, then we test them by recovering a known result for non-logarithmic terms at two loops. Finally we predict the precise value of the leading non-factorizing energy logarithms at three loops, and we uncover a set of all-order identities constraining infrared finite terms in quark and gluon amplitudes.

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arXiv2013

High-energy QCD amplitudes at two loops and beyond

Recent progress in our understanding of infrared singularities of multi-parton amplitudes has shown that the simplest form of Regge factorization for high-energy gauge-theory amplitudes fails starting at next-to-next-to-leading logarithmic accuracy. We provide a framework to organize the calculation of parton amplitudes at leading power in t/s, in terms of factorizing and non-factorizing contributions. This allows us to give explicit expressions for the leading Reggeization-breaking terms in two-loop and three-loop quark and gluon amplitudes in QCD. In particular, using only infrared information, we recover a known non-factorizing, non-logarithmic double-pole contribution at two-loops, and we compute the leading non-factorizing single-logarithmic contributions at three loops.

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arXiv2013

Integration of collinear-type doubly unresolved counterterms in NNLO jet cross sections

In the context of a subtraction method for jet cross sections at NNLO accuracy in the strong coupling, we perform the integration over the two-particle factorised phase space of the collinear-type contributions to the doubly unresolved counterterms. We present the final result as a convolution in colour space of the Born cross section and of an insertion operator, which is written in terms of master integrals that we expand in the dimensional regularisation parameter.

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arXiv2012

Infrared singularities in the high-energy limit

We use our current understanding of the all-order singularity structure of gauge theory amplitudes to probe their high-energy limit. Our starting point is the dipole formula, a compact ansatz for the soft anomalous dimension matrix of massless multi-particle amplitudes. In the high-energy limit, we find a simple and general expression for the infrared factor generating all soft and collinear singularities of the amplitude, which is valid to leading power in $|t|/s$ and to all logarithmic orders. This leads to a direct and general proof of leading-logarithmic Reggeization for infrared divergent contributions to the amplitude. Furthermore, we can prove explicitly that the simplest form of Reggeization, based on the absence of Regge cuts in the complex angular momentum plane, breaks down at the NNLL level. Finally, we note that the known features of the high-energy limit can be used to constrain possible corrections to the dipole formula, starting at the three-loop order.

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arXiv2012

Infrared singularities and the high-energy limit

We review recent results on the high-energy limit of gauge amplitudes, which can be derived from the universal properties of their infrared singularities. Using the dipole formula, a compact ansatz for infrared singularities of massless gauge amplitudes, and taking the high-energy limit, we provide a simple expression for the soft factor of a generic high-energy amplitude, valid to leading power in $t/s$ and to all logarithmic orders. This gives a direct and general proof of leading-logarithmic Reggeization for infrared divergent contributions to the amplitude, and it shows how Reggeization breaks down at NNLL level. We further show how the dipole formula constrains the high-energy limit of multi-particle amplitudes in multi-Regge kinematics, and how, on the other hand, Regge theory constrains possible corrections to the dipole formula.

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arXiv2011

The infrared structure of gauge theory amplitudes in the high-energy limit

We develop an approach to the high-energy limit of gauge theories based on the universal properties of their infrared singularities. Our main tool is the dipole formula, a compact ansatz for the all-order infrared singularity structure of scattering amplitudes of massless partons. By taking the high-energy limit, we show that the dipole formula implies Reggeization of infrared-singular contributions to the amplitude, at leading logarithmic accuracy, for the exchange of arbitrary color representations in the cross channel. We observe that the real part of the amplitude Reggeizes also at next-to-leading logarithmic order, and we compute the singular part of the two-loop Regge trajectory, which is universally expressed in terms of the cusp anomalous dimension. Our approach provides tools to study the high-energy limit beyond the boundaries of Regge factorization: thus we show that Reggeization generically breaks down at next-to-next-to-leading logarithmic accuracy, and provide a general expression for the leading Reggeization-breaking operator. Our approach applies to multiparticle amplitudes in multi-Regge kinematics, and it also implies new constraints on possible corrections to the dipole formula, based on the Regge limit.

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arXiv2011

An infrared approach to Reggeization

We present a new approach to Reggeization of gauge amplitudes based on the universal properties of their infrared singularities. Using the "dipole formula", a compact ansatz for all infrared singularities of massless amplitudes, we study Reggeization of singular contributions to high-energy amplitudes for arbitrary color representations, and any logarithmic accuracy. We derive leading-logarithmic Reggeization for general cross-channel color exchanges, and we show that Reggeization breaks down for the imaginary part of the amplitude at next-to-leading logarithms and for the real part at next-to-next-to-leading logarithms. Our formalism applies to multiparticle amplitudes in multi-Regge kinematics, and constrains possible corrections to the dipole formula starting at three loops.

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arXiv2011

The one-loop six-dimensional hexagon integral with three massive corners

We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum of 24 terms involving only one basic function, which is a simple linear combination of logarithms, dilogarithms, and trilogarithms of uniform degree three transcendentality. Our method uses differential equations to determine the symbol of the function, and an algorithm to reconstruct the latter from its symbol. It is known that six-dimensional hexagon integrals are closely related to scattering amplitudes in N=4 super Yang-Mills theory, and we therefore expect our result to be helpful for understanding the structure of scattering amplitudes in this theory, in particular at two loops.

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arXiv2011

The massless hexagon integral in D = 6 dimensions

We evaluate the massless one-loop hexagon integral in six dimensions. The result is given in terms of standard polylogarithms of uniform transcendental weight three, its functional form resembling the one of the remainder function of the two-loop hexagon Wilson loop in four dimensions.

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arXiv2010

A Two-Loop Octagon Wilson Loop in N = 4 SYM

In the planar N = 4 supersymmetric Yang-Mills theory at weak coupling, we perform the first analytic computation of a two-loop eight-edged Wilson loop embedded into the boundary of AdS3. Its remainder function is given as a function of uniform transcendental weight four in terms of a constant plus a product of four logarithms. We compare to the strong-coupling result, and test a conjecture on the universality of the remainder function proposed in the literature.

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arXiv2010

The Two-Loop Hexagon Wilson Loop in N = 4 SYM

In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry constrains multi-loop n-edged Wilson loops to be given in terms of the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a function of conformally invariant cross ratios. That function is termed the remainder function. In a recent paper, we have displayed the first analytic computation of the two-loop six-edged Wilson loop, and thus of the corresponding remainder function. Although the calculation was performed in the quasi-multi-Regge kinematics of a pair along the ladder, the Regge exactness of the six-edged Wilson loop in those kinematics entails that the result is the same as in general kinematics. We show in detail how the most difficult of the integrals is computed, which contribute to the six-edged Wilson loop. Finally, the remainder function is given as a function of uniform transcendental weight four in terms of Goncharov polylogarithms. We consider also some asymptotic values of the remainder function, and the value when all the cross ratios are equal.

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arXiv2010

An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM

In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry constrains multi-loop n-edged Wilson loops to be basically given in terms of the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a function of conformally invariant cross ratios. We identify a class of kinematics for which the Wilson loop exhibits exact Regge factorisation and which leave invariant the analytic form of the multi-loop n-edged Wilson loop. In those kinematics, the analytic result for the Wilson loop is the same as in general kinematics, although the computation is remarkably simplified with respect to general kinematics. Using the simplest of those kinematics, we have performed the first analytic computation of the two-loop six-edged Wilson loop in general kinematics.

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arXiv2009

The one-loop pentagon to higher orders in epsilon

We compute the one-loop scalar massless pentagon integral I_5^{6-2 eps} in D=6-2\eps dimensions in the limit of multi-Regge kinematics. This integral first contributes to the parity-odd part of the one-loop N=4 five-point MHV amplitude m_5^{(1)} at O(eps). In the high energy limit defined, the pentagon integral reduces to double sums or equivalently two-fold Mellin-Barnes integrals. By determining the O(eps) contribution to I_5^{6-2 eps}, one therefore gains knowledge of m_5^{(1)} through to O(eps^2) which is necessary for studies of the iterative structure of N=4 SYM amplitudes beyond one-loop. One immediate application is the extraction of the one-loop gluon-production vertex through to O(eps^2) and the iterative construction of the two-loop gluon-production vertex through to finite terms which is described in a companion paper. The analytic methods we have used for evaluating the pentagon integral in the high energy limit may also be applied to the hexagon integral and may ultimately give information on the form of the remainder function.

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arXiv2009

The five-gluon amplitude in the high-energy limit

We consider the high energy limit of the colour ordered one-loop five-gluon amplitude in the planar maximally supersymmetric N=4 Yang-Mills theory in the multi-Regge kinematics where all of the gluons are strongly ordered in rapidity. We apply the calculation of the one-loop pentagon in D=6-2 eps performed in a companion paper to compute the one-loop five-gluon amplitude through to O(eps^2). Using the factorisation properties of the amplitude in the high-energy limit, we extract the one-loop gluon-production vertex to the same accuracy, and, by exploiting the iterative structure of the gluon-production vertex implied by the BDS ansatz, we perform the first computation of the two-loop gluon-production vertex up to and including finite terms.

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arXiv2009

Higgs Boson Production in Association with Multiple Hard Jets

We elucidate a new technique for estimating the production of multiple (at least two) hard jets in Higgs production via gluon-gluon fusion. The approach is based upon high energy factorisation, with the region of applicability extended by constraints on the analytic behaviour of the scattering amplitudes stemming from known all-order results. The method approximates both real and virtual corrections, and allows for the resummation in an n-parton inclusive event sample of the terms dominant in the high energy limit. The resulting approximation is matched to the known tree level matrix elements for the production of a Higgs boson in association with 2 and 3 jets, and implemented in a Monte Carlo generator. Example results are presented and characteristic radiation patterns discussed.

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arXiv2008

Finite-top-mass effects in NNLO Higgs production

We construct an accurate approximation to the exact NNLO cross section for Higgs production in gluon-gluon fusion by matching the dominant finite top mass corrections recently computed by us to the known result in the infinite mass limit. The ensuing corrections to the partonic cross section are very large when the center of mass energy of the partonic collision is much larger than the Higgs mass, but lead to a moderate correction at the percent level to the total Higgs production cross section at the LHC. Our computation thus reduces the uncertainty related to these corrections at the LHC from the percent to the per mille level.

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arXiv2008

Analytic integration of real-virtual counterterms in NNLO jet cross sections I

We present analytic evaluations of some integrals needed to give explicitly the integrated real-virtual integrated counterterms, based on a recently proposed subtraction scheme for next-to-next-to-leading order (NNLO) jet cross sections. After an algebraic reduction of the integrals, integration-by-parts identities are used for the reduction to master integrals and for the computation of the master integrals themselves by means of differential equations. The results are written in terms of one- and two-dimensional harmonic polylogarithms, once an extension of the standard basis is made. We expect that the techniques described here will be useful in computing other integrals emerging in calculations in perturbative quantum field theories.

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