= Tadpole integral
{title2=$T_d(m)=\int\frac{d^dk}{(2\pi)^d}\frac1{k^2+m^2}$}
The one-propagator Euclidean <loop momentum> integral associated with a <tadpole diagram>. <Dimensional regularization> gives $T_d(m)=\Gamma(1-d/2)(m^2)^{d/2-1}/(4\pi)^{d/2}$. Near $d=3$ this has no pole and $T_3(m)=-m/(4\pi)$ for $m>0$. A momentum-cutoff definition instead contains a linear <ultraviolet divergence>; the absence of a dimensional-regularization pole here concerns logarithms, not the positivity or convergence of the unregularized integral.
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