  The LHCb experiment at CERN's Large Hadron Collider will soon allow us to
enter a new era in the exploration of B_s decays. A particularly promising
channel for the search of "new physics" is B^0_s -> mu^+ mu^-. The systematic
key uncertainty affecting the measurement of this -- and in fact all B_s-decay
branching ratios -- is the ratio of fragmentation functions f_d/f_s. As the
presently available methods for determining f_d/f_s are not sufficient to meet
the high precision at LHCb, we propose a new strategy using \bar B^0_s -> D_s^+
pi^- and \bar B^0_d -> D^+ K^-. It allows us to obtain a lower experimental
bound on BR(B^0_s -> mu^+ mu^-) which offers a powerful probe for new physics.
In order to go beyond this bound and to determine f_d/f_s with a theoretical
precision matching the experimental one it is sufficient to know the
SU(3)-breaking correction to a form-factor ratio from non-perturbative methods
at the level of 20%. Thanks to our strategy, we can detect new physics in B^0_s
-> mu^+ mu^- at LHCb with 5 sigma for a branching ratio as small as twice the
Standard-Model value, which represents an improvement of the new-physics reach
by about a factor of two with respect to the current LHCb expectation.
