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Estimates of the branching ratios for B_{d,s}->J/psi eta and B_{d,s}->etal+l- are obtained by SU(3) relation to B_d->J/psi K and B_d->K l+l-,respectively, as functions of the eta mixing parameter, theta_P. Based on theseestimates, a discussion of the prospects for HERA-B, CDF-II, and ATLAS on theseprocesses is given. The CP violation in B_{d,s}-> J/psi eta is analyzed indepth and a method to extract the angle gamma of the unitarity triangle isdiscussed. Finally, a possible method to constrain the Wilson coefficientC_{10A} from measurements on semileptonic B decays such as B_d->J/psi K andB_s->eta l+l- is proposed along with a discussion of the prospects for futureexperiments and form factor calculations to reach the precision required forthis method to be interesting.Comment: 14 pages, 2 figures, 4 tables. Fixed incorrect reference and replaced  U-spin by SU(3) in several places. Corrected inconsistency in definition of  a_s. Added various comment

the journal of high energy physics/the journal of high energy physics

Branching ratios for Bd,s→J/ψη and Bd,s→ηell+ell−, extracting γ from Bd,s→J/ψη, and possibilities for constraining C10A in semileptonic B decays.