Studying trilinear gauge couplings at LEP2 using optimal observables

We study the sensitivity of the processes e+e− → lν̄l qq̄′ at LEP2 energies on the non-standard trilinear gauge couplings (TGC), using the optimal observables method. All relevant leading logarithmic corrections to the tree-order cross section, as well as experimental resolution effects have been studied. Taking into account correlations among the different TGC parameters we show that the limits on the TGC can reach the level of 0.15 (1sd) at 161 GeV with 100 pb−1, a challenge for the first LEP2 phase. At higher energies this can be improved drastically, reaching the level of 0.02 (1sd). DEMO-HEP-96/01 May 1996 One of the two most important measurements at LEP2 energies will be the determination of the trilinear vector boson couplings [1, 2, 3, 4], a characteristic manifestation of the underlying non-Abelian symmetry of elementary particle interactions [5]. In order to study the trilinear boson couplings we need a parametrization of these interactions that goes beyond the Standard Model . There are, of course, several possibilities to accomplish this task, but we are going to restrict ourselves to the most economical one by considering C− and P− conserving interactions. The relevant interaction Lagrangian is usually written in the following form [2]: LTGC = ∑ V=γ,Z e gV ( VμW −μνW+ ν − VμWW ν + κV VμνWW ) + e λγ M2 W AμρW +ρνW−μ ν + e ctg θw λZ M2 W ZμρW +ρνW−μ ν (1) where Vμν = ∂μVν − ∂νVμ, W± μν = ∂μW ν − ∂νW μ . W± is the W -boson field, and gγ = 1, gZ = ctg θw, κγ = κZ = 1 and λγ = λZ = 0 at tree order in the Standard Model . It is more convenient to express the different couplings in terms of their deviations from the Standard Model values. For this we define the following deviation parameters[2]: δZ = gZ − ctg θw xγ = κγ − 1 xZ = (κZ − 1)(ctg θw + δZ) . (2) It is worth while to note that the interaction Lagrangian becomes linear with respect to the above parameters (including also λγ and λZ). During the last years, considerable progress has been achieved concerning the understanding of the physics underlying the non-standard boson self-couplings. As Gounaris and Renard [6] showed, the deviations from the Standard Model couplings can be parametrized in a manifestly gauge-invariant (but still non-renormalizable) way, by considering gauge-invariant operators involving higher-dimensional interactions among gauge bosons and Higgs field. These operators will be scaled by an unknown parameter ΛNP , which might be understood as the characteristic scale of New Physics effects. In order to describe all five C− and P− conserving couplings introduced in Eq.(1) we need operators with dimension up to eight. On the other hand restricting ourselves to SU(2)L ×U(1)Y -invariant operators with dimension up to six, which are the lowest order ones in 1/ΛNP expansion, we can have the following list [7]: OBΦ = B(DμΦ)(DνΦ) OWΦ = (DμΦ) τ ·W (DνΦ) OW = 1 3! (W ρ ×W ν) ·W μ (3) where τi = 1 2σi (σi are the Pauli matrices), Bμν = ∂μBν − ∂νBμ where Bμ is the U(1)Y gauge field, W μν = ∂μW ν − ∂νW μ − gW μ ×W ν