Abstract
We present an analytic three-loop result for the leading color contribution to the Higgs-gluon form factor in QCD. The leading color contribution is given at next-to-next-to-leading order by the {N}_c^2 -term in QCD with Nc colors. The main focus of this article lies on the evaluation of the relevant Feynman integrals with a special emphasis on the elliptic sector.
Highlights
The differential equations of the sectors depicted in figure 6 have homogeneous parts which can be transformed into -form geneities of both sectors depend as on mdeassctreirbiendteignraslesctoifotnhe3.c1a.noUnnicfoarltsuencatoterslyi,nt√hexiannhdomthoesector in figure 6(b) depends on the elliptic master integrals
We presented for the first time an analytic result for the leading color contribution to the three-loop ggH form factor in QCD with a finite mass of the mediating quark
We showed that our result requires the introduction of a new class of iterated integrals, eqs. (3.40), (3.41), with integration kernels involving elliptic integrals
Summary
The most complicated sector of the calculation is shown in figure 4. As a starting point for this elliptic sector, we define the basis integrals with. Even though the integrals I1(x, ), · · · , I6(x, ) are already finite for → 0, it is more convenient to proceed in a different basis where the differential equations are fuchsian and the eigenvalues of the residues are free from resonances. Such a basis is given by a1(x, ). The six remaining coefficients, arranged in a vector a(x), fulfill an inhomogeneous differential equation of the form da(x) dx. In section 3.3.1 we describe how to solve the homogeneous part of eq (3.30), while in section 3.3.2 we include the inhomogeneity k(t) into the calculation which requires the introduction of a new class of iterated integrals
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