Analytic coupled channel calculation of ultracold three-body collision rates

We analyze three-body recombination for positive two-body $s$-wave scattering lengths. Using the adiabatic hyperspherical representation as a starting point, we introduce coupling between the three-body continuum and the weakly bound diatom plus atom channel in the vicinity of $R\sim a$---the location where rigorous calculations have shown the coupling to peak~[1]. In order to model loss to deeply bound diatom channels, we introduce a complex short-range $K$-matrix. Analytic expressions for the loss rates are derived and we recover the behavior found previously~[2], including the overall $a^4$ scaling for identical bosons as well as the log-periodic modulation due to Efimov physics. Our formulation permits straightforward extensions to other symmetries and higher energies. \\[4pt] [1] J.~P.~D'Incao and B.~D.~Esry, Phys.~Rev.~A 72, 032710 (2005) \newline [2] B.~D.~Esry, C.~H.~Greene, and J.~P.~Burke, Jr., Phys.~Rev.~Lett. 83, 1751 (1999).