On the Four-Loop Higgs--Gluon Form Factor in Nonlocal Quantum Field Theory

Abstract:In particle physics the virtual N$^3$LO contribution to gluon-fusion Higgs production in the Standard Model requires four-loop multi-scale QCD amplitudes that in dimensional regularization are dominated by singular integral reduction and difficult master-integral evaluations. In this note we show that a nonlocal UV completion makes each fixed-order four-loop Feynman diagram fully convergent in four dimensions while keeping the analytic structure needed for Lehmann-Symanzik-Zimmermann (LSZ) reduction formula. For gluon-fusion $gg\!\to\!H$ we derive a closed form Schwinger-parameter representation where all loop-momentum integrals are performed analytically and thus leaving finite parameter integrals viable for direct numerical evaluation without needing the usual UV subtractions. This method heps to isolate the collider-hard contribution as a convergent four-loop form factor. The strong coupling then is defined by a finite normalization condition in the entire-function regularization scheme and it is related to the $\overline{\mathrm{MS}}$ coupling by finite matching where after this matching, the regulator-dependent corrections decouple in the local limit $E_M\!\to\!\infty$.

arXiv:2608.22623 [hep-ph]

(or arXiv:2608.22623v1 [hep-ph] for this version)

https://doi.org/10.48550/arXiv.2608.22623 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

Nucl. Phys. B 1030 (2026) 117618

https://doi.org/10.1016/j.nuclphysb.2026.117618 Focus to learn more DOI(s) linking to related resources

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