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High Precision PDFs for the precision Era at the Large Hadron Collider

Periodic Reporting for period 1 - HiPPiE_at_LHC (High Precision PDFs for the precision Era at the Large Hadron Collider)

Reporting period: 2017-11-01 to 2019-10-31

Research in fundamental science is driven by the curiosity of humans, to understand the Universe we live in.
Despite the absence of an applicative goal, history has shown that when science progresses, society also progresses.
An impressive example of all this is CERN, and its current experiments at the Large Hadron Collider (LHC).
The technological advancements achieved at CERN have application on our everyday life (from new materials to the world wide web).
But this progress is motivated by a single reason: discovering the unknown.
LHC looks for new particles beyond the ones that we already know, because we have clear indirect indications that something else must exist.
The way it does so is by colliding protons, to focus high energies in a point, thus being able to produce many particles, potentially including new unknown ones.
Protons are, however, composite objects, so the description of their interactions requires the knowledge of their internal structure.
The HiPPiE@LHC project has the goal of understanding the structure of protons to a higher level of precision, to be able to improve the discovery power of the LHC.
This goal is achieved by improving the theoretical description of the fundamental interactions taking place when protons collide, in order to be able to determine with greater precision the information on their structure by comparing theory with experimental data.
Our current understanding of elementary particle dynamics relies on Quantum Field Theory, an approach that combines quantum mechanics with the theory of special relativity. Quantum Field Theories are very complicated, and obtaining theoretical predictions for physical processes from the definition of the theory itself is an open challenge. Thus, in practice, we use a tool, called perturbation theory, to compute physical observables in an approximate way. This way is systematically improvable by including more and more orders in the perturbative expansion; however, computations at high orders become increasingly complicated, and thus unaccessible beyond some point.
The work performed in this project faces with this problem from two complementary directions.
- On the one hand, it overcomes the computational difficulties by using techniques to resum to all orders the perturbative expansion in certain kinematic limits. This approach is still approximate, but it can capture the bulk of higher order corrections, thus improving significantly the quality of the prediction. In this project a particular kinematic regime has been considered, the so-called high-energy limit, and state-of-the-art all-order theoretical predictions have been computed. In this regime these contributions have a sizeable effect, and allowed us to obtain a significantly better knowledge of the structure of the proton.
- On the other hand, this project proposes a novel way to quantify the uncertainty induced by our approximate knowledge, by constructing a statistical model to estimate unknown higher orders from the known ones.
Among the results of this project a very interesting one is the impact of the resummation of the aforementioned contributions in the prediction of the production rate of a Higgs boson at a proton-proton collider. At the energy of LHC, the impact of this resummation is mild, but for higher collider energies, such as those planned for a Future Circular Collider at CERN, the effect reaches up to 10%. This result is impressive, as the (indirect) discovery power of such machines requires accuracies at or below the percent level. This important achievement shows the need for considering such high order contributions and opens up a new phase of precision at colliders, with many potential future developments.

The outcome of the project includes 7 published papers, 3 conference proceedings, 5 working group reports. The dissemination has been performed also through the participation with oral contribution to 8 international conferences and workshops.
This project has introduced a novel and general approach, based on Bayesian statistics, to infer information on the unknown all-order sum of a perturbative expansion given the knowledge of the first few orders. The performance and reliability of this approach exceeds any previous method to estimate the uncertainty on theoretical predictions, and it has applications even beyond Quantum Field Theory, as the perturbative approach is a widely used technique in many branches of physics. This result has the potential of dramatically improve the reliability of any physics analysis.
In the specific context of high-energy physics, the progress made on the study of the high-energy resummation has demonstrated its importance for precision phenomenology at LHC and future colliders. Thus, it will become a fundamental ingredient in future theoretical predictions, and it will stimulate additional work towards the improvement of its accuracy.
Impact of small-x resummation on the Higgs cross section