Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD

Abstract

We present a calculation of all matching coefficients for $N$-jettiness beam functions at next-to-next-to-next-to-leading order (N${}^3$LO) in perturbative quantum chromodynamics (QCD). Our computation is performed starting from the respective collinear splitting kernels, which we integrate using the axial gauge. We use reverse unitarity to map the relevant phase-space integrals to loop integrals, which allows us to employ multi-loop techniques including integration-by-parts identities and differential equations. We find a canonical basis and use an algorithm to establish non-trivial partial fraction relations among the resulting master integrals, which allows us to reduce their number substantially. By use of regularity conditions, we express all necessary boundary constants in terms of an independent set, which we compute by direct integration of the corresponding integrals in the soft limit. In this way, we provide an entirely independent calculation of the matching coefficients which were previously computed in arXiv:2006.03056.

57 pages, 3 figures, 4 ancillary files

References in corpus (30)

• 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
• The Quark Beam Function at NNLL
• Four-Loop Non-Singlet Splitting Functions in the Planar Limit and Beyond
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• Large-nf Contributions to the Four-Loop Splitting Functions in QCD
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• The three-loop cusp anomalous dimension in QCD
• The three-loop unpolarized and polarized non-singlet anomalous dimensions from off shell operator matrix elements
• On the Generalized Harmonic Polylogarithms of One Complex Variable
• The Two-Loop Master Integrals for $q\bar{q}\to VV$
• Iterated Binomial Sums and their Associated Iterated Integrals
• Fragmentation in Jets at NNLO
• The Gluon Beam Function at Two Loops
• Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO
• The $n_f^2$ contributions to fermionic four-loop form factors
• Baikov representations, intersection theory, and canonical Feynman integrals
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Two-loop $gg\to Hg$ amplitude mediated by a nearly massless quark
• Adequate bases of phase space master integrals for $gg\to h$ at NNLO and beyond
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Triple collinear splitting functions at NLO for scattering processes with photons
• Collinear expansion for color singlet cross sections
• NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $\epsilon$
• The spin-dependent quark beam function at NNLO
• Same-hemisphere three-gluon-emission contribution to the zero-jettiness soft function at N3LO QCD
• On phase-space integrals with Heaviside functions
• Iterated integrals over letters induced by quadratic forms
• On the calculation of soft phase space integral

Cited by in corpus (8)

• The first-order factorizable contributions to the three-loop massive operator matrix elements $A_{Qg}^{(3)}$ and $\Delta A_{Qg}^{(3)}$
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• Renormalization of twist-two operators in covariant gauge to three loops in QCD
• Zero-jettiness soft function to third order in perturbative QCD
• One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• The DIS 1-Jettiness Event Shape at N${}^3$LL+$\mathcal{O}({\alpha }_s^2)$
• Region analysis of $H\to \gamma \gamma$ via a bottom quark loop