3-Dimensional Maps of the Spinning Nucleon

Project Information

3DSPIN

Grant agreement ID: 647981

DOI

10.3030/647981

Project closed

EC signature date 25 March 2015

Start date 1 July 2015

End date 31 December 2020

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 509 000,00

EU contribution

€ 1 509 000,00

Coordinated by

UNIVERSITA DEGLI STUDI DI PAVIA
Italy

Periodic Reporting for period 4 - 3DSPIN (3-Dimensional Maps of the Spinning Nucleon)

Reporting period: 2020-01-01 to 2020-12-31

Summary of the context and overall objectives of the project

How does the inside of the proton look like? What generates its spin?

3DSPIN has delivered essential information to answer these questions at the frontier of subnuclear physics.

Nucleons (protons and neutrons) are made of quarks and gluons, collectively called partons, confined inside nucleons by the forces described by Quantum Chromodynamics (QCD). Mapping the inner structure of the nucleon in higher and higher details is an essential step to better understand QCD and confinement. 3DSPIN led the way into a new stage of nucleon mapping, explored the distribution of quarks in full 3D momentum space and obtained unprecedented information.

In the last decades, we have obtained detailed maps of the distribution of quarks and gluons in the nucleon in 1D (as a function of their momentum in a single direction). They are encoded in the well-known Parton Distribution Functions (PDFs). Transverse Momentum Distributions (TMDs) are extensions of standard PDFs: they map the partonic distribution in 3D momentum space. The first goal of the research project was to reconstruct these three-dimensional maps from experimental data, a challenge at the frontiers of hadronic physics. 3DSPIN obtained outstanding results in this direction.

Out of the many questions that we can address using detailed 3D maps of the nucleon, one of the most important is the origin of the spin of the nucleon. Nowadays we know the spins of partons account for only about one-third of the total spin of the nucleon. Parton Orbital Angular Momentum (OAM) is still poorly known and should account for the remaining part. The 3DSPIN project planned to follow an innovative approach to quantify quark angular momentum, through its connections to the parton distribution in the full three-dimensional parton momentum space. This avenue turned out to be more complicated than expected and was partially reformulated.

The situation may be compared to protein studies: one-dimensional mapping corresponds to knowing the sequence of amino acids. It is an extremely important piece of information, but insufficient to understand proteins. The study of their 3D structure literally revolutionized our understanding of protein chemistry. Similarly, 3D partonic imaging can bring exceptional developments in our understanding of the nucleon.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

3DSPIN performed the first extraction of unpolarized Transverse Momentum Distributions (TMDs) from a fit of all available data. We considered in total more than 8000 data points from sharply different experiments (electron-proton and proton-proton collisions, fixed-target and collider experiments). We demonstrated for the first time that the formalism based on TMDs can reasonably describe this multitude of data points. This work inaugurated the age of global TMD extractions. The extracted TMDs describe the distribution of quarks inside the proton in 3-dimensional momentum space.

DSPIN drastically improved the perturbative accuracy of TMD extractions reaching an unprecedented level (N3LL). We published a new extraction, taking into account only a subset of presently available data, but including in particular several new measurements by LHC experimental collaborations. The theory/data agreement was excellent. To achieve this result, we created a platform of software tools for TMD phenomenology, called NangaParbat, which we made available for public use.

The second goal of 3DSPIN was obtaining from TMDs information on quark Orbital Angular Momentum (OAM). Unfortunately, we have not been able to achieve this goal. The main route we wanted to follow (based on the study of the so-called Sivers function), turned out not to be sufficiently motivated, as we demonstrated in a dedicated publication. The study of the Sivers function per se, however, remained a relevant goal of the project and we obtained a state-of-the-art extraction of this function, which necessarily relied on the knowledge of the unpolarized TMDs. This stands as another milestone achievement of the 3DSPIN project and made it possible to reconstruct the distribution of quarks in momentum space for a transversely polarized nucleon.

Apart from these core achievements, 3DSPIN also obtained the following non-exhaustive list of results:
- a series of studies on the transversity parton distribution function, opening the way to a global fit of this quantity;
- a series of studies on the possibility to access gluon unpolarized and polarized TMDs in future experiments, together with a model calculation of gluon TMDs, which are presently essentially unknown.
- a model calculation of pion TMDs based on the AdS/QCD correspondence principle, including the application of TMD evolution on this calculation, together with other results on the pion structure.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

Accurate three-dimensional maps of the inner structure of the nucleon can serve two purposes: on one hand, they can be used as tools to study any high-energy phenomena involving nucleons, make predictions, and possibly lead to the discovery of signs of physics beyond the Standard Model; on the other hand, they allow us to understand the dynamics of partons inside the nucleons and shed light on confinement, one of the deepest questions of subnuclear physics.

As an example of the first purpose, we demonstrated that the precise determination of the mass of the W boson can be affected by errors due to a limited knowledge of the quark transverse momentum (https://inspirehep.net/literature/1681006). 3DSPIN results and tools are also currently used for these kind of purposes in the context of the LHC Electro-Weak precision working group (https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCEW).

As an example of the second purpose, we reconstructed the 3D distribution of quarks inside a polarized proton (https://inspirehep.net/literature/1793441) which can in principle be compared with lattice QCD predictions (see, e.g. https://inspirehep.net/literature/1801417).

3DSPIN aimed at estimating quark angular momenta through the study of TMDs. Even if this goal was not achieved, the study of TMDs is part of a wider endeavor, including the study of collinear parton distributions (PDFs), generalized parton distributions (GPDs), gluon TMDs, and lattice QCD calculations. It is conceivable that, putting together all information obtained in the next twenty years, we will be able to give an unambiguous answer to the question of what generates the spin of the nucleon.

The results of our research influenced the plans for future experimental activities. In the near future: COMPASS II at CERN, and Hall A, B, C at Jefferson Lab. In the longer term: the new Electron-Ion Collider (EIC) in the US, a fixed-target experiment at LHC, an electron-ion collider in China (https://inspirehep.net/literature/1847312) the NICA collider in Russia (https://inspirehep.net/literature/1834232).

On top of strictly technical results, the research project had side effects on educational activities. Six graduate students have been directly involved in the project and had the opportunity to learn research by working on a gratifying project, in a young group with an excellent worldwide reputation. Finally, 3DSPIN consolidated the world-class reputation of the European community working on hadronic physics and make Europe attractive for foreign researchers in this field.

Massive amount of data (from the COMPASS collaboration) used to extract 3D maps of the nucleon