We present the asymptotic distribution for two-sided tests based on the profile likelihood ratio with lower and upper boundaries on the parameter of interest. This situation is relevant for branching ratios and the elements of unitary matrices such as the CKM matrix.
A search for the production and non-standard decay of a Higgs boson, h, into four taus through intermediate pseudoscalars, a, is conducted on 683 pb-1 of data collected by the ALEPH experiment at centre-of-mass energies from 183 to 209 GeV. No excess
of events above background is observed, and exclusion limits are placed on the combined production cross section times branching ratio, xi^2 = sigma(e+e- --> Zh)/sigma_{SM}(e+e- --> Zh) x B(h --> aa)x B(a --> tau^+tau^-)^2. For mh < 107 GeV/c2 and 4 < ma < 10 GeV/c2, xi^2 > 1 is excluded at the 95% confidence level.
