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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 1 - Resummation4PS (Advances in higher-order resummation and Parton Shower)

Teaser

Summary

For the decades to come, the LHC will continue its exploration of the
energy frontier by addressing several open questions in particle physics, notably the study
of the fine details of the Higgs sector, and the search for small
deviations from the SM which would ultimately diagnose the presence of
new physics. Besides the great complexity of the measurements, this program
requires an unprecedented level of precision in the theoretical
predictions of the SM, and specifically of Quantum Chromodynamics
(QCD).

In the perturbative approach to QCD at colliders, the hard scattering
is predicted by means of a power series in the strong coupling
constant, that is truncated at a fixed order once the
goal precision is achieved. However, a substantial part of the
information about what happened in any given high-energy LHC collision
is contained in the low-energy particles that are observed in the
detector. The description of the multiscale evolution of the system
from the energy of the hard scattering towards the low energies of the
observed hadrons crucially requires the summation of all orders
of the perturbative series in the soft and collinear limits, where the
emission probability is enhanced. Improving this
understanding is of paramount importance to derive the accurate
predictions necessary for the success of the LHC mission.

The objective of this proposal has been to explore the theoretical aspects
of this problem and to develop the theory and the computational methods
necessary to carry out accurate calculations of the the scattering process
for broad categories of collider physical observables.

Work performed

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 perf

Final results

The Resummation4PS project has produced 11 scientific articles, and 2 more are currently in preparation. All results have been and will be
disseminated in several international conferences and communicated to the research community. This will maximise the impact of
the research conducted during this fellowship, and promote further investigations in related directions. This research has led us to
understand deeply the perturbative structure of QCD at all orders, which in turn has allowed for a highly accurate description of
complex collider observables which are central to the physics program of the LHC.

Several advances beyond the state of the art have been achieved. Besides the theoretical progress outlined above, the project has brought
several innovations in the field of collider phenomenology. The novel methods created for the project have been used for the
calculation of the state of the current state-of-the-art predictions for differential distributions of the Higgs, Z and W bosons,
that are currently being adopted by the LHC experimental collaborations in their studies. A sample result is shown in the attached
figure. Moreover, a second application of the Resummation4PS technology has been the precise determination of the strong
coupling constant (i.e. the strength of the strong nuclear interaction), achieved by comparing precise theoretical calculation of jet rates at lepton colliders to the corresponding
experimental data. The strong coupling is currently among the least known parameters of the Standard Model of particle physics,
and plays a central role in the precision physics program at the LHC.