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Radiative capture rates of thermal $\Lambda\Lambda + \Xi$N states into Hdibaryon are calculated in the novel imaginary time method. The H dibaryon isassumed to be a bound state of $\Xi $N with spin $J^{\pi}= 0^+$, isospin $I=0$and strangeness $-2$. We consider $E1$ transition to H from $\Xi$N $(L=1)$scattering states which mix with $\Lambda\Lambda (L=1)$. In order to calculatethe transition rates, we formulate a coupled-channel imaginary time method byextending the one-channel formula originally proposed by Yabana and Funaki. Theimaginary time method allows us to avoid the sum over all the excited thermalinitial states, and thus to save computational time significantly. Thetransition rates are given as a function of temperature and the unknown bindingenergy of the H dibaryon, which we take as a parameter. It is found that thetransition rate is not sensitive to the choices of the H binding energy or thestrengths of the channel coupling for temperatures 3 MeV or higher.

The radiative capture reaction rate from $\Lambda \Lambda$ to H dibaryon in the imaginary time method