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

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.

Relativistic description of electron scattering on the deuteron

Within a quasipotential framework a relativistic analysis is presented of the deuteron current. Assuming that the singularities from the nucleon propagators are important, a so-called equal time approximation of the current is constructed. This is applied to both elastic and inelastic electron scattering. As dynamical model the relativistic one boson exchange model is used. Reasonable agreement is found with a previous relativistic calculation of the elastic electromagnetic form factors of the deuteron. For the unpolarized inelastic electron scattering effects of final state interactions and relativistic corrections to the structure functions are considered in the impulse approximation. Two specific kinematic situations are studied as examples.Comment: (19 pages in revtex + 15 figures not included, available upon request.) report THU-93-10

Nonperturbative calculation of the anomalous magnetic moment in the Yukawa model within truncated Fock space

Within the covariant formulation of light-front dynamics, we calculate the state vector of a physical fermion in the Yukawa model. The state vector is decomposed in Fock sectors and we consider the first three ones: the single constituent fermion, the constituent fermion coupled to one scalar boson, and the constituent fermion coupled to two scalar bosons. This last three-body sector generates nontrivial and nonperturbative contributions to the state vector, which are calculated numerically. Field-theoretical divergences are regularized using Pauli-Villars fermion and boson fields. Physical observables can be unambiguously deduced using a systematic renormalization scheme we have developed previously. As a first application, we consider the anomalous magnetic moment of the physical fermion.Comment: 24 pages, 16 figure

Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics

We show how the recently proposed Taylor-Lagrange renormalization scheme can lead to extensions of singular distributions which are reminiscent of the Pauli-Villars subtraction. However, at variance with the Pauli-Villars regularization scheme, no infinite mass limit is performed in this scheme. As an illustration of this mechanism, we consider the calculation of the self-energy in second order perturbation theory in the Yukawa model, within the covariant formulation of light-front dynamics. We show in particular how rotational invariance is preserved in this scheme.Comment: 9 pages, 1 figure To be published in Physical Review

Nucleon-Nucleon Correlations and Two-Nucleon Currents in Exclusive (e,e′NNe,e'NN) Reactions

The contributions of short-range nucleon-nucleon (NN) correlations, various meson exchange current (MEC) terms and the influence of $\Delta$ isobar excitations (isobaric currents, IC) on exclusive two-nucleon knockout reactions induced by electron scattering are investigated. The nuclear structure functions are evaluated for nuclear matter. Realistic NN interactions derived in the framework of One-Boson-Exchange model are employed to evaluate the effects of correlations and MEC in a consistent way. The correlations correlations are determined by solving the Bethe-Goldstone equation. This yields significant contributions to the structure functions W_L and W_T of the (e,e'pn) and (e,e'pp) reactions. These contributions compete with MEC corrections originating from the $\pi$ and $\rho$ exchange terms of the same interaction. Special attention is paid to the so-called 'super parallel' kinematics at momentum transfers which can be measured e.g. at MAMI in Mainz.Comment: 14 pages, 8 figures include

Student- and school-level belonging and commitment and student smoking, drinking and misbehaviour

Objectives: It has been suggested that students are healthier in schools where more students are committed to school. Previous research has examined this only using a proxy measure of value-added education (a measure of whether school-level attendance and attainment are higher than predicted by students’ social profile), finding associations with smoking tobacco, use of alcohol and illicit drugs, and violence. These findings do not provide direct insights into the associations between school-level aggregate student commitment and health behaviours, and may simply reflect the proxy measure being residually confounded by unmeasured student characteristics. We examined the previously used proxy measure of value-added education, as well as direct measures at the level of the school and the student of lack of student commitment to school to see whether these were associated with students’ self-reported smoking tobacco, alcohol use and school misbehaviour. Design: Cross-sectional survey. Setting: A total of 40 schools in south-east England. Methods: Multi-level analyses. Results: There were associations between school- and student-level measures of lack of commitment to school and tobacco smoking, alcohol use and school misbehaviour outcomes, but the proxy measure of school-level commitment, value-added education, was not associated with these outcomes. A sensitivity analysis focused only on violent aspects of school misbehaviour found a pattern of associations identical to that found for the measure of misbehaviour. Conclusion: Our study provides the first direct evidence in support of the Theory of Human Functioning and School Organisation

Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model

We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. Self-energy and vertex corrections are included approximately in a consistent way as well as crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. In a path integral description of an appropriate current-current correlator an effective, retarded action is obtained by integrating out the meson field. As in the polaron problem we employ a quadratic trial action with variational functions to describe retardation and binding effects through multiple meson exchange.The variational equations for these functions are derived, discussed qualitatively and solved numerically. We compare our results with the ones from traditional approaches based on the Bethe-Salpeter equation and find an enhanced binding contrary to some claims in the literature. For weak coupling this is worked out analytically and compared with results from effective field theories. However, the well-known instability of the model, which usually is ignored, now appears at smaller coupling constants than in the one-body case and even when self-energy and vertex corrections are turned off. This induced instability is investigated analytically and the width of the bound state above the critical coupling is estimated.Comment: 62 pages, 7 figures, FBS style, published versio

Quasi-Elastic Scattering in the Inclusive (3^3He, t) Reaction

The triton energy spectra of the charge-exchange $^{12}$C($^3$He,t) reaction at 2 GeV beam energy are analyzed in the quasi-elastic nucleon knock-out region. Considering that this region is mainly populated by the charge-exchange of a proton in $^3$He with a neutron in the target nucleus and the final proton going in the continuum, the cross-sections are written in the distorted-wave impulse approximation. The t-matrix for the elementary exchange process is constructed in the DWBA, using one pion- plus rho-exchange potential for the spin-isospin nucleon- nucleon potential. This t-matrix reproduces the experimental data on the elementary pn $\rightarrow$np process. The calculated cross-sections for the $^{12}$C($^3$He,t) reaction at $2^o$ to $7^o$ triton emission angle are compared with the corresponding experimental data, and are found in reasonable overall accord.Comment: 19 pages, latex, 11 postscript figures available at [email protected], submitted to Phy.Rev.