Type II gamma-factor mass poles ($s=4n/{\alpha }^{\prime },n=0,1,\dots$)

At generic fixed $t$, the factor $\Gamma (-{\alpha }^{\prime }s/4)$ has simple poles at the displayed nonnegative values of $s$. Its denominator $\Gamma (1+{\alpha }^{\prime }s/4)$ is finite there. The $t,u$ factors do not generically cancel those poles under $s+t+u=0$. Factorization identifies massless and massive intermediate states at those masses. The factor has no negative-mass-squared poles; special polarization or momentum choices can suppress individual residues and cannot establish the degeneracy of an entire level.