The impact of LEP 2 data on possible anomalous enhancements of Re ǫ ′ / ǫ Francesco Terranova

It has been shown in the past that the real part of the ǫ/ǫ ratio is particularly sensitive to anomalous gauge couplings that modify the Standard Model Lagrangian. Due to the loose bounds on these couplings coming from low energy processes and to the poor sensitivity of hadron colliders to couplings such as ∆g 1 , it has been argued that anomalous couplings could still produce an enhancement of Re ǫ/ǫ bringing this observable closer to the experimental value obtained by KTeV, NA31 and NA48. The impact of the new measurements done at LEP 2 in these years is discussed and new severe constraints to this hypothesis are determined. Since 1995, it has been noted [1] that anomalous triple gauge couplings (TGC) involving WWγ and WWZ vertices could modify significantly the Standard Model (SM) prediction concerning ǫ/ǫ . More precisely, strong penguin diagrams and isospin breaking due to quark masses completely dominate the SM prediction of Re ǫ/ǫ for low values of mt. However, for mt of the order of 170 GeV, the effects of electroweak penguin diagrams are sizeable [2] and therefore Re ǫ/ǫ becomes sensitive to anomalies in the bosonic sector of the SM. The possibility that anomalous TGC could modify and, particularly, enhance Re ǫ/ǫ has been considered with interest, especially because several experimental measurements still point towards a rather high value of Re ǫ/ǫ with respect to the SM expectation. In fact, present theoretical errors on Re ǫ/ǫ , coming mainly from the uncertainties in the models for hadronic matrix elements, prevent us from drawing conclusions about the effectiveness of SM in the CP violating sector. On the other hand, it is interesting to quantify to what extent the hypothesis of anomalous enhancement of Re ǫ/ǫ is corroborated by the intense experimental investigation on the bosonic sector of the SM carried out at LEP 2 since 1996. It is customary to express general deviations from the SM in the bosonic sector in the framework of effective theories [3]. In this case, the most general Lagrangian invariant under Uem(1) that contributes to WWV vertices (V = Z, γ) [4,5] is: iL eff = gWWV · [g V 1 V (W μνW +ν −W μνW ) + κVW + μ W − ν V μν + + λV M W V W ν W − ρν + ig V 5 εμνρσ((∂ W)W −W(∂W))V + +ig 4 W − μ W + ν (∂ V ν + ∂V )− κ̃V 2 W μ W + ν ε Vρσ − λ̃V 2M W W ρμW +μ ν ε Vαβ] , (1) where W are the W boson fields and V = γ, Z. Defining gWWγ = e and gWWZ = e cotθW , this Lagrangian allows anomalous values for the Cand P-conserving couplings κγ, κZ , g Z 1 , g 1 (equal to 1 in SM). Moreover, new contributions coming from operators absent in the standard theory are present. These are λV , which also conserves both C and P -parity; g V 5 (C and P violating but CP conserving) and the CP violating terms g 4 , κ̃V and λ̃V . In terms of the W magnetic dipole and electric quadrupole they contribute as μW = (g γ 1 + κγ + λγ) e 2mW s ;QW = − e(κγ−λγ) m W , (2) where eg γ is the W charge and s its spin. To simplify the notations, it is convenient to introduce the deviation from the SM couplings ∆g 1 ≡ g V 1 − 1 , ∆κV ≡ κV − 1 .