  In the context of planar holography, integrability plays an important role
for solving certain massless quantum field theories such as N=4 SYM theory. In
this letter we show that integrability also features in the building blocks of
massive quantum field theories. At one-loop order we prove that all massive
n-gon Feynman integrals in generic spacetime dimensions are invariant under a
massive Yangian symmetry. At two loops similar statements can be proven for
graphs built from two n-gons. At generic loop order we conjecture that all
graphs cut from regular tilings of the plane with massive propagators on the
boundary are invariant. We support this conjecture by a number of numerical
tests for higher loops and legs. The observed Yangian extends the bosonic part
of the massive dual conformal symmetry that was found a decade ago on the
Coulomb branch of N=4 SYM theory. By translating the Yangian level-one
generators from dual to original momentum space, we introduce a massive
generalization of momentum space conformal symmetry. Even for non-dual
conformal integrals this novel symmetry persists. The Yangian can thus be
understood as the closure of massive dual conformal symmetry and this new
massive momentum space conformal symmetry, which suggests an interpretation via
AdS/CFT. As an application of our findings, we bootstrap the hypergeometric
building blocks for examples of massive Feynman integrals.
