No abstract

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 a \ . . . ,/0*",) is generally not OiMw/E) suppressed.I. Renormalization schemes in the R$ gauge.-Consider the standard model. The Higgs and ghost fields ...

No abstract

Stimulated by both new experimental data and theoretical interest, the properties of the spinsinglet P state ( ' P I ) in the c r and b6 system have been reexamined in the framework of the QCD multipole expansion. We have estimated various rates for producing $4 1 ' P , I and T( 1 ' P I ) in hadronic transitions, and for producing *( 1 ' P I I in pp annihilation. The aa mass spectrum in the transition T"-T( 1 ' P , )aa has been computed, and the two pions peak at low masses. An interesting approximation proposed by Voloshin and Zakharov is explored further in conjunction with the axial anomaly to relate many isospin-violating aO transitions involving ' p I to the known rate of 3'-J/GaO. The rates for *'-*( 1 ' P , )a0 and G( 1 ' P I )-J/*aO are found to be large. The implications are discussed.

We propose two models for a heavy-quark potential with possible natural QCD interpretations. The potentials approach the two-loop perturbative QCD formula at short distance and a linear confining potential at large distance, and their predicted cT and b6 spectra all fit the data very well for Am in the range 100-500 MeV, where MS denotes the modified minimal subtraction scheme. Furthermore, the potentials are described directly in coordinate space with explicit AM, dependence so that they are convenient for practical calculations. Some of their phenomenological predictions are given, especially, in the picture regarding a confining potential as a scalar exchange. The predicted masses of 4 (1 ' P , ) and Y( 1 'P,) are higher than the center-of-gravity values of the 1 'P, states by 0.9-1.8 MeV and 0.40.7 MeV, respectively, for Am in the range 100-200 MeV. PACS numberk): 12.40.Qq, 14.40.J~Because of the nonrelativistic motion of the heavy quark Q and the antiquark g in heavy quarkonium, the interaction between Q and can be well described by a static potential. Phenomenological study of the potential provides a simple link between nonperturbative QCD calculations (for instance, lattice calculation) and the experimental data. Many potential models have been proposed and they can fit the c F and b6 data very well. However,

We formally derive the chiral Lagrangian for low lying pseudoscalar mesons from the first principles of QCD considering the contributions from the normal part of the theory without taking approximation.The derivation is based on the standard generating functional of QCD in the path integral formalism.The gluon-field integration is formally carried out by expressing the result in terms of physical Green's functions of the gluon. To integrate over the quark-field, we introduce a bilocal auxiliary field Φ(x, y) representing the mesons. We then develop a consistent way of extracting the local pseudoscalar degree of freedom U (x) in Φ(x, y) and integrating out the rest degrees of freedom such that the complete pseudoscalar degree of freedom resides in U (x). With certain techniques, we work out the explicit

The hadronic transition 1,!43770)+J/++.rr.rr is studied in the framework of the QCD multipole expansion. The calculated rate compares favorably with the recent result from the Mark I11 Collaboration. We also have compared our theoretical approach with others.