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In this dissertation, they present a study of the untagged decay of B{sub s}{sup 0} {yields} J/{psi}{phi}, the final state of which is a superposition of the CP-even and CP-odd states. Within the framework of the standard model (SM), to a good approximation, the two CP eigenstates of the (B{sub s}{sup 0}, {bar B}{sub s}{sup 0}) system are equivalent to mass eigenstates. The data collected by the D0 detector between June 2002 to August 2004 (an integrated luminosity of approximately 450 pb{sup -1}) has been used for the analysis presented in this thesis. From a simultaneous fit to the B{sub s}{sup 0} candidate mass, lifetime, and the angular distribution of the decay products, they obtain the CP-odd fraction in the final state at production time to be 0.16 {+-} 0.10(stat) {+-} 0.02(syst). The average lifetime of the (B{sub s}{sup 0}, {bar B}{sub s}{sup 0}) system is measured to be 1.39{sub -0.16}{sup +0.13}(stat){sub -0.02}{sup +0.01}(syst) ps, with the relative width difference between the heavy and light mass eigenstates, {Delta}{Gamma}/{bar {Gamma}} = ({Gamma}{sup L}/{Gamma}{sup H})/{bar {Gamma}} = 0.24{sub -0.38}{sup +0.28}(stat){sub -0.04}{sup +0.03}(syst). With the additional constraint from the world average of the B{sub s}{sup 0} lifetime measurements using semileptonic decays, they find average lifetime of the (B{sub s},{sup 0}, {bar B}{sub s}{sup 0}) system 1.39 {+-} 0.06 ps with {Delta}{Gamma}/{bar {Gamma}} = 0.25{sub -0.15}{sup +0.14}. They have also done B{sup 0} lifetime measurement for its analogous decay mode to J/{psi}K*. With this measurement they get B{sup 0} lifetime 1.530 {+-} 0.043(stat) {+-} 0.023(syst) ps. Using above results, they get 0.91 {+-} 0.09(stat) {+-} 0.003(syst), for the ratio of the B{sub s}{sup 0} and B{sup 0} lifetimes ({bar {Gamma}}(B{sub s}{sup 0})/{Gamma}(B{sup 0})). These measurements are consistent with the predictions of SM within the measurement uncertainty

Lifetime difference in the B$0\atop{s}$ system from untagged B$0\atop{s}$ → J/ΨΦ decay at √s= 1.96 TeV at D0 detector