Mistake in equation 5.4 for quantum gravity baryon decay and fermion case

Question

In the paper https://projecteuclid.org/euclid.cmp/1103922050, the equation 5.4 seems to be lacking a minus:
$$left(dfrac{m_B}{m_P}right)^8dfrac{1}{m_B}sim 10^{122}yrs$$
seems to be OK only if $n=-8$ (anyway, I am also doubtful about how he computes the 8 factor), since if we plug $hbarsim 10^{-34}Jcdot s$, $c^2=10^{17}m^2/s^2$, $m_Bsim 1GeV=10^{-27}kg$ and $m_Psim 10^{19}GeV$, then
$$(10^{-19})^{-8}cdot dfrac{10^{-34}}{10^{-10}}sim 10^{128}ssim 10^{122}yrs$$
Am I right? Is the argumenf of the paper also valid about for the fermion case? Should it be
$$tau=left(dfrac{m_f}{m_P}right)^ndfrac{1}{m_f}$$
and how to get the thumb rule for guessing the $n$ for fermions?

riemannium · Answer

Maybe, I think I got partial answer to my confusion...
The RATE of proton decay should be
$$Gamma=left(dfrac{m_B}{m_P}right)^8m_Bsim 10^{-128}s^{-1}sim (10^{122}yr)^{-1}$$
However, I do not understand yet how to pick up the $8th$ power (i.e. the power counting is a mystery yet from the paper Feynman rules, but I presume it has to do with the Born rule and the coefficient of the Feynman graphs...). Moreover, I am not sure of how to get a similar result for fermions. Why should the coefficient for fermions be different from baryons? After all, if we allow for B and/or L symmetries, maybe B-L symmetry, how to understand all this?

Mistake in equation 5.4 for quantum gravity baryon decay and fermion case

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