Two-loop helicity amplitudes for W/Z boson pair production in gluon fusion with exact top mass dependence

We compute the top quark contribution to the two-loop amplitudes for on-shell ${W/Z}$ boson pair production in gluon fusion, ${gg→WW}$ and ${gg→ZZ}$. Exact dependence on the top quark mass is retained, the bottom quark is considered massless. Integral reduction is performed numerically for each phase space point and the master integrals are evaluated using the auxiliary mass flow method. This allows for fast computation of the amplitudes to very high precision

Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion

We compute the contribution of third generation quarks ($t,\ b$) to the two-loop amplitude for on-shell $W$ boson pair production in gluon fusion $gg \to WW$. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations

Top quark contribution to two-loop helicity amplitudes for ZZ boson pair production in gluon fusion

We compute the top quark contribution to the two-loop amplitude for on-shell $Z$ boson pair production in gluon fusion, $gg \to ZZ$. Exact dependence on the top quark mass is retained. For each phase space point the integral reduction is performed numerically and the master integrals are evaluated using the auxiliary mass flow method, allowing fast computation of the amplitude with very high precision

Contribution of third generation quarks to two-loop helicity amplitudes for W boson pair production in gluon fusion

We compute the contribution of third generation quarks (t, b) to the two-loop amplitude for on-shell W boson pair production in gluon fusion gg -> WW. We present plots for the amplitude across partonic phase space as well as reference values for two kinematic points. The master integrals are efficiently evaluated by numerically solving a system of ordinary differential equations

New results for two-loop scattering in quantum chromodynamics

Decreasing statistical and systematic uncertainties for particle collisions experiments at the Large Hadron Collider (LHC) put increasing demands on precision in theoretical predictions. At the LHC protons are collided at high energy in order to study fundamental interactions. The scattering processes are dominated by strong interactions which are modelled by Quantum Chromodynamics (QCD). In this energy regime theoretical predictions can be calculated using perturbation theory in the coupling constant and hence higher precision is achieved by including higher orders. The higher orders include both processes of additional unresolved external states (higher multiplicity) or internal states (more loops). Currently, calculations at next-to-next-to-leading order (NNLO) precision are in demand for current and future analyses. These calculations require the development of new techniques to handle the growth in complexity. The topic of this thesis is loop calculations in QCD using modern on-shell techniques. We present new results for planar 2 → 3 gluon scattering at two loops. The amplitudes are obtained by employing generalised unitarity and finite field reconstruction methods. The universality of the pole structure is used for verification of the results, but also allows us to reconstruct only a finite remainder. Strategies to obtain compact analytic expressions both at the level of the integrand and after integration are discussed. Integrals are dealt with using a variety of approaches including sector decomposition, integration-by-parts identities, and dimensional shifting and recurrence relations. We also describe a new unitarity compatible method for dealing with massive fermions at one loop. This method involves an explicit construction of six-dimensional spinors and a discussion of the renormalisation of effective field theories