The Ward Identities of the Gauge Invariant Three Boson Vertices

We outline the pinch technique for constructing gauge invariant Green's functions in gauge theories and derive the Ward identities that must be satisfied by the gauge invariant three boson vertices of the standard model. They are generalizations of their tree level Ward identities and are shown to be crucial for the delicate gauge cancellations of the S-matrix.Comment: 6 pages Latex, uses revtex[aps,aipbook,floats]. To appear in the proceedings of the International Symposium on Vector Boson Self Interactions, Feb. 1-3, 1995 UCLA, Los Angeles, California US

The dual gauge fixing property of the S matrix

The $S$-matrix is known to be independent of the gauge fixing parameter to all orders in perturbation theory. In this paper by employing the pinch technique we prove at one loop a stronger version of this independence. In particular we show that one can use a gauge fixing parameter for the gauge bosons inside quantum loops which is different from that used for the bosons outside loops, and the $S$-matrix is independent from both. Possible phenomenological applications of this result are briefly discussed.Comment: 17 pages, Late

A method for determining anomalous gauge boson couplings from e^{+}e^{-} experiments

We present a model-independent method for determining anomalous gauge boson couplings from ongoing and future e^{+}e^{-} -> W^{+} W^{-} experiments. First we generalize an already existing method, which relies on the study of four observables constructed through appropriate projections of the unpolarized differential cross-section. In particular, we retain both linear and quadratic terms in the unknown couplings, and compute contributions to these observables originating from anomalous couplings which do not separately conserve the discrete C, P, and T symmetries. Second, we combine the above set of observables with three additional ones, which can be experimentally obtained from the total cross-sections for polarized final state W bosons. The resulting set of seven observables may provide useful information for constraining, and in some cases for fully determining, various of the possible anomalous gauge boson couplings.Comment: 15 pages, Latex, 1 Figure, uses axodra

A set of sum rules for anomalous gauge boson couplings

The dependence of the differential cross-section for on-shell W-pair production on the anomalous trilinear gauge couplings invariant under C and P is examined. It is shown that the contributions of the anomalous magnetic moments of the W boson due to the photon and the Z can be individually projected out by means of two appropriately constructed polynomials. The remaining four anomalous couplings are shown to satisfy a set of model-independent sum rules. Specific models which predict special relations among the anomalous couplings are then studied; in particular, the composite model of Brodsky and Hiller, and the linear and non-linear effective Lagrangian approaches. The relations predicted by these models, when combined with the aforementioned sum rules, give rise to definite predictions, particular to each model. These predictions can be used, at least in principle, in order to exclude or constrain such models.Comment: 19 pages, 2 figures, uses axodraw.st

Consistency Condition for the Pinch Technique Self-Energies at Two Loops

A simple and testable necessary condition for the gauge independence of the Pinch Technique self-energies at two loops is discussed. It is then shown that, in the case of the $Z$ and $W$ self-energies, the condition is indeed satisfied by the Papavassiliou-Pilaftsis formulation.Comment: 7 pages, Latex, 1 PostScript figur

The heavy quark decomposition of the S-matrix and its relation to the pinch technique

We propose a decomposition of the S-matrix into individually gauge invariant sub-amplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompsition is obtained by considering limits of the S-matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic $n$-point functions is briefly discussed.Comment: 11 uuencoded pages, NYU-TH-94/10/0

Application of the Pinch Technique to Neutral Current Amplitudes and the Concept of the Z Mass

The pinch technique (PT) is applied to neutral current amplitudes, focusing on the mixing problem. Extending recent arguments due to Papavassiliou and Pilaftsis, it is shown that the use of the PT self-energies does not shift the complex-valued position of the pole through order {\cal O}($g^4$). This leads (to the same accuracy) to a simple interpretation of $M_Z$, the mass measured at LEP, in terms of the PT self-energies. It is pointed out that the PT approach provides a convenient and rather elegant formalism to discuss important neutral current amplitudes, such as those relevant to four-fermion processes and LEP2.Comment: 13 pages, Latex, 3 PostScript figure

LEADING VACUUM-POLARIZATION CONTRIBUTIONS TO THE RELATION BETWEEN POLE AND RUNNING MASSES

The vacuum--polarization contributions of {\cal O}(b^{n-1} \al_s^n) to the relation between the pole--mass $M$ of a quark and the \MS parameter \mh (M) are evaluated by a straightforward method. They are found to approximate very well the exact answer, known through {\cal O}(\al_s^2), thus providing a simple physical interpretation. Results are also given for the cases when the vacuum--polarization contributions are defined by the pinch technique prescription and specific background field gauges. Assuming that the terms $n \geq 3$ are also dominant, we evaluate $M_t/\hat{m}_t(M_t)$, compare the results with those of optimization methods, briefly discuss M_b/\mh_b (M_b), and estimate the irreducible errors in the perturbative series. Implications for the electroweak amplitude $\Delta\rho$ are emphasized. An update of the QCD corrections to this amplitude, including an estimate of the theoretical error, is given.Comment: 27 pages, 1 figure and 5 tables all included in the text in a compressed ps fil

Two-loop electroweak corrections to the ρ\rho parameter beyond the leading approximation

We show that in the framework of the pinch technique the universal part of the $\rho$ parameter can be meaningfully defined, beyond one loop. The universal part so obtained satisfies the crucial requirements of gauge-independence, finiteness, and process-independence, even when subleading contributions of the top quark are included. The mechanism which enforces the aforementioned properties is explained in detail, and several subtle field theoretical issues are discussed. Explicit calculations of the sub-leading two-loop corrections of order $O(G_{\mu}^{2}m^{2}_{t}M_{Z}^{2})$ are carried out in the context of an $SU(2)$ model, with $M_{W}=M_{Z}$, and various intermediate and final results are reported.Comment: 40 pages, TeXsis, uu encoded ps files, 14 figures include