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.
Canonical differential equations and intersection matrices
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Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in the Gauss-Manin connection.
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
A strategy is introduced to solve canonical differential equations for Feynman master integrals on arbitrary geometries by reducing numerical evaluation to an enlarged system of rational differential equations.
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
IterInt package evaluates iterated integrals by transforming them into solvable differential equation systems with built-in regularization.
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
citing papers explorer
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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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Integrand Analysis, Leading Singularities and Canonical Bases beyond Polylogarithms
Feynman integrals selected for unit leading singularities in complex geometries satisfy epsilon-factorized differential equations with new transcendental functions corresponding to periods and differential forms in the Gauss-Manin connection.
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A construction of single-valued elliptic polylogarithms
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
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Solution of Canonical Differential Equations for Integrals on Arbitrary Geometries
A strategy is introduced to solve canonical differential equations for Feynman master integrals on arbitrary geometries by reducing numerical evaluation to an enlarged system of rational differential equations.
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New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
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IterInt: Evaluating iterated integrals via differential equations
IterInt package evaluates iterated integrals by transforming them into solvable differential equation systems with built-in regularization.
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From geometry to phenomenology
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.