Leonardo Vernazza has focused on developing new calculation techniques for particle scattering near threshold and in the high-energy limit. Both these correspond to particular kinematic limits of scattering processes, and require resummation of high-order corrections in perturbation theory. In each case the simplification associated with the kinematic limit provides means to compute such high-order corrections, which are inaccessible with present techniques for general kinematics.
An important example is the case of logarithms associated with partonic threshold. Large logarithms arise as an effect of dynamical enhancement of soft radiation in conjunction with small phase space. Techniques for resumming threshold logarithms at leading power have been known for a while. However, in order to match the precision goals set by the LHC experiments, it is necessary to resum an additional tower of logarithms occurring at the next-to-leading power (NLP). Leonardo Vernazza studied NLP logarithms with collaborators at the university of Amsterdam, Queen Mary (London) and Turin, establishing a factorisation theorem describing how these logarithms arise in the case of the Drell-Yan. They have exploited this factorisation theorem to show that scattering cross sections near threshold exhibit a universal structure at next-to-leading order (NLO) in the strong coupling, and at NLP in the threshold expansion. This result is very interesting, because it allows them to provide approximate predictions at NLO for processes such as double Higgs production, which are otherwise difficult to calculate.
Leonardo Vernazza has been working on this subject during the entire timeframe of the fellowship. Results have been published into two papers, listed as no. 1 and 3 in section “Publications”.
Leonardo Vernazza also exploited the possibility given by the Higgs Centre to organise a Workshop on this subject:
https://higgs.ph.ed.ac.uk/workshops/threshold-logarithms-beyond-leading-power(odnośnik otworzy się w nowym oknie). The workshop provided a great occasion to disseminate his results and discuss the topic with world-leading experts in the field.
During the timeframe of the fellowship Leonardo Vernazza studied also the the high-energy limit of scattering processes, in collaboration with the supervisor, Einan Gardi, and Simon Caron Huot (McGill University, Montreal) as well as with Joscha Reichel, a PhD student in Edinburgh. In this limit the structure of the amplitude simplifies, and it is possible to calculate it to higher orders in perturbation theory. With this motivation in mind we developed a framework to calculate scattering amplitudes in the high-energy limit, in the context of the shockwave formalism. This work allowed us to establish an explicit connection between concepts from Regge theory and perturbative QCD in the high-energy limit. We have derived the factorisation structure of amplitudes in the presence of Regge cuts, and provided a way to calculate the latter as iterated integrals in perturbation theory, up to next-to-next-to leading logarithmic accuracy. Furthermore, we achieved a breakthrough concerning the calculation of two-parton scattering at next-to-leading logarithmic accuracy. At this logarithmic accuracy we have been able to calculate the infrared divergent part of the amplitude to all orders in the strong coupling, and thus extract the soft anomalous dimension, a function responsible for generating all the infrared singularities in an amplitude, to all orders in the strong coupling.
These results have been published into two papers, listed as no. 2 and 4 in section “Publications”.
Furthermore, we exploited the possibility given by the Higgs Centre to organise a workshop on this subject:
http://higgs.ph.ed.ac.uk/workshops/iterated-integrals-and-regge-limit(odnośnik otworzy się w nowym oknie). The workshop has provided a great occasion to disseminate our results and discuss the subject with world-leading experts in the field.
