The 3-loop anomalous dimensions from off-shell operator matrix elements

Blümlein, J.; Marquard, Peter; Schneider, Carsten; Schönwald, Kay

doi:10.22323/1.416.0048

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Pos(ll2022)0631

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2022

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“…The three-loop non-singlet splitting functions were rederived with this method in Ref. [29,30]. At four loops, partial results for the non-singlet splitting functions have been obtained in Ref.…”

Section: Pos(ll2022)063mentioning

confidence: 99%

Renormalization of twist-two operators in QCD and its application to singlet splitting functions

Yang¹,

Gehrmann²,

Manteuffel³

2022

Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2022)

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Splitting functions govern the scale evolution of parton distribution functions. Through a Mellin transformation, they are related to anomalous dimensions of twist-two operators in the operator product expansion. We study off-shell operator matrix element, where the physical operators mix under renormalization with other gauge-variant operators of the same quantum numbers. We devise a new method to systematically extract the Feynman rules resulting from those operators without knowing the operators themselves. As a first application of the new approach, we independently reproduce the well-known three-loop singlet splitting functions obtained from computations of on-shell quantities.

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Section: Pos(ll2022)063mentioning

confidence: 99%