The spin-dependent quark beam function at NNLO

Abstract

We calculate the beam function for longitudinally-polarized quarks through next-to-next-to-leading order (NNLO) in QCD perturbation theory. This is the last missing ingredient needed to apply the factorization theorem for the $N$-jettiness event-shape variable in polarized collisions through the NNLO level. We present all technical details of our derivation. As a by-product of our calculation we provide the first independent check of the previously-obtained unpolarized quark beam function. We anticipate that our result will have phenomenological applications in describing data from polarized collisions.

18 pages, 3 figures, references added, corrections made in some equations

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Cited by in corpus (14)

• N-Jettiness Subtractions for $gg\to H$ at Subleading Power
• Power Corrections for N-Jettiness Subtractions at $\mathcal{O}({\alpha }_s)$
• Mixed EW-QCD two-loop amplitudes for $q\bar{q}\to {\ell }^{+}{\ell }^{-}$ and ${\gamma }_5$ scheme independence of multi-loop corrections
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Inclusive jet production as a probe of polarized PDFs at a future EIC
• Jet production in Polarized DIS at NNLO
• NNLO zero-jettiness beam and soft functions to higher orders in the dimensional-regularization parameter $\epsilon$
• On phase-space integrals with Heaviside functions
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• Zero-jettiness soft function to third order in perturbative QCD
• $W$-boson production in polarized proton-proton collisions at RHIC through next-to-next-to-leading order in perturbative QCD
• Two-loop $N$-jettiness soft function for $pp\to 2j$ production
• One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD
• Jet Charge with Global Event Shapes: Probing Quark Flavor Dynamics