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.

Analysis of theZ0Resonant Amplitude in GeneralRξGauges

“…In this case we can set ImA ′′ (M 2 ) = 0 in Eq. (14). For ImA(M 2 ) we again employ the unitarity relation (Eq.…”

“…[11]. Recently, there has been significant progress in the construction of the PT selfenergies in higher orders [12,13,14]. In the expansion analogous to Eq.…”

“…(3) the conventional self-energy A is replaced by its PT counterpart A which is ξ-independent and, moreover, Im A ′ b (M 2 ) = 0. Thus, the gauge dependence does not arise and one obtains [14] an expression analogous to Eq. (7), with ReA ′ (M 2 ) → Re A ′ (M 2 ) and Φ → Φ = −(3/4π √ 2)G µ m 2 b , a very small and gauge independent scale-breaking term.…”

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

“…The explicit construction of R ZZ 2 (s) in the ξ i = 1 gauges has been given in Ref. [5]. We must now generalize this procedure to a general gauge.…”

“…As explained in Refs. [5], [6], using the scaling approximation for One can readily carry out the same analysis for the W self-energy . In this case there are no mixing complications but the R ξ gauge dependence is governed by three parameters…”