exchange $e_u \leftrightarrow e_d$. Hence, we will only consider the proton transition.

Definitions
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In order to study the $p \gamma \to \Delta^{+}$ transition using LCSRs, it is convenient to consider the correlation function corresponding to the diagram in Fig.\[PtoPgamma\]:

$$\label{correlatorPreBackground}
\Pi^{\mu \nu}(p,q) =i^2\int \!\! d^4x \int \!\! d^4y\; e^{ipx+iqy} {\left\langle 0 \right|}\mathcal{T} \left \lbrace  \eta^{\mu}(x) j^{\nu}(y) \bar{\eta}(0) \right \rbrace {\left| 0 \right\rangle} \mbox{ .}$$

For the current $\eta^{\mu}$ that creates states with the quantum numbers of the $\Delta^{+}$, we will follow a suggestion by Ioffe [@Ioffe:1981kw] and use $$\begin{aligned}
\label{DeltaCurrent}
\eta^{\mu}(x)=& \left[\left(u^a(x)\mathcal{C}\gamma^{\mu} u^{b}(x) \right) d^{c}(x)+2\left(u^a(x)\mathcal{C}\gamma^{\mu} d^{b}(x) \right) u^{c}(x) \right]\varepsilon^{abc} \mbox{ .}\end{aligned}$$

Note that the current $\eta$, Eq., has isospin $1/2$, whereas $\eta^{\mu}$ has isospin $3/2$, therefore only the isovector part of the electromagnetic current $$\label{EmCurrentIsoVector}
j_{\mu}^{(I=1)}=\frac{1}{2}\left(e_u-e_d \right) \left({\overline{u}}\gamma_{\mu} u - {\overline{d}}\gamma_{\mu} d \right)$$ can induce the $p \gamma \to \Delta^{+}$ transition [@Belyaev:1995ya].

We will also use a correlation function in an electromagnetic background field $F_{\mu \nu}$ $$\label{correlator}
\Pi^{\mu \nu}_{\Delta}(p,q) e^{\left( \lambda \right)}_ {\nu}=i\int \!\! d^4x\; e^{ipx} {\left\langle 0 \right|}\mathcal{T} \left \lbrace  \eta^{\mu}(x) \bar{\eta}(0) \right \rbrace {\left| 0 \right\rangle}_F \mbox{ .}$$

The quantities, which can be measured experimentally, are the magnetic dipole transition form factor $G_{M}(0)$ and the electric quadrupole 