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German Rodrigo

Publications and source records attributed to German Rodrigo.

At least 37 records · Page 2Linked to original sources
arXiv2016

Towards regularized higher-order computations in QFT without DREG

In this talk, we review the basis of the loop-tree duality theorem, which allows to rewrite loop scattering amplitudes in terms of tree-level like objects. Since the loop measure is converted into a phase-space one, both virtual and real contributions are expressible using the same integration variables. A physically motivated momentum mapping allows to generate the real emission process starting from the Born kinematics and the loop momenta. The integrand-level combination leads to regular functions, which can be integrated without using dimensional regularization (DREG) and correctly reproduce the finite higher-order corrections to physical observables. We explain the implementation of this novel approach to compute some benchmark physical processes, and we show how to deal with both infrared and ultraviolet divergences in four space-time dimensions.

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arXiv2016

Four-dimensional unsubtraction from the loop-tree duality

We present a new algorithm to construct a purely four dimensional representation of higher-order perturbative corrections to physical cross-sections at next-to-leading order (NLO). The algorithm is based on the loop-tree duality (LTD), and it is implemented by introducing a suitable mapping between the external and loop momenta of the virtual scattering amplitudes, and the external momenta of the real emission corrections. In this way, the sum over degenerate infrared states is performed at integrand level and the cancellation of infrared divergences occurs locally without introducing subtraction counter-terms to deal with soft and final-state collinear singularities. The dual representation of ultraviolet counter-terms is also discussed in detail, in particular for self-energy contributions. The method is first illustrated with the scalar three-point function, before proceeding with the calculation of the physical cross-section for $γ^* \to q \bar{q}(g)$, and its generalisation to multi-leg processes. The extension to next-to-next-to-leading order (NNLO) is briefly commented.

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arXiv2016

Applications of the loop-tree duality

We describe a new method to perform NLO calculations, combining real and virtual amplitudes at the integrand level, with a fully local compensation between them in the IR, and between the virtual integrand and properly defined counter-terms in the UV, in such a way that physical observables can be computed in 4 dimensions. One of the advantages of the method is that all the scattering amplitudes are integrated simultaneously, without the need for tensor reduction, or projection onto sets of master integrals. As such, it could offer great progress in the automation of NLO calculations, where the actual bottle-necks are the complexity of the analytical calculations for multi-leg processes, and the numerical stability of the result.

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arXiv2016

Four-dimensional unsubtraction with massive particles

We extend the four-dimensional unsubtraction method, which is based on the loop-tree duality (LTD), to deal with processes involving heavy particles. The method allows to perform the summation over degenerate IR configurations directly at integrand level in such a way that NLO corrections can be implemented directly in four space-time dimensions. We define a general momentum mapping between the real and virtual kinematics that accounts properly for the quasi-collinear configurations, and leads to an smooth massless limit. We illustrate the method first with an scalar toy example, and then analyse the case of the decay of a scalar or vector boson into a pair of massive quarks. The results presented in this paper are suitable for the application of the method to any multipartonic process.

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arXiv2016

Attacking One-loop Multi-leg Feynman Integrals with the Loop-Tree Duality

We discuss briefly the first numerical implementation of the Loop-Tree Duality (LTD) method. We apply the LTD method in order to calculate ultraviolet and infrared finite multi-leg one-loop Feynman integrals. We attack scalar and tensor integrals with up to six legs (hexagons). The LTD method shows an excellent performance independently of the number of external legs.

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arXiv2016

Towards gauge theories in four dimensions

The abundance of infrared singularities in gauge theories due to unresolved emission of massless particles (soft and collinear) represents the main difficulty in perturbative calculations. They are typically regularized in dimensional regularization, and their subtraction is usually achieved independently for virtual and real corrections. In this paper, we introduce a new method based on the loop-tree duality (LTD) theorem to accomplish the summation over degenerate infrared states directly at the integrand level such that the cancellation of the infrared divergences is achieved simultaneously, and apply it to reference examples as a proof of concept. Ultraviolet divergences, which are the consequence of the point-like nature of the theory, are also reinterpreted physically in this framework. The proposed method opens the intriguing possibility of carrying out purely four-dimensional implementations of higher-order perturbative calculations at next-to-leading order (NLO) and beyond free of soft and final-state collinear subtractions.

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arXiv2015

Higher-order QCD corrections to triple collinear splitting functions

We present splitting functions in the triple collinear limit at next-to-leading order in the strong coupling. We performed the computation in the context of massless QCD+QED, and consider first collinear processes which include at least one photon. The IR divergent structure of the multi-partonic splitting functions agrees with the Catani's formula. Consistency checks based on symmetry arguments have been implemented and results for different configurations have been cross-checked. Studying photon-started processes, we obtained very compact results: this allowed us to simplify the expressions for the remaining splitting functions.

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arXiv2015

From dimensional regularization to NLO computations in four dimensions

Loop-tree duality (LTD) allows to express virtual contributions in terms of phase-space integrals, thus leading to a direct mapping with real radiation terms. We review the basis of the method and describe its application to regularize Feynman integrals. Performing an integrand-level combination of real and virtual terms, we show how to recover physical results by simply taking the four-dimensional limit of $d$-dimensional expressions. Moreover, this method provides a natural physical interpretation of infrared singularities, their origin and the way that they cancel in the complete computation.

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arXiv2015

Numerical implementation of the Loop-Tree Duality method

We present a first numerical implementation of the Loop-Tree Duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable contour deformation in the loop three-momentum space to carry out the numerical integration. Then, we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and present explicit results for scalar integrals with up to five external legs (pentagons) and tensor integrals with up to six legs (hexagons). The LTD method features an excellent performance independently of the number of external legs.

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arXiv2015

Towards a Numerical Implementation of the Loop-Tree Duality Method

We review the recent progress on the numerical implementation of the Loop-Tree Duality Method (LTDM) for the calculation of scattering amplitudes. A central point is the analysis of the singularities of the integrand. In the framework of the LTDM some of these singularities cancel out. The ones left over are dealt with by contour deformation. We present details on how to achieve this as well as first results.

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arXiv2015

Single bottom quark production in kT-factorisation

We present a study within the kT-factorisation scheme on single bottom quark production at the LHC. In particular, we calculate the rapidity and transverse momentum differential distributions for single bottom quark/anti-quark production. In our setup, the unintegrated gluon density is obtained from the NLx BFKL Green function whereas we included mass effects to the Lx heavy quark jet vertex. We compare our results to the corresponding distributions predicted by the usual collinear factorisation scheme. The latter were produced with Pythia 8.1.

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arXiv2015

Polarized triple-collinear splitting functions at NLO for processes with photons

We compute the polarized splitting functions in the triple collinear limit at next-to-leading order accuracy (NLO) in the strong coupling $α_{\rm S}$, for the splitting processes $γ\to q \bar{q} γ$, $γ\to q \bar{q} g$ and $g \to q \bar{q} γ$. The divergent structure of each splitting function was compared to the predicted behaviour according to Catani's formula. The results obtained in this paper are compatible with the unpolarized splitting functions computed in a previous article. Explicit results for NLO corrections are presented in the context of conventional dimensional regularization (CDR).

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arXiv2014

Triple collinear splitting functions at NLO for scattering processes with photons

We present splitting functions in the triple collinear limit at next-to-leading order. The computation was performed in the context of massless QCD+QED, considering only processes which include at least one photon. Through the comparison of the IR divergent structure of splitting amplitudes with the expected known behavior, we were able to check our results. Besides that we implemented some consistency checks based on symmetry arguments and cross-checked the results among them. Studying photon-started processes, we obtained very compact results.

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arXiv2014

On the singular behaviour of scattering amplitudes in quantum field theory

We analyse the singular behaviour of one-loop integrals and scattering amplitudes in the framework of the loop--tree duality approach. We show that there is a partial cancellation of singularities at the loop integrand level among the different components of the corresponding dual representation that can be interpreted in terms of causality. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.

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arXiv2014

The loop-tree duality at work

We review the recent developments of the loop-tree duality method, focussing our discussion on analysing the singular behaviour of the loop integrand of the dual representation of one-loop integrals and scattering amplitudes. We show that within the loop-tree duality method there is a partial cancellation of singularities at the integrand level among the different components of the corresponding dual representation. The remaining threshold and infrared singularities are restricted to a finite region of the loop momentum space, which is of the size of the external momenta and can be mapped to the phase-space of real corrections to cancel the soft and collinear divergences.

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arXiv2014

Double collinear splitting amplitudes at next-to-leading order

We compute the next-to-leading order (NLO) QCD corrections to the $1 \to 2$ splitting amplitudes in different dimensional regularization (DREG) schemes. Besides recovering previously known results, we explore new DREG schemes and analyze their consistency by comparing the divergent structure with the expected behavior predicted by Catani's formula. Through the introduction of scalar-gluons, we show the relation among splittings matrices computed using different schemes. Also, we extended this analysis to cover the double collinear limit of scattering amplitudes in the context of QCD+QED.

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arXiv2013

Oriented Event Shapes at N3LL + O(as^2)

We analyze oriented event-shapes in the context of Soft-Collinear Effective Theory (SCET) and in Fixed-Order perturbation theory. Oriented event-shapes are distributions of event-shape variables which are differential on the angle theta_T that the thrust axis forms with the electron-positron beam. We show that at any order in perturbation theory and for any event shape, only two angular structures can appear: F_0 = 3/8(1 + cos^2 theta_T) and F_1 = (1 - 3cos^2 theta_T). When integrating over theta_T to recover the more familiar event-shape distributions, only F_0 survives. The validity of our proof goes beyond perturbation theory, and hence only these two structures are present at the hadron level. The proof also carries over massive particles. Using SCET techniques we show that singular terms can only arise in the F_0 term. Since only the hard function is sensitive to the orientation of the thrust axis, this statement applies also for recoil-sensitive variables such as Jet Broadening. We carry out resummation at N3LL of singular terms for Thrust, Heavy-Jet Mass, the sum of the Hemisphere Masses and C-parameter. We also compute the Fixed-Order distributions for these event-shapes at O(as) analytically and at O(as^2) with the program Event2.

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