Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
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Analytic expressions for the finite remainders of two-loop leading-color helicity amplitudes in Higgs plus two-jet production are obtained in the heavy-top effective theory using numerical unitarity and a new partial-fraction algorithm.
Two-loop all-plus helicity amplitudes for self-dual Higgs plus gluons are obtained via four-dimensional unitarity cuts into one-loop and tree amplitudes plus finite-field tensor reduction.
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
The paper decomposes two-loop Yang-Mills gluon amplitudes into color structures via trace and structure-constant bases and organizes relations between the resulting partial amplitudes.
Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via differential equations solved numerically by generalized power series expansion.
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The spectrum of Feynman-integral geometries at two loops
Two-loop Feynman integrals involve Riemann spheres, elliptic curves, hyperelliptic curves of genus 2 and 3, K3 surfaces, and a rationalizable Del Pezzo surface of degree 2.
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Two-loop leading-color QCD corrections for Higgs plus two-jet production in the heavy-top limit
Analytic expressions for the finite remainders of two-loop leading-color helicity amplitudes in Higgs plus two-jet production are obtained in the heavy-top effective theory using numerical unitarity and a new partial-fraction algorithm.
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Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
Two-loop all-plus helicity amplitudes for self-dual Higgs plus gluons are obtained via four-dimensional unitarity cuts into one-loop and tree amplitudes plus finite-field tensor reduction.
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Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
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Color Decompositions of the Two Loop Amplitudes of Yang-Mills theory
The paper decomposes two-loop Yang-Mills gluon amplitudes into color structures via trace and structure-constant bases and organizes relations between the resulting partial amplitudes.
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One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}(\epsilon^2)$
Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via differential equations solved numerically by generalized power series expansion.