Suppose EW theory generating functional:

Z[sources]=∫D(A,ψ,ψˉ,H,H†)exp[i∫d4x(−14gEW2FEW2+ψˉ(D−m)ψ+DH†DH+Z[\text{sources}] = \int D(A,\psi,\bar{\psi}, H,H^{\dagger})\text{exp}\bigg[i\int d^{4}x\bigg(-\frac{1}{4g_{EW}^2}F_{EW}^2 + \bar{\psi}(D - m)\psi + DH^{\dagger}DH + +θFEWF~EW+gauge fix+ghost+sources)](1)\tag 1 +\theta F_{EW}\tilde{F}_{EW} + \text{gauge fix} +\text{ghost} +\text{sources}\bigg)\bigg]

I need to calculate topological susceptibility

κ(0)≡∫d4x⟨0∣T(FEWF~EW(x)FEWF~EW(0))∣0⟩θ=sources=0≡∫d4xδ2Zδθ2θ=sources=0(2)\tag 2 \kappa (0) \equiv \int d^4 x\langle 0|T\left( F_{EW}\tilde{F}_{EW}(x)F_{EW}\tilde{F}_{EW}(0)\right) |0\rangle_{\theta=\text{sources}= 0} \equiv \int d^4 x \frac{\delta^2 Z}{\delta \theta^2}_{\theta=\text{sources}= 0}

I know that for SUL(2)SU_{L}(2) theory I can perform chiral rotations of ψ\psi fields (electron, neutrino etc.) so that θ\theta term wil disappear from generating functional in the limit of zero sources. Does this mean that (2)(2) is equal to zero?