can be written as $$\begin{gathered}
\label{Pcontrib}
T_{P}^{\mu} \left(p,q \right) e^{\left( \lambda \right)}_ {\mu}=\frac{|\lambda_P|^2}{(2\pi)^4} \frac{\slashed{p}+m_p}{m_p^2-p_1^2} \left[\gamma^{\mu} F_1(Q^2) -i \frac{1}{2m_p} \sigma^{\mu \nu} q_{\nu} F_2(Q^2) \right] \frac{\slashed{p}+\slashed{q}+m_p}{m_p^2-p_2^2} e^{\left( \lambda \right)}_{\mu} \mbox{ ,}\end{gathered}$$ with $p_1=p$ and $p_2=p+q$.\
The Lorentz structure $$\begin{aligned}
    \slashed{p} \sigma^{\mu \nu} \slashed{p} q_{\nu} e_{\mu}^{(\lambda)} {\nonumber}\end{aligned}$$ is free of contributions due to $F_1(0)$, already satisfies the Ward identity, as it is proportional to $f^{\mu \nu}$, and has the highest possible number of momenta $p$. Therefore it seems advisable to focus on structures containing an even number of $\gamma$-matrices.

After reducing to the Dirac basis we will only consider the structure $p^{\alpha} p_{\beta} \sigma^{\beta \zeta} f_{\alpha \zeta}$, following [@Braun:1988qv]. Then one gets for Eq. $$\begin{aligned}
\label{ProtonOnHadron}
T_{P}^{\mu} \left(p,q \right) e^{\left( \lambda \right)}_ {\mu}= -\left( \frac{|\lambda_p|^2}{(2\pi)^4 m_p(m_p^2-p_1^2)(m_p^2-p_2^2)}F_2(0) \right)p^{\alpha} p_{\beta} \sigma^{\beta \zeta} f_{\alpha \zeta}+\ldots \mbox{ .}\end{aligned}$$ The dots represent terms of different Lorentz structure.

In the Euclidean region, where $p_1^2 \ll 0$ and $p_2^2 \ll 0$, one can express the correlation function Eq. in terms of photon distribution amplitudes of increasing twist. To this end we insert the expressions for the current $\eta$, Eq., into the correlator . $$\begin{gathered}
\Pi^{\mu \nu}(p,q) e^{\left( \lambda \right)}_ {\nu}= i\int \!\! d^4x\; e^{ipx+iqy} {\left\langle 0 \right|}\mathcal{T} \left \lbrace  \left( 