Imaginary free energy and decay rate

[santale]

In euclidean quantum field theory, the imaginary part of the free energy, defined as the logaritm of the partition function, is it connected to the decay rate?

 

[LLSM]

The free energy has two types of components, one without Levi-Civita pseudotensor (normal parity) and another with the epsilon tensor (abnormal parity).
In Euclidean field theory the normal parity component is always real, and the abnormal parity component is imaginary (see e.g.,
L. Alvarez-Gaume. E. Witten, Nucl.Phys. B234 (1984) 269).
In Minkowskian space both components are real if there is no phase space to decay, but develop an imaginary part above threshold (decay, inelastic channels, etc).