We present the leading colour and light fermionic planar two-loop corrections for the production of two photons and a jet in the quark-antiquark and quark-gluon channels. In particular, we compute the interference of the two-loop amplitudes with the corresponding tree level ones, summed over colours and polarisations. Our calculation uses the latest advancements in the algorithms for integration-by-parts reduction and multivariate partial fraction decomposition to produce compact and easy-to-use results. We have implemented our results in an efficient C++ numerical code. We also provide their analytic expressions in Mathematica format.

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We study the implications of the ELKO fermions as a cold dark matter candidate. Such fermions arise in theories that are not symmetric under the full Lorentz group. Although they do not carry electric charge, ELKOs can still couple to photons through a nonstandard interaction. They also couple to the Higgs but do not couple to other standard model particles. We impose limits on their coupling strength and the ELKO mass assuming that these particles give dominant contribution to the cosmological cold dark matter. We also determine limits imposed by the direct dark matter search experiments on the ELKO-photon and the ELKO-Higgs coupling. Furthermore we determine the limit imposed by the gamma ray bursts time delay observations on the ELKO-Higgs coupling. We find that astrophysical and cosmological considerations rule out the possibility that ELKO may contribute significantly as a cold dark matter candidate. The only allowed scenario in which it can contribute significantly as a dark matter candidate is that it was never in equilibrium with the cosmic plasma. We also obtain a relationship between the ELKO self-coupling and its mass by demanding it to be consistent with observations of dense cores in the galactic centers.

We calculate the two-loop QCD corrections to gg → ZZ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we also allow for irreducible numerators, higher powers of propagators, dimensionally shifted integrals, and subsector integrals. The amplitude is expressed in terms of such finite integrals by employing syzygies derived with linear algebra and finite field techniques. Evaluating the amplitude using numerical integration, we find agreement with previous expansions in asymptotic limits and provide ab initio results also for intermediate partonic energies and non-central scattering at higher energies.