FDR, an easier way to NNLO calculations: a two-loop case study

Abstract

In this paper we illustrate the simplifications produced by FDR in NNLO computations. We show with an explicit example that - due to its four-dimensionality - FDR does not require an order-by-order renormalization and that, unlike the one-loop case, FDR and dimensional regularization (DR) generate intermediate two-loop results which are no longer linked by a simple subtraction of the ultraviolet (UV) poles in epsilon. Our case study is the two-loop amplitude for H -> gamma gamma, mediated by an infinitely heavy top loop, in the presence of gluonic corrections. We use this to elucidate how gauge invariance is preserved with no need of introducing counterterms in the Lagrangian. In addition, we discuss a possible four-dimensional approach to the infrared (IR) problem compatible with the FDR treatment of the UV infinities.

34 pages, 8 figures, version enlarged to be published in EPJC

References in corpus (7)

• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• A novel subtraction scheme for double-real radiation at NNLO
• Direct extraction of one-loop integral coefficients
• A four-dimensional approach to quantum field theories
• Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams

Cited by in corpus (13)

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• Dimensional regularization vs methods in fixed dimension with and without ${\gamma }_5$
• Two-loop off-shell QCD amplitudes in FDR
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Regularization-scheme dependence of QCD amplitudes in the massive case
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• NNLO final-state quark-pair corrections in four dimensions
• Integration-by-parts identities in FDR
• Numerical Evaluation of Two-Loop Integrals in FDR
• Dimensional schemes for cross sections at NNLO
• Matching high-energy electroweak fermion loops onto the Fermi theory without higher dimensional operators
• Monte Carlo evaluation of divergent one-loop integrals without contour deformation