Making the small oblique parameters large.

We compute the oblique parameters, including the three new parameters V , W and X introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin J and weak hypercharge Y . We show that, when the masses of the heaviest and lightest components of the multiplet remain constant, but J increases, the oblique parameter U and the three new oblique parameters increase like J3, while T only increases like J . For large multiplets with masses not much higher than mZ , the oblique parameters U and V may become much larger than T and S. The oblique parameters characterize the influence of physics beyond the standard model on the experimentally measurable quantities in terms of their contributions to the usual gaugeboson propagators. The first oblique parameter considered by the theorists [1] was T , which in many cases is larger than the other oblique parameters, because of its quadratic, instead of logarithmic, dependence on the masses of the new particles. Later [2], the parameter S was introduced, and it was shown that, because S receives a significant mass-independent contribution from each chiral fermion doublet, the experimentally allowed range for that parameter severely constrains technicolor theories. A more general parametrization of the effects of new physics, under the assumption that the mass scale of that physics is much higher than the Z mass, which implies that the vacuum-polarization functions are approximately linear in p up to p = mZ , requires one more oblique parameter, U [3]. Recently [4], the above assumption has been relaxed, and it has been shown that, whatever the mass scale of the new physics may be, the fact that all precision electroweak measurements are made at either p = 0 or p = mZ (or, in the case of mW and ΓW , at p 2 = mW ), requires the use of a total of six oblique parameters, thereby introducing three new parameters, which were named V , W and X. The definitions of the six oblique parameters given in reference [4] are S ≡ 16πc 2 ws 2 w e2 [ AZZ(MZ)−AZZ(0) MZ − c 2 w − sw cwsw ∂AγZ(P ) ∂P ∣∣∣∣ P=0 − ∂Aγγ(P ) ∂P ∣∣∣∣ P=0 ] , (1) ∗On leave of absence from Universidade Técnica de Lisboa, Lisbon, Portugal