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.
Analytic treatment of the two loop equal mass sunrise graph
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
abstract
The two loop equal mass sunrise graph is considered in the continuous d-dimensional regularisation for arbitrary values of the momentum transfer. After recalling the equivalence of the expansions at d=2 and d=4, the second order differential equation for the scalar Master Integral is expanded in (d-2) and solved by the variation of the constants method of Euler up to first order in (d-2) included. That requires the knowledge of the two independent solutions of the associated homogeneous equation, which are found to be related to the complete elliptic integrals of the first kind of suitable arguments. The behaviour and expansions of all the solutions at all the singular points of the equation are exhaustively discussed and written down explicitly.
citation-role summary
background 3
citation-polarity summary
verdicts
UNVERDICTED 5roles
background 3polarities
background 3representative citing papers
New algorithm identifies complete Landau singularities of Feynman integrals via Euler characteristic drops over finite fields, applied to non-planar two-loop six-point and massive three-loop graphs.
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
IterInt package evaluates iterated integrals by transforming them into solvable differential equation systems with built-in regularization.
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynman integrals.
citing papers explorer
-
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.
-
Landau's Leviathans
New algorithm identifies complete Landau singularities of Feynman integrals via Euler characteristic drops over finite fields, applied to non-planar two-loop six-point and massive three-loop graphs.
-
Discrete symmetries of Feynman integrals
Discrete symmetries of Feynman integral families correspond to permutations of Feynman parameters and induce group actions on twisted cohomology whose characters are Euler characteristics of fixed-point sets, yielding a formula for master integral counts in symmetric banana diagrams up to four loops
-
IterInt: Evaluating iterated integrals via differential equations
IterInt package evaluates iterated integrals by transforming them into solvable differential equation systems with built-in regularization.
-
Genus drop involving non-hyperelliptic curves in Feynman integrals
The extra-involution mechanism for genus drop is a special case of unramified double covering between curves, which explains genus drops with non-hyperelliptic to hyperelliptic transitions in certain three-loop Feynman integrals.