Relative Efficiency for Cross-Section Calculation

To estimate the B_c->J/&psi &mu &nu cross-section time branching ratio relative to B^±->J/&psi K^± we must first calculate the efficiencies to recontruct both B_c->J/&psi &mu and B^±->J/&psi K^± events in our analysis chain. Table 4 summarizes the efficiences for our analysis cuts on B_c->J/&psi &mu and B^±->J/&psi K^±. We define a relative efficiency, &epsilon_rel=&epsilon_B/&epsilon_Bc. Table 5 summarizes the corrections we make to &epsilon_rel and the sources of systematic error. Applying the corrections we estimate &epsilon_rel= 3.29 ± 0.11(stat.) ± 0.81(syst.) ^+1.08_-0.43(life.).

Table 4: The selection cut efficiencies.

Table 5: Errors and corrections associated with the B^±->J/&psi K^± and B_c->J/&psi &mu efficiency calculations. The errors and corrections are for the quantity &epsilon_rel = &epsilon_B/&epsilon_Bc.