The project Resummation4PS involved two main lines of investigation, in the fields of Resummations
and Partons Showers, respectively. Both areas of research have been addressed during the project, leading to the
development of novel theoretical tools for the understanding of the all-order perturbative dynamics of
scattering processes, as well as to considerable technology to carry out practical calculations for physical
observables whose accurate description is central to the modern collider physics program.
The first part of the project concerns the area of Resummations, that indicate theoretical techniques
that address multi-scale problems by tailoring the calculation to the observable under consideration.
In particular, the project addressed the following aspects of this field:
Objective O1:
A first important goal of the project concerns the resummation of so-called non-global QCD observables.
These observables are characterised by the fact that they are sensitive only to radiation in limited angular
regions of the phase space. For this reason their perturbative structure is rather complicated and a
resummation beyond the lowest order (leading logarithmic) has never been achieved. During the last (second)
year of the Fellowship, I have developed the theoretical framework to describe the all-order structure of these
observables at higher perturbative orders. This work, together with the first application to collider phenomenology,
will be finalised in the next 6 months.
Objective O2:
A second important achievement of the Resummation4PS project has been the formulation of momentum space
resummation for large families of collider observables, such as event shapes, jet rates, and kinematical
distributions of the final state produced in a hadronic collision.
An example of observable studied during the project is given by the transverse momentum distribution of a
colour singlet system produced in a hadronic scattering, for which this method has been exploited to
obtain several state of the art calculations in the context of the electro-weak and Higgs physics program
of the Large Hadron Collider.
In the second year of the Fellowship, the research has been oriented towards more complex, multi-differential observables.
In this context, I have extended the theory framework outlined above to describe the simultaneous measurement of the
transverse momentum of a Higgs boson and the transverse momentum of the hardest hadronic jet produced in the same
hadronic scattering. This is the first calculation of its kind, and it is currently being exploited in a number of phenomenological
applications at the LHC.
A final sub-project involves the formulation of a novel theoretical approach to tackle the description of observables in reactions with
many particles. This is currently under development in the context of Soft Collinear Effective Theory (SCET), by exploiting the synergy
between SCET and advanced numerical techniques to tame the complexity of the calculation.
Objective O3:
The second line of investigation regards the field of parton showers (PS). These are computer algorithms
in which the evolution of the hard system towards smaller energy scales is simulated through a Markovian
chain of emissions that is realised by means of a Monte Carlo algorithm. Unlike for resummations, the
flexibility of the algorithm makes it applicable to any physical observable, at the cost of a lower
logarithmic accuracy.
Together with my CERN supervisor, we have worked on the development of a novel formulation of parton shower
algorithms that, through the connection to the field of resummations, paved the way to the creation
of a new generation of PS capable of achieving higher perturbative accuracy.
A second crucial aspect of PS simulations is their matching to higher order perturbative predictions for the hard scattering process.
In this context, within a separate collaboration I have developed a novel method to perform a consistent combination (matching) of
the PS simulation to NNLO predictions for a broad class of hadronic observables.
