I see unevaluated (lower case findroot, integrate, 1^-20 -> 1.0^-20)
findRoot[
mSigma[T]^2/mSigma[0]^2 ==
1 + 1/(16 \[Pi]^2 mSigma[0]^2) 3 gSigmaPiPi^2 mPi^2 *
integrate[((1 + 2/(-1 + E^(E1/T))) *
Sqrt[ E1^2 - mPi^2]) / (-1.`*^-20 + E1 - mSigma[T]^2/4),
{E1, mPi, -1.`*^-20 + mSigma[T]/2, 1.`*^-20 + mSigma[T]/2 , Lambda}],
{mSigma[T], 550}]
There is a fourth parameter Lambda in the domain bracket of integrate. Whats it for?