Explicit Cancellation Research Articles

Approximately diabatic states: A relation between effective Hamiltonian techniques and explicit cancellation of the derivative coupling

The identification of specific electronic structures that do not interchange with varying geometry is related to the problem of finding a set of approximately diabatic states. We propose a new transformation to identify such structures from one nuclear configuration to another one. This transformation, used in previously proposed schemes to construct nearly diabatic states, improves the efficiency of these procedures which can be related to the methods minimizing explicitly the nonadiabatic coupling.

Divergence cancellations to full two-loop order in the effective potential of a gauge theory spontaneously broken in the tree-approximation

We demonstrate the explicit cancellation to full two-loop order of all non-counterterm-absorbable divergences within the effective potential of an abelian gauge theory spontaneously broken in the tree-approximation. The inclusion of surface terms, associated with shifts in the variable of integration within more-than-logarithmically divergent integrals, is shown to lead to additional divergences which are shown to be removable by a shift in an (arbitrary) renormalization-mass parameter.

Relating hard QCD processes through universality of mass singularities (II)

Extending previous techniques we obtain at all orders the factorization of mass singularities for every hard QCD process. These appear in a universal factor that can be reabsorbed into the standard parton density. Thus suitable ratios of cross sections can be computed by a perturbative expansion in the running coupling constant. Moreover, at the leading log level we obtain, after explicit cancellation of infrared divergences, the scaling violation of the operator product expansion.

Current algebra formulation of radiative corrections in gauge theories and the universality of the weak interactions

A current algebra formulation of the radiative corrections in gauge theories, with special applications to the analysis of the universality of the weak interactions, is developed in the framework of quantum chromodynamics. For definiteness, we work in the SU(2)\ifmmode\times\else\texttimes\fi{}U(1) model with four quark flavors, but the methods are quite general and can be applied to other theories. The explicit cancellation of ultraviolet divergences for arbitrary semileptonic processes is achieved relying solely on the Ward identities and general considerations, both in the $W$ and Higgs sectors. The finite parts of order ${G}_{F}\ensuremath{\alpha}$ are then evaluated in the case of the superallowed Fermi transitions, including small effects proportional to ${g}_{s}^{\ensuremath{-}2}({\ensuremath{\kappa}}^{2})$, which are induced by the strong interactions in the asymptotic domain. We consider here both the simplest version of the Weinberg-Salam model in which the Higgs scalars transform as a single isospinor, as well as the case of general symmetry breaking. Except for the small effects proportional to ${g}_{s}^{\ensuremath{-}2}({\ensuremath{\kappa}}^{2})$, the results are identical to the answers previously found on the basis of heuristic arguments. The phenomenological verification of Cabibbo universality on the basis of these corrections and the superallowed Fermi transitions has been discussed before and found to be in very good agreement with present experimental evidence. The analogous calculation for the transition rate of pion $\ensuremath{\beta}$ decay is given. Theoretical alternatives to quantum chromodynamics as a framework for the evaluation of the radiative corrections are briefly discussed. The appendixes contain a generalization of an important result in the theory of radiative corrections due to L. S. Brown, G. Preparata, and W. I. Weisberger, an analysis of the hadronic contributions to the $W$ and $\ensuremath{\varphi}$ propagators, mathematical methods for evaluating the ${g}_{s}^{\ensuremath{-}2}({\ensuremath{\kappa}}^{2})$ corrections, and discussions of quark mass renormalization and the absence of operator seagulls in the hadronic correlation functions. Some of the methods discussed in this paper can also be applied to the study of radiative corrections of order ${G}_{F}\ensuremath{\alpha}$ to other processes affected by the strong interactions.

Argand loops in the Lee model

We study with the help of Argand diagrams the elastic amplitudes in the scalar Lee model in order to determine the relative importance of inelastic thresholds and the Peierls (P) singularity. An input Nθ resonance, constructed separately by either the choice of the cut-off function or by a CDD pole, leads to non-resonant loops in the Argand diagram of the elastic Vθ amplitude which are associated with the N ∗θ threshold. The P-mechanism works neither in the non-CDD case because the Nθ resonance is necessarily too large, nor in the CDD case because of an explicit cancellation. The low-energy part of the Vθ spectrum, in the absence of input resonances, is characterized by simultaneous Vθ boundstates and anti-resonances. The absence of low-energy Vθ resonances, in the non-CDD case, is connected to the cusp in the elastic Nθ denominator at the Nθ threshold.