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# Light Cone 2018

14-18 May 2018
Jefferson Lab - CEBAF Center
US/Eastern timezone

## Fermion-antifermion phenomenology in Minkowski space

15 May 2018, 15:20
20m
F113 (Jefferson Lab - CEBAF Center)

### Speaker

Mr Jorge Henrique De Alvarenga Nogueira (Instituto Tecnológico de Aeronáutica & 'La Sapienza' Università di Roma & INFN, Sezione di Roma)

### Description

The advent of approaches based on the Euclidean space for studying hadron observables, such as lattice QCD and Schwinger-Dyson equations, has been remarkable and responsible to produce important understanding on the non-perturbative dynamical regime. However, the quantum field theory formulation in Minkowski space has subtle and essential signatures as, e.g., the ones related to the spin degrees of freedom, that require to be evaluated in a theoretical framework developed in the physical space, where the dynamical processes take place. One important tool is the Fock space expansion, which allows one to construct a probabilistic description of hadrons and to explore relativistic effects on the dynamics as, e.g., through the analysis of the electromagnetic (EM) form factors beyond the impulse approximation [1]. In recent years, studies based on actual solutions of the homogeneous Bethe-Salpeter equation directly in Minkowski space have becoming available. This achievement makes feasible to start phenomenological investigations of the hadron structure, shedding light on the intrinsic dynamics that is formally and conceptually connected with the physical space, i.e. the Minkowski one [2,3]. The new framework for solving the Bethe-Salpeter equation has a main ingredient given by the the so-called Nakanishi Integral Representation of the Bethe-Salpeter amplitude that allows one to explicitly deal with its analytic structure, without resorting to the Wick rotation. In order to illustrate the phenomenological potential of the aforementioned framework we explore the $0^-$ quark-antiquark bound state, by the solution of the coupled integral equations. The study is done in the ladder approximation, based on the suppression of the cross-ladder contribution found for bosonic systems [2]. By taking the constituents and exchanged-boson masses from, e.g., lattice calculations, dynamical observables like the light-cone momentum distributions are predicted. The decay constant $f_\pi$ is also computed, as well as the electromagnetic form factors. Such a preliminary investigation of the phenomenology of what we call mock pion will allow to settle the framework where one can develop more and more realistic description in Minkowski space. [1] V. Gigante, J. H. Alvarenga Nogueira, E. Ydrefors, C. Gutierrez, V. A. Karmanov and T. Frederico, Phys. Rev. D 95, 056012 (2017) [2] J. H. Alvarenga Nogueira, Chueng-Ryong Ji, E. Ydrefors and T. Frederico, Phys. Lett. B 777, 207-211 (2018)] [3] W. de Paula, T. Frederico, G. Salmè, M. Viviani, R. Pimentel, %Fermionic bound states in Minkowski space: light-cone singularities and structure, Eur. Phys. J. C 77, 764 (2017)

### Primary author

Mr Jorge Henrique De Alvarenga Nogueira (Instituto Tecnológico de Aeronáutica & 'La Sapienza' Università di Roma & INFN, Sezione di Roma)

### Co-authors

Dr Cédric Mezrag (Argonne National Laboratory) Dr Emanuel Ydrefors (Instituto de Aeronautica) Dr Giovanni Salmè (INFN, Sezione di Roma) Prof. Tobias Frederico (Instituto Tecnologico de Aeronautica) Prof. Wayne De Paula (ITA)

 Slides