Two loop QCD corrections for the process pseudo-scalar Higgs → 3 partons

2021

Form factors, as quantities involving both local operators and asymptotic particle states, contain information of both the spectrum of operators and the on-shell amplitudes. So far the studies of form factors have been mostly focused on the large Nc planar limit, with a few exceptions of Sudakov form factors. In this paper, we discuss the systematical construction of full color dependent form factors with generic local operators. We study the color decomposition for form factors and discuss the general strategy of using on-shell unitarity cut method. As concrete applications, we compute the full two-loop non-planar minimal form factors for both half-BPS operators and non-BPS operators in the SU(2) sector in $$ \mathcal{N} $$ N = 4 SYM. Another important aspect is to investigate the color-kinematics (CK) duality for form factors of high-length operators. Explicit CK dual representation is found for the two-loop half-BPS minimal form factors with arbitrary number of external legs. The full-color two-loop form factor result provides an independent check of the infrared dipole formula for two-loop n-point amplitudes. By extracting the UV divergences, we also reproduce the known non-planar SU(2) dilatation operator at two loops. As for the finite remainder function, interestingly, the non-planar part is found to contain a new maximally transcendental part beyond the known planar result.

Section: Jhep04(2021)176supporting

confidence: 80%

Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality

Lin

2021

“…We obtain the analytic expressions, and find that maximal transcendental part is universal, namely, independent of the operators. This provides further support of the maximal transcendentality principle introduced in study of anomalous dimensions in [41,42] and then observed for the form factor of tr(F 2 ) in [43] and later also for other operators [12,13,31,[44][45][46][47][48][49][50][51][52]. Besides, the lower transcendentality degree-3 and degree-2 parts also contain universal building blocks, which was also observed in the previous results with dimension-six operators [13].…”

Section: Introductionsupporting

confidence: 87%

Two-loop anomalous dimensions of QCD operators up to dimension-sixteen and Higgs EFT amplitudes

Jin

Ren

2021

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.

“…This has been known for the kinematic independent quantities such as anomalous dimensions [38,39]. For pseudo-scalar Higgs amplitudes involving qqg states, the universal maximally transcendental part was also noted in [89].…”

Section: Discussionmentioning

confidence: 81%

Two-Loop QCD Corrections to the Higgs Plus Three-parton Amplitudes with Top Mass Correction

Jin

2020

We obtain the two-loop QCD corrections to Higgs plus three-parton amplitudes with dimension-seven operators in Higgs effective field theory. This provides the two-loop S-matrix elements for Higgs plus one-jet production at LHC with top-mass correction. We apply efficient unitarity plus IBP methods which are described in detail. We also study the color decomposition of the fermion cuts and find a connection between fundamental and adjoint representations which can reduce non-planar to planar unitarity cuts. We obtain final results in simple analytic form which exhibits intriguing hidden structure. The principle of maximal transcendentality is found to be satisfied for all results. The lower transcendentality parts also contain universal building blocks and can be written in compact analytic forms, suggesting further hidden structures.