Papers › Genus Drop in Hyperelliptic Feynman Integrals
Genus Drop in Hyperelliptic Feynman Integrals
Robin Marzucca, Andrew J. McLeod, Ben Page, Sebastian Pögel, Stefan Weinzierl
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The maximal cut of the nonplanar crossed box diagram with all massive internal propagators was long ago shown to encode a hyperelliptic curve of genus 3 in momentum space. Surprisingly, in Baikov representation, the maximal cut of this diagram only gives rise to a hyperelliptic curve of genus 2. To show that these two representations are in agreement, we identify a hidden involution symmetry that is satisfied by the genus 3 curve, which allows it to be algebraically mapped to the curve of genus 2. We then argue that this is just the first example of a general mechanism by means of which hyperelliptic curves in Feynman integrals can drop from genus g to ⌈g/2 ⌉ or ⌊g/2 ⌋, which can be checked for algorithmically. We use this algorithm to find further instances of genus drop in Feynman integrals.
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