transition form factor $G_{E}(0)$. They are given by [@Jones:1972ky] $$\begin{aligned}
\label{GM}
G_M(0)=&\frac{m_P}{3\left(m_P+m_{\Delta}\right)} \bigg[  \left( 3m_{\Delta} +m_P \right) \left( m_{\Delta}+m_P \right) \frac{G_1(0)}{m_{\Delta}}{\nonumber}\\
&\phantom{\frac{m_P}{3\left(m_P+m_{\Delta}\right)} \bigg[} +\left(m_{\Delta}^2-m_P^2 \right) G_2(0) \bigg] \qquad \\
\label{GE}
G_E(0)=& \frac{m_P}{3\left(m_P+m_{\Delta}\right)} \bigg[ \left(m_{\Delta}^2-m_P^2 \right) \left(\frac{G_1(0)}{m_{\Delta}} + G_2(0)\right) \bigg]\end{aligned}$$ and $$\begin{aligned}
\label{REM}
R_{EM}=&-\frac{G_{E}(0)}{G_{M}(0)}\end{aligned}$$ where $G_{i}(0)$, $i=1,2$ are form factors defined in Eq..

Contribution of $p \gamma \to \Delta^{+}$ to the correlation function
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The contribution of the $p \gamma \to \Delta^{+}$ transition to the correlator is given by $$\begin{aligned}
\label{NDcontribution}
T^{\mu \nu}_{\Delta} e^{\left( \lambda \right)}_ {\nu}=&\frac{1}{m_{\Delta}^2-p^2} \frac{1}{m_{P}^2-(p+q)^2} \sum_{s,s'}{\left\langle 0 \right|} \eta_{\mu}(0) {\left| \Delta(p,s) \right\rangle} \times {\nonumber}\\& {\left\langle \Delta(p,s) \right|} j^{\nu}(0) {\left| P(p+q,s') \right\rangle} {\left\langle P(p+q,s') \right|} \overline{\eta}(0){\left| 0 \right\rangle} e^{(\lambda)}_{\nu} \mbox{ .}\end{aligned}$$ The matrix element $$\begin{aligned}
\label{DeltaCoupling}
{\left\langle 0 \right|} \eta_{\mu}(0){\left| \Delta(p,s) \right\rangle}=\frac{\lambda_{\Delta}}{(2\pi)^2} \Delta^{(s)}_{\mu}(p)\end{aligned}$$ is parametrised via the coupling constant $\lambda_{\Delta}$. Here $\Delta^{(s)}_{\mu}(p)$ is a Rarita-Schwinger spinor for the $\Delta$. Inserting the general expression for the transition matrix element $$\label{DeltaNTranstion}
{\left\langle \Delta^{\mu}(p,s) \right|} j_{\nu}(0){\left| P(p+q,s') \right\rangle}=\overline{\Delta}^{\mu}(p,s) \Gamma_{\mu \nu} \gamma_5 P(p+q,s') \mbox{ ,}$$ where the vertex $\Gamma_{\mu \nu}$ defines the three form factors $G_{1}(Q^2)$, $G_{2}(Q^2)$ and $G_{3}(Q^2)$, $$\begin{aligned}
\label{DeltaNVertex}
\Gamma_{\mu \nu}=& \phantom{+} G_1\left(Q^2 \right)\left(g_{\mu \nu} \slashed{q} - q_{\mu} \gamma_{\nu} \right) +G_2\left(Q^2 \right)\left( g_{\mu \nu} q\cdot\left(p+\frac{q}{2} \right)-q_{\mu} \left( p+\frac{q}{2}\right)_{\nu}  \right) \nonumber \\ 