We constrain the analytic structure of 2-loop Feynman integrals dimensionally regularized in the ‘t Hooft-Veltman scheme in the Standard Model (arXiv:2408.06325). We present an explicit reduction resulting from partial fractioning the high-multiplicity integrands into subsectors of the 12 distinct topologies with 11 generalized propagators. It improves the performance of the IBP reduction and numerical evaluation of integrals beyond 5-point scattering. We also present a functionally distinct basis of 347 Master Integrals arising from 84 distinct Feynman graphs which spans the whole corresponding 2-loop transcendental function space (arXiv:2503.16299). In addition, we indicate that all the 2-loop Master Integrals with more than 8 denominators, in an appropriate basis, do not contribute to the finite part of any 2-loop scattering amplitude. Moreover, we analyze the spectrum of special functions and the corresponding geometries appearing in any 2-loop amplitude. Then, we exploit the analytic structure of amplitudes using dispersion relations (arXiv:2403.18047). Such an Integrated Unitarity approach extends Generalized Unitarity by constraining not only the integrand of the amplitude but also its full integrated form. Since our approach improves the performance of the calculation, we provide a new result in terms of Harmonic Polylogarithms for the 4-loop 4-point massless planar ladder Feynman integral. Finally, we exploit the singular structure of massless QCD amplitudes. We express the singular part of the amplitude in terms of Feynman integrals compatible with topologies appearing in the bare amplitude, and we choose a basis of locally finite Master Integrals. As an example application, we write the finite part of an amplitude for the digluon production in quark annihilation for some helicity configurations as manifestly locally finite.
