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In this thesis we present the first measurement of the polarization amplitudes for the charmless B{sub s} {yields} {phi}{phi} {yields} [K{sup +}K{sup -}][K{sup +}K{sup -}] decay of the B{sub s} meson. The result is achieved using an unbinned Maximum Likelihood fit to the data collected by the Collider Detector at Fermilab (CDF) in Run II (CDFII), in a period starting from March 2001 till April 2008, which corresponds to an integrated luminosity of 2.9 fb{sup -1}. The resulting yield consists of 300 signal events selected by the Two Track Trigger (TTT). Furthermore, our work puts in evidence an original topic, that was never observed until now: an unexpected dependence of the signal acceptance on the proper decay time (t) of the B{sub s} mesons. This specific issue, which is most likely a general feature induced by any signal selection based on the lifetime information, is supposed to be related to the on-line TTT and off-line selections based on the impact parameter. The involved fit, indeed, reproduces the biases observed in large statistics Monte Carlo (MC) samples. The thesis presents the same analysis performed for the B{sub s}{sup 0} {yields} J{psi}{phi} decay as well, which is used as a control sample. The polarizations amplitudes we find are consistent with the published ones; this result contributes to enforce the reliability of the analysis. This work is considered ready to begin the procedure for official approval by the CDF collaboration pending the finalization of the systematic uncertainty which has not yet been fully completed

Measurement of the polarization amplitudes of the Bs -> PhiPhi decay at CDF II