Kostas Philippides

Gauge invariant three boson vertices in the Standard Model and the static properties of the W

We use the [ital S]-matrix pinch technique to derive to one-loop order gauge-independent [gamma][ital W][sup +][ital W[minus]] and [ital ZW][sup +][ital W[minus]] vertices in the context of the standard model, with all three incoming momenta off shell. We show that the [gamma][ital W][sup +][ital W[minus]] vertex so constructed is related to the gauge-independent [ital W] self-energy, derived by Degrassi and Sirlin, by a very simple QED-like Ward identity. The same results are obtained by the pinch technique applied directly to the process [ital e][sup +][ital e[minus]][r arrow][ital W][sup +][ital W[minus]]. Explicit calculations give rise to expressions for static properties of the [ital W] gauge bosons such as the magnetic dipole and electric quadrupole moments, which satisfy the crucial properties of infrared finiteness as well as gauge independence.

Application of the pinch technique to neutral current amplitudes and the concept of the Z mass

Abstract 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 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.

Gauge-invariant three-boson vertices and their Ward identities in the standard model.

In the context of the standard model we extend the {ital S}-matrix pinch technique for nonconserved currents to the case of three-boson vertices. We outline in detail how effective gauge-invariant three-boson vertices can be constructed, with all three incoming momenta {ital off} {ital shell}. Explicit closed expressions for the vertices {gamma}{ital W}{sup {minus}}{ital W}{sup +}, {ital ZW}{sup {minus}}{ital W}{sup +}, and {chi}{ital W}{sup {minus}}{ital W}{sup +} are reported. The three-boson vertices so constructed satisfy naive QED-like Ward identities which relate them to the gauge-invariant gauge boson self-energies previously constructed by the same method. The derivation of the aforementioned Ward identities relies on the sole requirement of complete gauge invariance of the {ital S}-matrix element considered; in particular, no knowledge of the explicit closed form of the three-boson vertices involved is necessary. The validity of one of these Ward identities is demonstrated explicitly, through a detailed diagrammatic one-loop analysis, in the context of three different gauges.

Leading vacuum-polarization contributions to the relation between pole and running masses

Abstract The vacuum-polarization contributions of O(bn−1 σsn) to the relation between the pole-mass M of a quark and the MS parameter m (M) are evaluated by a straightforward method. They are found to approximate very well the exact answer, known through O(αs2), 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 ⩾ 3 are also dominant, we evaluate M t m t (M t ) , compare the results with those of optimization methods, briefly discuss M b m b (M b ) , and estimate the irreducible errors in the perturbative series. Implications for the electroweak amplitude Δϱ are emphasized. An update of the QCD corrections to this amplitude, including an estimate of the theoretical error, is given.

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

We show that in the framework of the pinch technique the universal part of the

Consistency condition for the pinch technique self-energies at two loops

\rho

Heavy quark decomposition of the S matrix and its relation to the pinch technique.

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

The ward identities of the gauge invariant three boson vertices

O(G_{\mu}^{2}m^{2}_{t}M_{Z}^{2})

Dual gauge-fixing property of the S matrix

are carried out in the context of an

A Method for determining anomalous gauge boson couplings from

SU(2)