Shell-restricted scalar propagator (${\tilde{C}}_{>}(p)=1_{{\Lambda }^{\prime }<|p|\le \Lambda }/(p^2+m^2)$)

The Gaussian contraction used while integrating out a momentum shell. Its Fourier support lies entirely in that shell. In particular, convolution with a purely low-momentum field is zero. This distinguishes shell Feynman diagrams from unrestricted loop diagrams.