The quark-ghost scattering kernel at one-loop dressed approximation

• Grant number: 11/02883-1
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2011
• End date: August 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Arlene Cristina Aguilar
• Grantee: Jeyner Castro Cardona
• Host Institution: Centro de Ciências Naturais e Humanas (CCNH). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

The basic building blocks of QCD are the Green's functions of the fundamental physical degrees of freedom, gluons andquarks, and of the unphysical ghosts. Even though it is well-known that these quantities are not physical, since they depend on thegauge-fixing scheme and parameters used to quantize the theory, it is widely believed that QCD Green's functions encode crucial information about the infrared dynamics of the theory. One of the most important Green's functions for the QCD infrared dynamics is the non-abelian quark-gluon vertex, which plays a central role in various non-perturbative phenomena. The fully-dressed quark-gluon vertex is not obtained from the corresponding dynamical equation, but is rather expressed in terms of the quark propagator, such that its Slavnov-Taylor identity is automatically satisfied. The Slavnov-Taylor identity itself contains explicit reference to both the ghost dressing function and the so-called quark-ghost scattering kernel'. This latter quantity satisfies its own, largely unexplored, dynamical equation, which may be decomposed into individual integral equations for itsfour form factors. In this project, we will determine the form factor of the quark-ghost scattering kernel using the "one-loop dressed'' approximation for a general kinematic configuration. To the best of our knowledge, this study constitutes a novel result, and it will open a window of oportunity to make progress on the construction of a non-abelian Ansatz for the fully-dressed quark-gluon vertex. (AU)