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| Author(s): |
Cleiton de Oliveira Ambrosio
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Física Gleb Wataghin |
| Defense date: | 2021-06-16 |
| Examining board members: |
Arlene Cristina Aguilar;
Adriano Antonio Natale;
Donato Giorgio Torrieri
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| Advisor: | Arlene Cristina Aguilar |
| Abstract | |
In this work, we present a detailed study of the Schwinger-Dyson equation, which governs the dynamical evolution of the nonperturbative behavior of the ghost-gluon vertex in the Landau gauge. In particular, we focus on the determination of its classical form factor, B1. We derive the integral equation for this form factor in the so-called "one-loop dressed" approximation. In this work, we consider two distinct scenarios: in the first one, we derive the equation for the ghost-gluon vertex form factor in general kinematics. In this case, instead of considering the fourteen possible tensorial structures of the nonperturbative three-gluon vertex, we keep only the three tree-level tensorial structures. Nonetheless, these tensorial structures are dressed with Ansätze, whose functional form is based on the non-Abelian Ball-Chiu construction. In the second approach, we derive the equation describing the ghost-gluon vertex in the so-called soft-gluon configuration. We show that in this limit, where the gluon momentum vanishes, the Schwinger-Dyson equation for the ghost-gluon vertex is greatly simplified, and the form factor B1 can be accurately determined. The main simplification occurs in the nonperturbative structure of the three-gluon vertex. More specifically, we show that only a special projection of the three-gluon vertex, which can be obtained from the simulations on the lattice, contributes to this equation in this kinematic limit. We solve the Schwinger-Dyson equation for the ghost-gluon vertex in the soft-gluon limit numerically, using as external inputs for the gluon propagator, ghost dressing and the projection of the three-gluon vertex the data obtained from the lattice QCD simulations. Finally, we employ our numerical results to set up two combinations that are invariants under the renormalization group, which correspond to the effective running couplings defined from the three-gluon and ghost-gluon vertices (AU) | |
| FAPESP's process: | 19/05656-8 - Gluon-ghost vertex and kernel in the Background Field Method |
| Grantee: | Cleiton de Oliveira Ambrósio |
| Support Opportunities: | Scholarships in Brazil - Master |