A prescription for projectors to compute helicity amplitudes in D dimensions

Abstract

This article discusses a prescription to compute polarized dimensionally regularized amplitudes, providing a recipe for constructing simple and general polarized amplitude projectors in D dimensions that avoids conventional Lorentz tensor decomposition and avoids also dimensional splitting. Because of the latter, commutation between Lorentz index contraction and loop integration is preserved within this prescription, which entails certain technical advantages. The usage of these D-dimensional polarized amplitude projectors results in helicity amplitudes that can be expressed solely in terms of external momenta, but different from those defined in the existing dimensional regularization schemes. Furthermore, we argue that despite being different from the conventional dimensional regularization scheme (CDR), owing to the amplitude-level factorization of ultraviolet and infrared singularities, our prescription can be used, within an infrared subtraction framework, in a hybrid way without re-calculating the (process-independent) integrated subtraction coefficients, many of which are available in CDR. This hybrid CDR-compatible prescription is shown to be unitary. We include two examples to demonstrate this explicitly and also to illustrate its usage in practice.

Matched to the version to be published in Eur. Phys. J. C

References in corpus (33)

• An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC
• A novel subtraction scheme for double-real radiation at NNLO
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• GoSam-2.0: a tool for automated one-loop calculations within the Standard Model and beyond
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Four-dimensional formulation of the sector-improved residue subtraction scheme
• NLO QCD corrections to Higgs boson plus jet production with full top-quark mass dependence
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: the Quark-Antiquark Channel
• Hard-Soft-Collinear Factorization to All Orders
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Scattering Amplitudes For All Masses and Spins
• Tensor decomposition for bosonic and fermionic scattering amplitudes
• NNLO corrections to inclusive semileptonic B decays in the shape-function region
• Physical projectors for multi-leg helicity amplitudes
• Geometric IR subtraction for real radiation
• NLO Antenna Subtraction with Massive Fermions
• NNLO predictions for Z-boson pair production at the LHC
• Dimensional Reduction applied to QCD at three loops
• Factorisation and Subtraction beyond NLO
• Heavy Quark Form Factors at Three Loops in the Planar Limit
• ${\gamma }_5$ in FDH
• Top-quark effects in diphoton production through gluon fusion at NLO in QCD
• Quark and gluon form factors in four loop QCD: the $N_f^2$ and $N_{q\gamma }{N}_f$ contributions
• Polarised Amplitudes and Soft-Virtual Cross Sections for $b\bar{b}\to ZH$ at NNLO in QCD
• Calculation of two-loop QCD corrections for hadronic single top-quark production in the t channel
• Kira 1.2 Release Notes
• Efficient integrand reduction for particles with spin
• Three-loop quark form factor at high energy: the leading mass corrections
• Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator
• A minimal approach to the scattering of physical massless bosons
• Fermion Traces Without Evanescence
• Regularization-scheme dependence of QCD amplitudes in the massive case

Cited by in corpus (25)

• Tensor decomposition for bosonic and fermionic scattering amplitudes
• N${}^3$LO gravitational spin-orbit coupling at order $G^4$
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Two-loop leading-color helicity amplitudes for three-photon production at the LHC
• Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC
• $ZH$ production in gluon fusion: two-loop amplitudes with full top quark mass dependence
• N${}^3$LO Quadratic-in-Spin Interactions for Generic Compact Binaries
• N${}^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects
• Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel
• ZH production in gluon fusion at NLO in QCD
• Polarised Amplitudes and Soft-Virtual Cross Sections for $b\bar{b}\to ZH$ at NNLO in QCD
• An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting ${\gamma }_5$
• The complete singlet contribution to the massless quark form factor at three loops in QCD
• Reduction of Feynman Integrals in the Parametric Representation II: Reduction of Tensor Integrals
• Computational challenges for multi-loop collider phenomenology
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• Natural Boundaries for Scattering Amplitudes
• One-loop squared amplitudes for hadronic $tW$ production at next-to-next-to-leading order in QCD
• Two-loop Vertices with Vacuum Polarization Insertion
• OPITeR: A program for tensor reduction of multi-loop Feynman Integrals
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• Top-Quark Decay at Next-to-Next-to-Next-to-Leading Order in QCD
• Two-loop amplitude for mixed QCD-EW corrections to $gg\to Hg$
• Renormalization of the flavor-singlet axial-vector current and its anomaly in QCD
• Photon pair production in gluon fusion: Top quark effects around threshold