Roles of <inline-formula><tex-math id="M1">\begin{document}${\boldsymbol\Delta(\bf 1232)}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0061_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0061_M1.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}${\boldsymbol N^*(\bf 1520)}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0061_M2.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0061_M2.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M3">\begin{document}${\boldsymbol N^*(\bf 1650)}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0061_M3.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0061_M3.png"/></alternatives></inline-formula> resonances in <inline-formula><tex-math id="M4">\begin{document}${\boldsymbol\gamma \boldsymbol p\to \boldsymbol\pi^{\bf 0} \boldsymbol\pi^{\bf 0}\boldsymbol p}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0061_M4.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="CPC-2025-0061_M4.png"/></alternatives></inline-formula> reaction within an effective Lagrangian approach

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