Bootstrapping the Four-Point NMHV Stress-Tensor Form Factor

Abstract

We bootstrap the four-point next-to-maximally helicity-violating (NMHV) form factor of the chiral stress-tensor supermultiplet in planar maximally supersymmetric Yang-Mills theory through three loops at the symbol level. At two loops, an ansatz built from NMHV leading singularities and the relevant five-point one-mass integral function space is fixed uniquely by physical constraints; the resulting ratio function symbol contains 78 letters, all drawn from the 88-letter alphabet previously identified in the four-point MHV sector. At three loops, using this 88-letter alphabet as input and imposing extended Steinmann relations satisfied by the minimally-subtracted hard function, together with other physical constraints, we determine the three-loop symbol uniquely. Both results pass soft, double-soft and directional dual conformal invariance (DDCI) checks, provide the first multi-loop non-MHV form-factor data, and support the universality of the 88-letter alphabet for four-point form factors beyond the MHV sector.