Effects of the hadronic molecule <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2080</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:msu

In our previous work [], we analyzed all available data on differential cross sections and spin density matrix elements for the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>γ</a:mi> <a:mi>p</a:mi> <a:mo>→</a:mo> <a:msup> <a:mi>K</a:mi> <a:mrow> <a:mo>*</a:mo> <a:mo>+</a:mo> </a:mrow> </a:msup> <a:mi mathvariant="normal">Λ</a:mi> </a:mrow> </a:math> reaction using an effective Lagrangian approach. There, the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mi>t</c:mi> </c:math> -channel <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>K</d:mi> <d:mo>,</d:mo> <d:mo> </d:mo> <d:msup> <d:mi>K</d:mi> <d:mo>*</d:mo> </d:msup> </d:math> , and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>κ</e:mi> </e:math> exchanges, the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>u</f:mi> </f:math> -channel <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi mathvariant="normal">Λ</g:mi> <g:mo>,</g:mo> <g:mo> </g:mo> <g:mi mathvariant="normal">Σ</g:mi> </g:math> , and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:msup> <j:mi mathvariant="normal">Σ</j:mi> <j:mo>*</j:mo> </j:msup> </j:math> exchanges, the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mi>s</l:mi> </l:math> -channel <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>N</m:mi> <m:mo>,</m:mo> <m:mo> </m:mo> <m:mrow> <m:mi>N</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mn>2060</m:mn> <m:mo>)</m:mo> </m:mrow> <m:mn>5</m:mn> <m:mo>/</m:mo> <m:msup> <m:mn>2</m:mn> <m:mo>−</m:mo> </m:msup> </m:mrow> </m:math> , and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:mrow> <n:mi>N</n:mi> <n:mrow> <n:mo>(</n:mo> <n:mn>2000</n:mn> <n:mo>)</n:mo> </n:mrow> <n:mn>5</n:mn> <n:mo>/</n:mo> <n:msup> <n:mn>2</n:mn> <n:mo>+</n:mo> </n:msup> </n:mrow> </n:math> exchanges, and the interaction current were taken into account in constructing the reaction amplitudes. It was found that, overall, the agreement of the theoretical results with the corresponding data is fairly good. However, noticeable discrepancies between the model results and the data on spin density matrix elements <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:msub> <o:mi>ρ</o:mi> <o:mn>00</o:mn> </o:msub> </o:math> are still observed in the center-of-mass energy region around <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:mrow> <p:mi>W</p:mi> <p:mo>≈</p:mo> <p:mn>2.08</p:mn> </p:mrow> </p:math> GeV, indicating the need for additional reaction mechanisms. On the other hand, the hidden-strange pentaquark-like state <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:mi>N</q:mi> <q:mrow> <q:mo>(</q:mo> <q:mn>2080</q:mn> <q:mo>)</q:mo> </q:mrow> <q:mn>3</q:mn> <q:mo>/</q:mo> <q:msup> <q:mn>2</q:mn> <q:mo>−</q:mo> </q:msup> </q:mrow> </q:math> , which is proposed to be a <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mrow> <r:msup> <r:mi>K</r:mi> <r:mo>*</r:mo> </r:msup> <r:mi mathvariant="normal">Σ</r:mi> </r:mrow> </r:math> molecular state as the strange partner of the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"> <t:mrow> <t:msub> <t:mi>P</t:mi> <t:mi>c</t:mi> </t:msub> <t:mrow> <t:mo>(</t:mo> <t:mn>4457</t:mn> <t:mo>)</t:mo> </t:mrow> </t:mrow> </t:math> hadronic molecule, has been found to play quite active roles in reproducing the data for <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:mrow> <u:msup> <u:mi>K</u:mi> <u:mrow> <u:mo>*</u:mo> <u:mo>+</u:mo> </u:mrow> </u:msup> <u:msup> <u:mi mathvariant="normal">Σ</u:mi> <u:mn>0</u:mn> </u:msup> </u:mrow> <u:mo>,</u:mo> <u:mo> </u:mo> <u:mrow> <u:msup> <u:mi>K</u:mi> <u:mrow> <u:mo>*</u:mo> <u:mn>0</u:mn> </u:mrow> </u:msup> <u:msup> <u:mi mathvariant="normal">Σ</u:mi> <u:mo>+</u:mo> </u:msup> </u:mrow> </u:math> , and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML"> <x:mrow> <x:mi>ϕ</x:mi> <x:mi>p</x:mi> </x:mrow> </x:math> photoproduction reactions. Based on these observations, in the present work, we reanalyze the data for the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML"> <y:mrow> <y:mi>γ</y:mi> <y:mi>p</y:mi> <y:mo>→</y:mo> <y:msup> <y:mi>K</y:mi> <y:mrow> <y:mo>*</y:mo> <y:mo>+</y:mo> </y:mrow> </y:msup> <y:mi mathvariant="normal">Λ</y:mi> </y:mrow> </y:math> reaction by incorporating the pentaquark-like state <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML"> <ab:mrow> <ab:mi>N</ab:mi> <ab:mrow> <ab:mo>(</ab:mo> <ab:mn>2080</ab:mn> <ab:mo>)</ab:mo> </ab:mrow> <ab:mn>3</ab:mn> <ab:mo>/</ab:mo> <ab:msup> <ab:mn>2</ab:mn> <ab:mo>−</ab:mo> </ab:msup> </ab:mrow> </ab:math> in our previously proposed model. The results show that, with the inclusion of the contributions of <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML"> <bb:mrow> <bb:mi>N</bb:mi> <bb:mrow> <bb:mo>(</b