Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors

Abstract

By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like ${\gamma }^{\ast }\gamma \to Q\bar{Q}$, $e^{+}{e}^{-}\to \gamma +Q\bar{Q}$,~and~$H/Z^0\to \gamma +Q\bar{Q}$, heavy quarkonium exclusive decays, and also the CP-even heavy quarkonium inclusive production and decays.

23 pages, 3 figures, more discussions and references added

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Cited by in corpus (15)

• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• Elliptic Feynman integrals and pure functions
• Elliptic symbol calculus: from elliptic polylogarithms to iterated integrals of Eisenstein series
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Two-loop diagrams in non-relativistic QCD with elliptics
• Symbology for elliptic multiple polylogarithms and the symbol prime
• Next-to-next-to-leading order matching of beauty-charmed meson $B_c$ and $B_c^{\ast }$ decay constants
• Average speed and its powers $v^n$ of a heavy quark in quarkonia
• Study on ${\eta }_{c2}({\eta }_{b2})$ electromagnetic decay into double photons
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• Calculation of master integrals in terms of elliptic multiple polylogarithms
• Two-loop master integrals for pseudo-scalar quarkonium and leptonium production and decay
• Transition Form-Factor for ${\eta }_Q$ at NNLO in the strong coupling ${\alpha }_s$ and with all-order $v^2$ resummation