Dynamical relativistic corrections to the leptonic decay width of heavy quarkonia

We calculate the dynamical relativistic corrections, originating from radiative one-gluon-exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of Light-Front Dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J=1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in $\alpha_s$, even in the charmonium sector. This is in contrast with the ongoing belief based on calculations in the non-relativistic limit. Consequences for the ability of several phenomenological potential to describe these decays are drawn.Comment: 17 pages, 7 figure

Non-perturbative renormalization in Light Front Dynamics with Fock space truncation

Within the framework of the Covariant formulation of Light-Front Dynamics, we develop a general non-perturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The explicit dependence of our formalism on the orientation of the light front is essential in order to analyze the structure of the counterterms and bare parameters needed to renormalize the theory. We present here a general strategy to determine the dependence of these quantities on the Fock sectors. We apply our formalism to QED for the two-body (one fermion and one boson) truncation and recover analytically, without any perturbative expansion, the renormalization of the electric charge according to the requirements of the Ward Identity.Comment: 7 pages, 6 figures, to appear in the proceedings of the Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, Cairns, Australia, July 7-15, 200

The pion wave function in covariant light-front dynamics

The structure of the pion wave function in the relativistic constituent quark model is investigated in the explicitly covariant formulation of light-front dynamics. We calculate the two relativistic components of the pion wave function in a simple one-gluon exchange model and investigate various physical observables: decay constant, charge radius, electromagnetic and transition form factors. We discuss the influence of the full relativistic structure of the pion wave function for an overall good description of all these observables, including both low and high momentum scales.Comment: 12 pages, 10 figure

The fine-tuning problem revisited in the light of the Taylor-Lagrange renormalization scheme

We re-analyse the perturbative radiative corrections to the Higgs mass within the Standard Model in the light of the Taylor-Lagrange renormalization scheme. This scheme naturally leads to completely finite corrections, depending on an arbitrary dimensionless scale. This formulation avoids very large individual corrections to the Higgs mass. In other words, it is a confirmation that the so-called fine-tuning problem in the Standard Model is just an artefact of the regularization scheme and should not lead to any physical interpretation in terms of the energy scale at which new physics should show up, nor to the appearance of a new symmetry. We analyse the characteristic physical scales relevant for the description of these radiative corrections.Comment: 8 pages, 2 figure

Taylor-Lagrange renormalization scheme. Application to light-front dynamics

The recently proposed renormalization scheme based on the definition of field operators as operator valued distributions acting on specific test functions is shown to be very convenient in explicit calculations of physical observables within the framework of light-front dynamics. We first recall the main properties of this procedure based on identities relating the test functions to their Taylor remainder of any order expressed in terms of Lagrange's formulae, hence the name given to this scheme. We thus show how it naturally applies to the calculation of state vectors of physical systems in the covariant formulation of light-front dynamics. As an example, we consider the case of the Yukawa model in the simple two-body Fock state truncation.Comment: 18 pages, 6 figures, introduction changed, corrected typos, to be published in Physical Review

Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model

Within the covariant formulation of light-front dynamics, we calculate the state vector of a fermion coupled to identical scalar bosons (the Yukawa model). The state vector is decomposed in Fock sectors and we consider the first three ones: a single fermion, a fermion coupled to one boson, and a fermion coupled to two bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, and these contributions are calculated with no approximations. The divergences of the amplitudes are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we developed. This renormalization scheme is a necessary condition in order to avoid uncancelled divergences when Fock space is truncated. As an example, we present preliminary numerical results for the anomalous magnetic moment of a fermion in the Yukawa model.Comment: 7 pages, 7 figures. Contribution to the proceedings of the Workshop: Light-Cone 2008, "Relativistic Nuclear and Particle Physics", Mulhouse, France, July 7-11, 2008. To be published in the online journal "Proceedings of Science" - Po

Nonperturbative renormalization in light-front dynamics and applications

We present a general framework to calculate the properties of relativistic compound systems from the knowledge of an elementary Hamiltonian. Our framework provides a well-controlled nonperturbative calculational scheme which can be systematically improved. The state vector of a physical system is calculated in light-front dynamics. From the general properties of this form of dynamics, the state vector can be further decomposed in well-defined Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of light-front dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane \omega \cd x=0 defined by a light-like four-vector $\omega$. This enables us to control any violation of rotational invariance due to the truncation of the Fock expansion. We then present a general nonperturbative renormalization scheme in order to avoid field-theoretical divergences which may remain uncancelled due to this truncation. This general framework has been applied to a large variety of models. As a starting point, we consider QED for the two-body Fock space truncation and calculate the anomalous magnetic moment of the electron. We show that it coincides, in this approximation, with the well-known Schwinger term. Then we investigate the properties of a purely scalar system in the three-body approximation, where we highlight the role of antiparticle degrees of freedom. As a non-trivial example of our framework, we calculate the structure of a physical fermion in the Yukawa model, for the three-body Fock space truncation (but still without antifermion contributions). We finally show why our approach is also well-suited to describe effective field theories like chiral perturbation theory in the baryonic sector.Comment: 17 pages, 19 figures "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT*, October 19-23 200

Ab initio nonperturbative calculation of physical observables in light-front dynamics. Application to the Yukawa model

We present a coherent and operational strategy to calculate, in a nonperturbative way, physical observables in light-front dynamics. This strategy is based on the decomposition of the state vector of any compound system in Fock components, and on the covariant formulation of light-front dynamics, together with the so-called Fock sector dependent renormalization scheme. We apply our approach to the calculation of the electromagnetic form factors of a fermion in the Yukawa model, in the nontrivial three-body Fock space truncation, for rather large values of the coupling constant. We find that, once the renormalization conditions are properly taken into account, the form factors do not depend on the regularization scale, when the latter is much larger than the physical masses. We then extend the Fock space by including antifermion degrees of freedom.Comment: 22 pages, 16 figure

Systematic renormalization scheme in light-front dynamics with Fock space truncation

Within the framework of the covariant formulation of light-front dynamics, we develop a general non-perturbative renormalization scheme based on the Fock decomposition of the state vector and its truncation. The counterterms and bare parameters needed to renormalize the theory depend on the Fock sectors. We present a general strategy in order to calculate these quantities, as well as state vectors of physical systems, in a truncated Fock space. The explicit dependence of our formalism on the orientation of the light front plane is essential in order to analyze the structure of the counterterms. We apply our formalism to the two-body (one fermion and one boson) truncation in the Yukawa model and in QED, and to the three-body truncation in a scalar model. In QED, we recover analytically, without any perturbative expansion, the renormalization of the electric charge, according to the requirements of the Ward identity.Comment: 32 pages, 14 figures, submitted in Phys. Rev.