Wow. I was a CERN summer student in 1995 and me and another student worked on the tagging of B-meson decays in ATLAS. Hers was exactly the B->K mu+mu- decay. So 20 years later, it's observed... ;-)
(Incidentally, the particle physics publication system is beyond screwed up. We, who did the actual work, weren't even allowed to be authors on the paper where the results were described, because we weren't "members of the ATLAS collaboration". We merely got an acknowledgement.)
The idea is that you need to quickly identify ("tag") interesting reactions out of the millions happening, so there are a set of increasingly stringent but slower filters that select events. Muons are good because they are easy to identify, then you look back at where they came from and see what other things were created. Typically mesons (and other hadrons) create a "shower" of particles and by adding upp all their energies you can estimate what particle they came from.
But all that stuff is mostly repressed from my memory. I decided that particle physics wasn't for me after that summer... ;-)
(Incidentally, the particle physics publication system is beyond screwed up. We, who did the actual work, weren't even allowed to be authors on the paper where the results were described, because we weren't "members of the ATLAS collaboration". We merely got an acknowledgement.)