I used this syntax from documentation center "NIntegrate[f,{x,x0,x1,…,xk}] tests for singularities in a one-dimensional integral at each of the intermediate points xi. If there are no singularities, the result is equivalent to an integral from x0 to xk. You can use complex numbers xi to specify an integration contour in the complex plane."

Lambda is the upper integration limit, it´s a cut-off frequency for the integral, the original upper limit was infinity but then the integral becomes divergent

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?