arXiv:hep-ph/9707453v2 6 Nov 1997 Constraint on the magnetic moment of the top quark R. Mart´ ınez 1 and J.-Alexis Rodr´ ıguez 1,2 1. Depto. de F´ ısica, Universidad Nacional, Bogot´ a, Colombia 2. Centro Internacional de F´ ısica, Bogot´ a, Colombia () We derive a bound on the magnetic dipole moment of the top quark in the context of the effective Lagrangian approach by using the ratios R b =Γ b /Γ h , R l =Γ h /Γ l and the Z width. We take into account the vertex and oblique corrections. The most recent analyses of precision measurements at the Large Electron Positron (LEP) collider lead to the conclusion that the predictions of the Standard Model (SM) of electroweak interactions, based on the gauge group SU (2) L ⊗ U (1) Y are in excellent agreement with the experimental results. Recently the discovery of the top quark has been announced by the Collider Detector at Fermilab (CDF) and D0 collaborations [1]. The direct measurement of the top quark mass m t is in agreement with the indirect estimates derived by confronting the SM m t dependent higher order corrections with the LEP and other experimental results. The measurement of the top quark mass reduced the number of free parameters of the SM. A precise knowledge of the value of the top mass will improve the sensitivity of searches of new physics through small indirect effects. The precise measurements of the g − 2 value of the electron provides a test of its point-like character. Similarly, measurements of the electric- and chromo- magnetic moments of the quarks can be important to study physics beyond the SM. In particular, the chromomagnetic moment of the top quark can affect its production in the p p and e + e - reactions [2]. The SM predicts how the top quark should behave under these interactions, so any deviation from this behaviour would provide us with a probe of new physics beyond the SM. If new physics is found in this sector, it could probably originates from a non standard symmetry breaking mechanism. This is because the top mass is of the order of the electroweak (EW) breaking scale, and hence it is conceivable that the top-quark properties are sensitive to unsuppressed EW breaking effects [3]. The aim of the present work is to extract indirect information on the magnetic dipole moment of the top quark from LEP data, specifically we use the ratios R b and R l defined by R b = Γ(Z → b ¯ b) Γ(Z → hadron) , R l = Γ(Z → hadron) Γ(Z → l ¯ l) (0.1) and the Z width, in the context of an effective Lagrangian approach. The oblique and QCD corrections to the b quark and hadronic Z decay widths cancel off in the ratio R b . This property makes R b very sensitive to direct corrections to the Zb b vertex, specially those involving the heavy top quark [4], while Γ Z and R l are more sensitive to oblique corrections. The effective Lagrangian approach is a convenient model independent parametrization of the low-energy effects of the new physics that may show up at high energies [5]. Effective Lagrangians, employed to study processes at a typical energy scale E can be written as a power series in 1/Λ, where the scale Λ is associated with the heavy particles masses of the underlying theory [6]. The coefficients of the different terms in the effective Lagrangian arise from integrating out the heavy degrees of freedom that are characteristic of a particular model for new physics. In order to define an effective Lagrangian it is necessary to specify the symmetry and the particle content of the low- energy theory. In our case, we require the effective Lagrangian to be CP -conserving, invariant under SM symmetry SU (2) L ⊗ U (1) Y , and to have as fundamental fields the same ones appearing in the SM spectrum. Therefore we consider a Lagrangian in the form L ef f = L SM +  n α n O n (0.2) where the operators O n are of dimension greater than four. In the present work, we consider the following dimension six and CP -conserving operators, O ab uW = ¯ Q a L σ µν W i µν τ i ˜ φU b R , O ab uB = ¯ Q a L σ µν YB µν ˜ φU b R , (0.3) 1