Interpretation
The parameter may be viewed as a renormalization of Newton's constant. Various speculative proposals to explain this parameter have been suggested: for example, an argument due to Olaf Dreyer based on quasinormal modes.
Another more recent interpretation is that it is the measure of the value of parity violation in quantum gravity, and its positive real value is necessary for the Kodama state of loop quantum gravity. As of today, no alternative calculation of this constant exists. If a second match with experiment or theory (for example, the value of Newton's force at long distance) were found requiring a different value of the Immirzi parameter, it would constitute evidence that loop quantum gravity cannot reproduce the physics of general relativity at long distances. On the other hand, the Immirzi parameter seems to be the only free parameter of vacuum LQG, and once it is fixed by matching one calculation to an "experimental" result, it could in principle be used to predict other experimental results. Unfortunately, no such alternative calculations have been made so far.
Read more about this topic: Immirzi Parameter