Master Thesis defense by Dídac Roca Mandri

Title: Exploring Analytical Approaches to Data-Driven Reconstruction of the Nucleon Form Factors in the Time-Like Domain

Abstract:

Hadron colliders are essential tools in particle physics. Notable examples include the Large Hadron Collider at CERN, whose aim is to validate the Standard Model of particle physics and potentially identify deviations from established particle physics laws. Such deviations become apparent through mismatches between theoretical predictions and experimental data.

These predictions are particularly challenging for hadron colliders where the theory of strong interaction, known as quantum chromodynamics (QCD), operates mainly in a non-perturbative regime. A key analytic method to describe strong interactions involves the concept of form factors - phenomenologically determined matrix elements of the quark current between various hadron states. Form factors (FFs) differ depending on the type of current (electromagnetic or weak) and the transferred momentum, q2, exhibiting distinct behavious in time-like (q^2 > 0) and space-like (q^2 < 0) domains. Although electromagnetic FFs are well-measured in the space-like domain, their behaviour in the time-like domain remains poorly understood.

This study aims to use analytical and physical properties of FFs as functions of q2 to extrapolate them from the space-like to the time-like domains. We explore the current state of nucleon form factor data employing Padé approximants within the extended vector meson dominance model (eVMD). We apply physically motivated constraints to the Padés to explore the limitations of the current description and data. Initially, we focus on linear Padés to replicate previous works, then expand to include complex coefficients to better capture the physical resonances predicted by eVMD.

At the final step we introduce quadratic Padés, which incorporate energy-dependent decay width, to assess their effectiveness compared to linear models. Our findings highlight the sensitivity of FFs to modelling approaches and the importance of data quality in constraining theoretical frameworks. The analysis suggests that quadratic Padés may more accurately represent the high-energy behaviour of FFs, providing deeper insights into the underlying dynamics of nucleon structure. Overall, this research emphasizes the adaptability of Padé approximants in nuclear physics and the delicate balance between model complexity and data accuracy.