Antiparticle Contribution in the Cross Ladder Diagram for Bethe-Salpeter Equation in the Light-Front

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Light composite Higgs boson from the normalized Bethe-Salpeter equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Mass and width of a composite Higgs boson

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Three-body model of the final state interaction in heavy meson decay

We develop a relativistic three-body model for the final state interaction in D(+) -> K(-) pi(+) pi(+) decay based on the ladder approximation of the Bethe-Salpeter equation. The decay amplitude has the standard two-meson resonant transition matrix modulated by a spectator amplitude that carries a fully interacting three-body contribution and a smooth background term from the partonic amplitude. Our calculations are compared with D decay data.

Scalar bosons in minimal and ultraminimal technicolor: Masses, trilinear couplings, and widths

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .1. THEORETICAL DEVELOPMENT

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three-dimensional scattering integral equations satisfying constraints of relativistic unitarity and convariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, we derive several three-dimensional three-particle scattering equations satisfying constraints of relativistic unitarity and convariance. We relate two of these three-particle equations by a transformation of variables as in the two-particle case. The three-particle equations we derive are very practical and suitable for performing relativistic scattering calculations. (C) 1994 Academic Press, Inc.

Lower bound to the mass of a relativistic three-boson system in the lightcone

The lower bound masses of the ground-state relativistic three-boson system in 1 + 1, 2 + 1 and 3 + 1 spacetime dimensions are obtained. We have considered a reduction of the ladder Bethe-Salpeter equation to the lightfront in a model with renormalized two-body contact interaction. The lower bounds are deduced with the constraint of reality of the two-boson subsystem mass. It is verified that, in some cases, the lower bound approaches the ground-state binding energy. The corresponding non-relativistic limits are also verified.

Relativistic three-body model for final state interaction in D+ → K-π+π+ decay

A challenge in mesonic three-body decays of heavy mesons is to quantify the contribution of re-scattering between the final mesons. D decays have the unique feature that make them a key to light meson spectroscopy, in particular to access the Kn S-wave phase-shifts. We built a relativis-tic three-body model for the final state interaction in D+ → K -π+π+ decay based on the ladder approximation of the Bethe-Salpeter equation projected on the light-front. The decay amplitude is separated in a smooth term, given by the direct partonic decay amplitude, and a three-body fully interacting contribution, that is factorized in the standard two-meson resonant amplitude times a reduced complex amplitude that carries the effect of the three-body rescattering mechanism. The off-shell reduced amplitude is a solution of an inhomogeneous Faddeev type three-dimensional integral equation, that includes only isospin 1/2 K -π+ interaction in the S-wave channel. The elastic K-π+ scattering amplitude is parameterized according to the LASS data[1]. The integral equation is solved numerically and preliminary results are presented and compared to the experimental data from the E791 Collaboration[2, 3] and FOCUS Collaboration[4, 5].

Light front fermion model propagation

In this work we consider the propagation of two fermion fields interacting with each other by the exchange of intermediate scalar bosons in the light front. We obtain the corrections up to fourth order in the coupling constant using hierarchical equations in order to obtain the bound state equation (Bethe - Salpeter equation). © 2013 Chinese Physical Society and IOP Publishing Ltd.

The 125 GeV boson: A composite scalar?

Assuming that the 125 GeV particle observed at the LHC is a composite scalar and responsible for the electroweak gauge symmetry breaking, we consider the possibility that the bound state is generated by a non-Abelian gauge theory with dynamically generated gauge boson masses and a specific chiral symmetry breaking dynamics motivated by confinement. The scalar mass is computed with the use of the Bethe-Salpeter equation and its normalization condition as a function of the SU(N) group and the respective fermionic representation. If the fermions that form the composite state are in the fundamental representation of the SU(N) group, we can generate such a light boson only for one specific number of fermions for each group. We address the uncertainties underlying this result, when considering the strong dynamics in isolation. © 2013 American Physical Society.

Limit on the pion distribution amplitude

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Studies on Wilson loops, correlators and localization in supersymmetric quantum field theories

In this thesis we study at perturbative level correlation functions of Wilson loops (and local operators) and their relations to localization, integrability and other quantities of interest as the cusp anomalous dimension and the Bremsstrahlung function. First of all we consider a general class of 1/8 BPS Wilson loops and chiral primaries in N=4 Super Yang-Mills theory. We perform explicit two-loop computations, for some particular but still rather general configuration, that confirm the elegant results expected from localization procedure. We find notably full consistency with the multi-matrix model averages, obtained from 2D Yang-Mills theory on the sphere, when interacting diagrams do not cancel and contribute non-trivially to the final answer. We also discuss the near BPS expansion of the generalized cusp anomalous dimension with L units of R-charge. Integrability provides an exact solution, obtained by solving a general TBA equation in the appropriate limit: we propose here an alternative method based on supersymmetric localization. The basic idea is to relate the computation to the vacuum expectation value of certain 1/8 BPS Wilson loops with local operator insertions along the contour. Also these observables localize on a two-dimensional gauge theory on S^2, opening the possibility of exact calculations. As a test of our proposal, we reproduce the leading Luscher correction at weak coupling to the generalized cusp anomalous dimension. This result is also checked against a genuine Feynman diagram approach in N=4 super Yang-Mills theory. Finally we study the cusp anomalous dimension in N=6 ABJ(M) theory, identifying a scaling limit in which the ladder diagrams dominate. The resummation is encoded into a Bethe-Salpeter equation that is mapped to a Schroedinger problem, exactly solvable due to the surprising supersymmetry of the effective Hamiltonian. In the ABJ case the solution implies the diagonalization of the U(N) and U(M) building blocks, suggesting the existence of two independent cusp anomalous dimensions and an unexpected exponentation structure for the related Wilson loops.

Quarkonia and heavy-light mesons in a covariant quark model

Preliminary calculations using the Covariant Spectator Theory (CST) employed a scalar linear confining interaction and an additional constant vector potential to compute the mesonic mass spectra. In this work we generalize the confining interaction to include more general structures, in particular a vector and also a pseudoscalar part, as suggested by a recent study. A one-gluon-exchange kernel is also implemented to describe the short-range part of the interaction. We solve the simplest CST approxima- tion to the complete Bethe-Salpeter equation, the one-channel spectator equation, using a numerical technique that eliminates all singularities from the kernel. The parameters of the model are determined through a fit to the experimental pseudoscalar meson spectra, with a good agreement for both quarkonia and heavy-light states.

Excitonic properties of transition metal oxide perovskites and workflow automatization of GW schemes

The Many-Body-Perturbation Theory approach is among the most successful theoretical frameworks for the study of excited state properties. It allows to describe the excitonic interactions, which play a fundamental role in the optical response of insulators and semiconductors. The first part of the thesis focuses on the study of the quasiparticle, optical and excitonic properties of \textit{bulk} Transition Metal Oxide (TMO) perovskites using a G$_0$W$_0$+Bethe Salpeter Equation (BSE) approach. A representative set of 14 compounds has been selected, including 3d, 4d and 5d perovskites. An approximation of the BSE scheme, based on an analytic diagonal expression for the inverse dielectric function, is used to compute the exciton binding energies and is carefully bench-marked against the standard BSE results. In 2019 an important breakthrough has been achieved with the synthesis of ultrathin SrTiO3 films down to the monolayer limit. This allows us to explore how the quasiparticle and optical properties of SrTiO3 evolve from the bulk to the two-dimensional limit. The electronic structure is computed with G0W0 approach: we prove that the inclusion of the off-diagonal self-energy terms is required to avoid non-physical band dispersions. The excitonic properties are investigated beyond the optical limit at finite momenta. Lastly a study of the under pressure optical response of the topological nodal line semimetal ZrSiS is presented, in conjunction with the experimental results from the group of Prof. Dr. Kuntscher of the Augsburg University. The second part of the thesis discusses the implementation of a workflow to automate G$_0$W$_0$ and BSE calculations with the VASP software. The workflow adopts a convergence scheme based on an explicit basis-extrapolation approach [J. Klimeš \textit{et al.}, Phys. Rev.B 90, 075125 (2014)] which allows to reduce the number of intermediate calculations required to reach convergence and to explicit estimate the error associated to the basis-set truncation.