Generalized parton distributions of the pionmodeling, evolution and observable implications

Abstract

Yet the Standard Model of particle physics is so far the most successful theory ever conceived in science, with countless of achievements in the description of Nature; still a number of phenomena remains to be properly understood. A paradigmatic example is confinement. Paving the road towards the understanding of such essential feature thus requires a detailed knowledge of hadrons' inside. The main subject covered in this thesis is precisely the study of hadron structure. Nonetheless this is a really broad field. We thus set sights on an exemplary case: The pions. As mesons, they are potentially simpler to describe that other hadrons like the proton. At the same time, as the pseudo Nambu-Goldstone modes associated to the dynamical breakdown of chiral symmetry, its description is of uttermost relevance for the comprehension of the origin of mass in Nature. We thus address the problem of assessing pions' structure, from first principles up to its observable manifestations. This work is thus divided into two parts: First, the issue of a formal description of hadron's structure is addressed. Relying on the role played by Compton scattering as an essential window into hadrons' inside, we review its formal treatment as understood in the generalized Bjorken limit, leading to the introduction of generalized parton distributions (GPDs). Those parametrize the amplitudes for deeply virtual Compton scattering (DVCS) on hadrons to take place, yielding a unique source of information about the way hadrons are built up from elementary constituents. In the second chapter of this dissertation we review the formal definition and primary properties of generalized parton distributions, together with the main strategies allowing for their evaluation. We identify two essential attributes to be fulfilled: Positivity and polynomiality; a task which, regardless, conventional approaches fail to accomplish. In the third chapter of this thesis we face the problem of obtaining models for pion GPDs which fulfill, by construction, these two features. Following an approach to the description of bound-state systems in quantum field theory based on continuum Schwinger methods, we find the hypothesis of decoupling between longitudinal and transverse degrees of freedom at the level of parton dynamics to be associated with the dynamical breakdown of chiral symmetry. On that assumption, a novel family of generalized parton distributions within the DGLAP region is derived and showed to exhibit two striking characteristics: They satisfy the positivity constraints, and are built from the sole knowledge of parton distribution functions. From that point on we exploit the covariant extension strategy, allowing us to find the corresponding ERBL GPDs, such that polynomiality is also fulfilled by construction. Armed with models for pion GPDs that are complete, in the sense that they satisfy every necessary property, the second part of this work thus exploits them in the derivation of their observable manifestations, allowing for a practical assessment of pions' structure as well their benchmarking. To this end, the fourth chapter pursues the necessary evaluation of scale-evolution for GPDs through an effective approach which encompasses some non-perturbative aspects of the procedure. The results hint the crucial role played by gluons in building pions' up, their associated distributions being commensurate with those for quarks. We thus round-off this dissertation by exploiting the evolved models to deliver predictions on event-rates and beam-spin asymmetries as they could be measured at forthcoming electron-ion colliders. The results reveal that indeed DVCS on pions is expected to be measurable at future facilities; and reveals that gluons dominate the response of pions subjected to DVCS, identifying a sign inversion in the beam-spin asymmetries as clear signal for pinning-down the regime for gluon dominance.