We review the developments of the multipole expansion approach in quantum chromodynamics and its applications to hadronic transitions and some radiative decays of heavy quarkonia. Theoretical predictions are compared with updated experimental results.
A systematic analysis of renormalization schemes and a general proof of the precise formulation of the equivalence theorem are given in the R$ gauge for both the SU(2)z: and the SU(2)xU(l) theories. The precise formula for the modification factor C mo & is obtained, and a convenient particular scheme in which C m od is exactly unity is proposed. C m0 d in other schemes are discussed up to one loop in the heavy Higgs boson limit.PACS numbers: 1 l.lO.Gh, 12.15.Ji Longitudinal weak boson scattering K£K£ -V c L Vi (VI stands for W ± or Z°) is one of the most important processes to be studied at the Superconducting Super Collider and the CERN Large Hadron Collider. The longitudinal component VI arises from "eating" the would-be Goldstone boson <; therefore VIK£-V c L Vl is related to the scattering of Goldstone bosons, which probes the mechanism of electroweak symmetry breaking. It is well known that the relation between the two scattering amplitudes at energy E^>Mw can be described by the equivalence theorem (ET), which stateswhere O denotes other possible physical particles. This simple relation was given by many authors [1] and was claimed to hold to all orders in perturbation theory for any value of the Higgs boson mass m//. Equation (1) is very useful for calculating T(Vl\ . . . ,KL",0) and has thus been widely used [2]. However, Yao and Yuan [3], and Bagger and Schmidt [4], pointed out recently from more careful examination of loop contributions that, in general, there should be a modification factor C for each external Goldstone boson field 0 fl/ , and CV1 beyond the tree level, i.e., (1) should be modified as T(Yi\ . . . , FZ\4>) -C H T(i* a \ . . . ,/> fl ",O) + 0(M^/£).(2) The formula for C to all orders in perturbation theory given in Ref.[3] is rather complicated, and the renormalization prescription they suggested for making C = l relies on the explicit calculation of C, so that it is cumbersome in practical calculation. Since the ET is so useful, it is of special importance to make this issue clearer and simplify the expression for C. In this Letter, we will give a brief account of our recent work [5], including (i) a sys-tematic analysis of the renormalization schemes in the R$ gauge for both the SU(2)jr theory and the SU(2)xTJ(l) electroweak theory, (ii) a general proof of the precise formulation of the ET in which a simple formula for C is obtained, and (iii) a proposal for a particular renormalization scheme in which C is exactly unity and which is easy to implement in practical calculations. The details of this study will be presented in a longer paper [6]. We shall also show results, explicit up to one loop, for the heavy Higgs boson decay H-* W^Wi in some currently used renormalization schemes which are different from our particular scheme, and we shall see that in those schemes C-1 is, in general, not small and the £-dependent part in T(i
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.