Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle

Abstract

We obtain for the first time the two-loop amplitudes for Higgs plus three gluons in Higgs effective field theory including dimension-seven operators. This provides the S-matrix elements for the top mass corrections for Higgs plus a jet production at LHC. The computation is based on the on-shell unitarity method combined with integration by parts reduction. We work in conventional dimensional regularization and obtain analytic expressions renormalized in the MS-bar scheme. The two-loop anomalous dimensions present operator mixing behavior. The infrared divergences agree with that predicted by Catani and the finite remainders take remarkably simple forms, where the maximally transcendental parts are identical to the corresponding results in N=4 super-Yang-Mills theory. The parts of lower transcendentality turn out to be also largely determined by the N=4 results.

v3: published version with supplemental material added

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• $\text{Tr}(F^3)$ supersymmetric form factors and maximal transcendentality Part II: $0<\mathcal{N}<4$ super Yang-Mills
• Full-color three-loop three-point form factors in N=4 SYM
• Bootstrapping a Two-Loop Four-Point Form Factor
• Two-Loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes
• Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD
• Two-Loop QCD Corrections to the Higgs plus three-parton amplitudes with Top Mass Correction
• Soft Theorem to Three Loops in QCD and $\mathcal{N}=4$ Super Yang-Mills Theory
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
• Form factors with two operator insertions and the principle of maximal transcendentality
• Gluonic evanescent operators: classification and one-loop renormalization
• Deciphering the Maximal Transcendentality Principle via Bootstrap
• Two-loop amplitudes for di-Higgs and di-pseudo-Higgs productions through quark annihilation in QCD
• The Curious Case of Leading Transcendentality: Three Point Form Factors
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• Gluonic evanescent operators: two-loop anomalous dimensions
• Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in $\mathcal{N}=4$ SYM
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Three-loop color-kinematics duality: A 24-dimensional solution space induced by new generalized gauge transformations
• On interpolating anomalous dimension of twist-two operators with general spins
• On-shell Methods for Form Factors in N=4 SYM and Their Applications