Size of flavor-changing effects induced by the symmetry-breaking sector

Abstract

It has recently been shown that strong interactions underlying electroweak symmetry breaking will induce four-fermion amplitudes proportional to m t 2 , which in turn will influence a variety of flavor-changing processes. We argue that the typical size of these effects is likely to be far below the current experimental bounds. ͓S0556-2821͑97͒04921-7͔PACS number͑s͒: 12.60. Fr, 12.39.Fe The corrections induced by a new strong sector underlying electroweak symmetry breaking are conveniently encoded in an effective chiral Lagrangian. Recently attention has focused on a particular term in this effective Lagrangian which induces corrections proportional to m t 2 in charged current interactions ͓1͔. Integrating out the t quark then yields interesting effects in the down-type quark sector, inducing corrections to R b and B d 0 -B d 0 mixing ͓1͔, and various rare B and K decays ͓2͔. All these effects are correlated since they are related to one parameter in the effective Lagrangian ͓2͔.In this work we will provide an estimate of the size of the new parameter, expressed in terms of the number of new fermion doublets in some underlying theory of electroweak symmetry breaking. Such an estimate in the case of the S parameter proved useful to constrain technicolor theories. The S parameter is related to a term in an effective Lagrangian with coefficient L 10 ϭϪS/16 which is completely analogous to the L 10 QCD term appearing at order p 4 in the low energy QCD chiral Lagrangian ͓3͔. Since L 10 QCD is a measured quantity, an estimate for S is thereby obtained ͓4͔ for QCD-like technicolor theories.The situation is somewhat different for the parameter of interest here, which is the coefficient of another term appearing at order p 4 . In the QCD case this coefficient is not a measurable quantity since the term can be removed by the equations of motion. Fortunately in the QCD case there are quark models which model the chiral symmetry breaking and which quite successfully reproduce the values of all ten measured parameters, L 1 -L 10 . Such models can then be expected to provide a reasonable estimate of the new parameter, which we will refer to as L 11 ͑corresponding to a 11 in ͓1͔ and ␣ 11 in ͓2͔͒.A naive quark model may be based on the nonlinear model where effects of a single quark loop are considered. This does a fair job of reproducing those L i 's which happen to correspond to convergent loop integrals ͓5͔. A more sophisticated quark-based approach leads to the extraction of all ten parameters ͓6͔. Most convenient for our purposes is the gauged nonlocal constituent ͑GNC͒ quark model ͓7͔, which incorporates the momentum dependence expected for dynamically generated fermion masses. In QCD the mass function is known to fall as the square of the momentum ͑up to logarithms͒ for large momentum. The GNC model can incorporate such momentum dependence in a manner which preserves the local chiral symmetries of the underlying theory. The mass function then naturally regulates the loop integrals, and successful values for L 1 -L 10 are...