Precision study of mechanical properties of hadronic matter

Full description

DESCRIPTION AND PROBLEMATICS

The experimental and theoretical study of the structure of the nucleon in terms of its elementary components, quarks and gluons, is a research focus at the heart of experimental programs currently being conducted at Jefferson Lab (US) or CERN. This is one of the major justifications for the construction of a future electron-ion collider (EIC) and its Chinese counterpart (EicC). This theme, at the confluence of special relativity and quantum mechanics, benefits from a well-established theoretical framework (Quantum Chromo-Dynamics, QCD), and well-defined experimental perspectives. Generalized parton distributions (GPD) [1] offer special insight on hadrons and nuclei. Two particularly interesting features of GPDs are: (1) they provide a tomographical picture (transverse-section imaging) of hadronic matter; and (2) they encode information on the mechanical properties of the nucleon and nuclei. The latter is a consequence of the intimate connection between moments of GPDs and the energy-momentum tensor carrying information on the mechanics of hadronic matter through its form factors, typically referred to as gravitational form factors (GFFs) [2].

Consequently, GFFs encode information on the internal pressure, shear tensions, linear and angular momentum distributions, radii, energy distribution, etc. The mechanisms behind these emergent properties are still mostly unknown and are actively investigated both theoretically and experimentally. The explored channels for accessing GPDs are known as exclusive processes, where all final-state particles are detected. Due to its large cross section, easy partonic interpretation and experimental feasibility, the exclusive electroproduction of a real photon off a hadron has gained the denomination as “golden” channel for accessing GPDs. This reaction is called Deeply Virtual Compton Scattering (DVCS). Other reactions exist and their understanding in terms of the same GPDs is a crucial property known as universality.

However, because of the complex nature of QCD-bounded systems, no ab-initio computation of GPDs has been performed yet, precluding any understanding of the underlying dynamics generating the structure of hadrons and nuclei. Thus far, exclusive processes have been mainly analyzed at the lowest order approximation, which limits the access to the hadronic properties and structure. Theoretical works including different types of corrections exist and have proven that a rich information is hidden under those, in particular under the so-called kinematic twists. These account for the recoil and mass of the target and provide an indirect but straightforward experimental access to the aforementioned mechanics of nucleons and nuclei encoded in the GFF.

DESCRIPTION TEAM/LABORATORY/ADVISING

The candidate will be hosted by the Nuclear Physics Division (DPhN) at the Institute of Research into the Fundamental Laws of the Universe (Irfu), in the Nucleon Structure Laboratory (LSN). The LSN is made of two experimental teams respectively based at Jefferson Lab and at CERN, and of a theory and phenomenology team, which will host the candidate. The candidate will have the opportunity to contribute to all aspects of the activity of its hosting team. This laboratory with experimental and theoretical activities is de facto the ideal place for the theoretical and phenomenological studies proposed here thanks to the proximity of these two communities.

PROPOSED WORK

The internee will focus on the leading contribution to the DVCS amplitude. Using the dispersion relation between the real and imaginary part of the amplitude, he or she will improve the process description in terms of the GFF. More precisely, the candidate will implement kinematic twist-6 corrections to the dispersion relation (DR) that ties the real and imaginary components of the DVCS amplitude to a constant given in terms of a linear combination of GFFs.

Due to its roots to the analytic properties of the scattering amplitude, the DR constitutes an ab initio tool for accessing GFFs from directly measurable quantities such as the amplitude. In this way, the DR makes it possible to extract the mechanical properties of hadrons and nuclei bypassing the modeling of the underlying partonic distributions, which typically introduce systematic uncertainties that are very difficult to estimate.

The candidate will follow the procedure developed in [3–5] where twist-4 corrections were already implemented in the dispersion relation. The result is that the term coming from the mass of the target dominate the one coming from the recoil, in a way that looks unsustainable when looking at nuclei rather than light mesons and nucleons. Studying the next correction is thus mandatory in order to conclude whether the target mass dependence of the dispersion relation stabilises, so that one can think of extracting the GFF of nuclei.

In that prospect, the goals of the work carried out by the internee are:
1) Extraction of the twist-6 component of the amplitude from earlier works on spin-
0 and spin-1/2 targets [6, 7].
2) Assessment of the “stability” of the mass corrections in the DR by completing its
previous twist-4 study of Ref. [4, 5] with the inclusion of twist-6 terms.
Note that this work is mostly theoretical, with a strong mathematical component (real and complex analysis).

TRAINING AND REQUISITE SKILLS

Basic knowledge of quantum field theory and phenomenology of elementary particle physics is required. A strong background in mathematics, mostly real and complex analysis is also required.
Lectures on QCD is a strong plus, due to the large theoretical part of the program. Previous experience of object-oriented programming, ideally in C++, would be an advantage when using existing computing tools.

ACQUIRED KNOWLEDGE AND SKILLS

Quantum mechanics. Special relativity. Quantum field theory. Numerical analysis. Detailed comparisons to experimental data. Ab initio and beyond leading power calculations (precision physics). Description of complex systems. Skills for synthesis. Team work.

COLLABORATIONS/PARTNERSHIPS

The candidate will interact with several regional actors, from CPhT at Ecole Polytechnique to IJCLab in University Paris-Saclay.

CONTACTS
Scientific : Cédric Mezrag

REFERENCES

[1] M. Diehl et al., Nucl. Phys. B 596 (2001), arxiv:hep-ph/0009255

[2] X. Ji et al., Nucl. Phys. B 652 (2003) arxiv:hep-ph/0210430.

[3] H. Dutrieux et al., Eur. Phys. J. C (2025) 85:105.

[4] V. Martinez-Fernandez and C. Mezrag, arXiv:2509.05059 (hep-ph).

[5] V. Martinez-Fernandez et al., arXiv:2509.06669 (hep-ph).

[6] V. M. Braun et al., JHEP 01 (2023) 078.

[7] V. M. Braun et al., Phys.Rev.D 111 (2025) 7, 076011.

Location

Saclay

Internship conditions

• Internship duration: 4 months
• Level of study: Bac+4/5
• Training: Master 1
• Continuation in PhD thesis: No
• Application deadline: 1 mars 2026

Useful methods and technics:
Dispersion relation, complex and real analysis

Computer languages and software:
C++

Supervisor

MEZRAG Cédric
Phone: +33 1 69 08 87 19
Email :

Head of the laboratory DPhN / LSN

Francesco Bossu
Phone: