Thesis

Lattice Study of Fundamental QCD Vertices

• Call:

  IDPASC Portugal - PHD Programme 2015

• Academic Year:

  2015 / 2016

• Domain:

  Theoretical Particle Physics

• Supervisor:

  Paulo Silva

• Co-Supervisor:

  Orlando Oliveira

• Institution:

  Universidade de Coimbra

• Host Institution:

  CFisUC

• Abstract:

  Quantum Chromodynamics (QCD) describes the interactions between quarks and gluons. At the lagrangian level, gluons are massless and the light up, down and strange quarks have masses of the order of a few MeV or about 100 MeV. However, their interaction generates a momentum dependent mass, the so-called running mass, which can be of the order 500 MeV for the gluon [1] and about 300 MeV for the lighter quarks [2]. The generation of a running mass lies clearly outside the perturbative solution of QCD and has an enormous impact on the total mass of the Universe. Indeed, it is this non-perturbative mass generation that is responsible for almost the entire mass of the Universe. The mechanism of mass generation, namely chiral symmetry breaking for the quarks, is related to the problem of confinement, i.e. why quarks and gluons are not observed as free particles. The confinement mechanism together with the chiral symmetry breaking are two of the major and fundamental problems of strong interaction physics. In a Quantum Field Theory, such as QCD, the dynamics of the interaction is encoded in the so-called Green’s functions of the theory. Although we have now a satisfactory description of two-point functions like gluon, ghost and quark propagators (see, for example, [3] and references therein), this is not the case for higher order vertices. For example, the quark-gluon vertex plays a major role in the computation of hadronic spectra, on the computation of strong decay rates, it defines the running strong coupling and so forth [4]. Another example is the four gluon Green's function. It requires the computation of a vacuum expectation value of gluon fields and it resumes the information on the glueball spectra, the hadronic states with no valence quark content, on the running coupling constant, etc [5]. In this project one aims to achieve a better understanding of the fundamental QCD Green’s functions relying on non-perturbative methods. Lattice QCD is one of the most successful approaches to investigate the non-perturbative regime of QCD [6]. The discretisation of the continuum space-time into a four dimensional lattice, together with the imaginary time formalism, allows for numerical simulations in a computer. The continuum approaches rely on the use of Dyson-Schwinger, Bethe-Salpeter or Faddeev equations. In this project we will use mainly the lattice formulation of QCD to investigate some of its fundamental vertices. The project will profit from the new supercomputer facilities currently under installation at the University of Coimbra [7] and computer time through PRACE projects [8]. Moreover, the project will be developed under PTQCD Lattice collaboration [9]. The first task is to extract the form factors associated with three and four gluon vertices. Although the three gluon vertex has already been partially studied using lattice methods for the SU(2) group [10], a more detailed investigation of its various form factors remain to be done. The three gluon vertex is important for phenomenological applications [11]. On the other hand, the four gluon vertex was less studied using continuum methods and has never been computed on the lattice. Lattice simulations do not allow access to the full quark-gluon vertex. In order to access all of its components, different non-perturbative methods have to be combined. We aim to extend the work [2] and use inputs from lattice simulations with the Dyson-Schwinger equations to improve our knowledge of the quark-gluon vertex. A good description of all these vertices will allow a first principles determination of the running coupling constant and, hopefully, will give further information about the nature of the confinement and the chiral symmetry breaking mechanisms. References: [1] O. Oliveira, P. Bicudo, J. Phys. G38, 045003 (2011) [2] See E. Rojas, J. P. B. C. de Melo, B. El-Bennich, O. Oliveira, T. Frederico, JHEP 10, 193 (2013) and references therein. [3] O. Oliveira, P. J. Silva, Phys. Rev. D86 (2012) 114513 [4] W. J. Marciano, H. Pagels, Phys. Rept. 36, 137 (1978) [5] C. Kellermann, C. S. Fischer, Phys. Rev. D78, 025015 (2008) [6] C. Gattringer, C. Lang, Quantum Chromodynamics on the Lattice: An Introductory Presentation (Lecture Notes in Physics), Springer, 2010 [7] http://www.uc.pt/lca/ClusterResources/Navigator [8] See http://www.prace-ri.eu for a description of PRACE. [9] http://nemea.ist.utl.pt/~ptqcd/ [10] A. Cucchieri, A. Maas, T. Mendes, Phys. Rev D77, 094510 (2008) ; B. Alles, D. S. Henty, H. Panagopoulos, C. Parrinello, C. Pittori, D. G. Richards, Nucl. Phys. B502, 329 (1997). [11] See e.g. G. Eichmann, R. Willians, R. Alkofer, M. Vujinovic, Phys. Rev. D89, 105014 (2014) and references therein.