Breakdown of global fits to the Wilson coefficients in rareBdecays: A left-right model example

In the standard model and many of its extensions, it is well known that all of the observables associated with the rare decays $\overrightarrow{b}s\gamma$ and $\overrightarrow{b}s{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ can be expressed in terms of the three Wilson coefficients $C_{7L,9L,10L}\left(\mu \sim m_b\right),$ together with several universal kinematic functions. In particular, it has been shown that the numerical values of these coefficients can be uniquely extracted by a three-parameter global fit to data obtainable at future B factories given sufficient integrated luminosity. In this paper we examine if such global fits are also sensitive to new operators beyond those which correspond to the above coefficients, i.e., whether it is possible that new operators can be of sufficient importance for the three-parameter fit to fail and for this to be experimentally observable. Using the left-right symmetric model as an example of a scenario with an extended operator basis, we demonstrate via Monte Carlo techniques that such a possibility can indeed be realized. In some sense this potential failure of the global fit approach can actually be one of its greatest successes in identifying the existence of new physics.