International Journal of Modern Physics A

After the first observations of W bosons in leptonic interactions, about 4000 WW candidate events per experiment have been collected at LEP2. This data allows the measurement of the WW production cross section at different center-of-mass energies, as well as W decay branching fractions. The W hadronic branching fraction can be converted into a test of the unitarity of the CKM matrix, or into an indirect determination of the matrix element |V_cs|. A more direct measurement coming from charm tagging is also performed. The W mass has been measured via the cross section (in the threshold region) and the direct reconstruction of the W decay products, using different techniques to account for the distortions due to experimental effects. The main systematic error to the mass reconstruction in the fully hadronic channel comes from QCD effects like Color reconnections and Bose–Einstein correlations, extensively studied in WW events. In e⁺e^- collisions W pairs can be produced in s-channel via a three-vector boson vertex, so a direct study of the trilinear gauge boson couplings is possible. Modification of WW cross section and distributions of W production and decay angles would be an indication of nonstandard couplings, thus a first hint for the presence of new physics.

We calculate the U(1) continuum gauge coupling using the values of action parameters coinciding with the multiple point. This is a point in the phase diagram of a lattice gauge theory where a maximum number of phases convene. We obtain for the running inverse fine structure constant the values and at the Planck scale and the M_Z scale, respectively. The gauge group underlying the phase diagram in which we seek multiple point parameters is what we call the Anti-grand-unified theory (AGUT) gauge group SMG³, which is the Cartesian product of three Standard Model Groups (SMG's). There is one SMG factor for each of the N_gen=3 generations of quarks and leptons. In our model, this gauge group SMG³ is the predecessor of the usual SMG. The latter arises as the diagonal subgroup surviving the Planck scale breakdown of SMG³. This breakdown leads to a weakening of the U(1) coupling by a N_gen-related factor. For N_gen=3, this factor would be N_gen(N_gen+1)/2=6 if phase transitions between all the phases convening at the multiple point were purely second order. The factor N_gen(N_gen+1)/2=6 corresponds to the six gauge-invariant combinations of the N_gen=3 different U(1)'s that give action contributions that are second order in F_μν. The factor analogous to this N_gen(N_gen+1)/2=6 in the case of the earlier considered non-Abelian couplings reduced to the factor N_gen=3 because action terms quadratic in F_μν that arise as contributions from two different of the N_gen=3 SMG factors of SMG³ are forbidden by the requirement of gauge symmetry.

Actually we seek the multiple point in the phase diagram of the gauge group U(1)³ as a simplifying approximation to the desired gauge group SMG³. The most important correction obtained from using multiple point parameter values (in a multiparameter phase diagram instead of the single critical parameter value obtained, say, in the one-dimensional phase diagram of a Wilson action) comes from the effect of including the influence of also having at this point phases confined solely w.r.t. discrete subgroups. In particular, what matters is that the degree of first-orderness is taken into account in making the transition from these latter phases at the multiple point to the totally Coulomb-like phase. This gives rise to a discontinuity Δγ_eff in an effective parameter γ_eff. Using our calculated value of the quantity Δγ_eff, we calculate the above-mentioned weakening factor to be more like 6.5 instead of the N_gen(N_gen+1)/2=6, as would be the case if all multiple point transitions were purely second order. Using this same Δγ_eff, we also calculate the continuum U(1) coupling corresponding to the multiple point of a single U(1). The product of this latter and the weakening factor of about 6.5 yields our Planck scale prediction for the continuum U(1) gauge coupling, i.e. the multiple point critical coupling of the diagonal subgroup of U(1)³∈SMG³. Combining this with the results of earlier work on the non-Abelian gauge couplings leads to our prediction of α^-1-137 ± 9 as the value for the fine structure constant at low energies.

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed.

This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations.

These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.⁹

We show for the case of interacting massless vector bosons, how the structure of Yang–Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-Abelian gauge theory is necessarily of Yang–Mills type plus divergence- and coboundary-couplings. The extension of the method to massive gauge theories is briefly discussed.