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

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

Maybe, I think I got partial answer to my confusion... The RATE of proton decay should be $$\Gamma=\left(\dfrac{m_B}{m_P}\right)^8m_B\sim 10^{-128}s^{-1}\sim (10^{122}yr)^{-1}$$ 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?