  We report the discovery of WTS-2 b, an unusually close-in 1.02-day hot
Jupiter (Mp=1.12MJ, Rp=1.363RJ) orbiting a K2V star, which has a possible
gravitationally-bound M-dwarf companion at 0.6 arcsec separation contributing
~20 percent of the total flux in the observed J-band light curve. The planet is
only 1.5 times the separation from its host star at which it would be destroyed
by Roche lobe overflow, and has a predicted remaining lifetime of just ~40 Myr,
assuming a tidal dissipation quality factor of Q'*=10^6. Q'* is a key factor in
determining how frictional processes within a host star affect the orbital
evolution of its companion giant planets, but it is currently poorly
constrained by observations. We calculate that the orbital decay of WTS-2 b
would correspond to a shift in its transit arrival time of T_shift~17 seconds
after 15 years assuming Q'*=10^6. A shift less than this would place a direct
observational constraint on the lower limit of Q'* in this system. We also
report a correction to the previously published expected T_shift for WASP-18 b,
finding that T_shift=356 seconds after 10 years for Q'*=10^6, which is much
larger than the estimated 28 seconds quoted in WASP-18 b discovery paper. We
attempted to constrain Q'* via a study of the entire population of known
transiting hot Jupiters, but our results were inconclusive, requiring a more
detailed treatment of transit survey sensitivities at long periods. We conclude
that the most informative and straight-forward constraints on Q'* will be
obtained by direct observational measurements of the shift in transit arrival
times in individual hot Jupiter systems. We show that this is achievable across
the mass spectrum of exoplanet host stars within a decade, and will directly
probe the effects of stellar interior structure on tidal dissipation.
