Abstract
We consider two-loop renormalization of high-dimensional Lorentz scalar operators in the gluonic sector of QCD. These operators appear also in the Higgs effective theory obtained by integrating out the top quark loop in the gluon fusion process. We first discuss the classification of operators and how to construct a good set of basis using both off-shell field theory method and on-shell form factor formalism. To study loop corrections, we apply efficient unitarity-IBP strategy and compute the two-loop minimal form factors of length-3 operators up to dimension sixteen. From the UV divergences of form factor results, we extract the renormalization matrices and analyze the operator mixing behavior in detail. The form factors we compute are also equivalent to Higgs plus three-gluon amplitudes that capture high-order top mass corrections in Higgs EFT. We obtain the analytic finite remainder functions which exhibit several universal transcendentality structures.
Highlights
The other hand, at high energy scale the asymptotic freedom ensures that a perturbative expansion still applies
We consider two-loop renormalization of high-dimensional Lorentz scalar operators in the gluonic sector of QCD. These operators appear in the Higgs effective theory obtained by integrating out the top quark loop in the gluon fusion process
The local operators we consider are related to the Higgs effective action, which describes the Higgs production via gluon fusion process at LHC
Summary
We consider the construction of operator basis. We will first consider the field theory method and apply the on-shell form factor method. Besides determining the dimension of the basis, a central goal is to explain how to construct a convenient set of basis operators that will facilitate the high loop computations. We will provide explicit basis for length-3 operators up to dimension 16, and in later sections we will compute their anomalous dimension and related Higgs EFT amplitudes
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