Dear Gordon, Polchinski didn't imply anything about the lightness of the monopoles. You are overinterpreting what he said: his statement was an in-principle statement by a theorist. Just to be sure, the MoEDAL collaboration has overinterpreted him, too: he has never suggested that an experiment of their kind will find the beast. Still, it's very important to know whether such qualitatively different particles exist even if we think it's very likely that they won't be directly detected in the near (or far) future. Most of the top contemporary state-of-the-art theoretical physics deals with objects that will probably never be detected by direct experiments, for obvious financial and technological limitations.

Directly experimentally, the lower bound on the mass is just 500 GeV or so, but when some theory is wisely added, the mass is pretty much required to be exponentially higher than the TeV scale. In particular, some kind of unification seems necessary to allow the magnetic monopoles, and unification such as GUT can only appear at very high scales, such as the GUT scale of $10^{16}$ GeV: that's where the electromagnetic $U(1)$ may be embedded in a larger group that allows a topologically nontrivial solution (the $SU(2)$ of the weak interactions is not enough - it doesn't contain the hypercharge which has to be twisted as well). So it's unlikely that direct detection succeeds. Inflation has probably diluted the concentration of those massive magnetic monopoles to a very tiny number.

With estimates of mass constraints on magnetic monopoles, how likely is one to be found by the LHC(MoEDAL)?
I mean, there are people who can't sing melodies correctly but they are able to play the guitar perfectly. Will such person be able to play the trumpet? When you hit the note on the trumpet do you have to worry about the correctness of the note or trumpet does it for you? I play the guitar, I even sing sometimes but I'm worried, will my musical hearing be good enough for the trumpet? Hope I made myself clear.
