Theorie Palaver

Top-quark pair production in association with a jet is a key process at the LHC. Its high sensitivity to the top mass and the increasing experimental precision call for the QCD corrections to be computed at the next-to-next-to-leading order (NNLO). In this seminar, I will present the computation of the two-loop Feynman integrals required to obtain NNLO QCD predictions in the leading colour approximation. These integrals are characterised by significant algebraic complexity—stemming from the multi-scale, five-particle kinematics—as well as analytic complexity, due to the appearance of nested square roots and elliptic functions. I will discuss modern methods for tackling multi-scale integrals in a way that is suitable for phenomenology, and outline first steps to extend these techniques to cases involving elliptic functions.

By employing the Bloch-sphere formalism, I will present a novel class of unstable qubits, which are called Critical Unstable Qubits (CUQs). The characteristic property of CUQs is that the energy-level and decay-width Pauli vectors, E and Γ, are orthogonal to one another, and the key parameter r = |Γ|/(2|E|) is less than 1. A remarkable feature of CUQs is that they exhibit atypical behaviours like coherence-decoherence oscillations when analysed in an appropriately defined co-decaying frame of the system. In the same frame, I will show how a unit Bloch vector b describing a pure CUQ sweeps out unequal areas during equal intervals of time, while rotating about the vector E. These phenomena emerge beyond the usual oscillatory pattern due to the energy-level difference of a standard two-level quantum system. I will illustrate how these new features are relatively robust and persist even for quasi-CUQs, in which the vectors E and Γ are not perfectly orthogonal to each other. I discuss potential applications of our results to quantum information and to unstable meson-antimeson and other systems.

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