Analysis of the data on differential cross sections and spin density matrix elements for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>γ</mml:mi><mml:mi>p</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>ρ</mml:mi><mml:mn>0</m

The newly published data on spin density matrix elements from the GlueX Collaboration, along with the previously released differential cross-section data from the CLAS Collaboration and the other two experiments 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>ρ</a:mi><a:mn>0</a:mn></a:msup><a:mi>p</a:mi></a:mrow></a:math> reaction, are systematically investigated using an effective Lagrangian approach within the tree-level Born approximation. The model combines contributions from <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>t</b:mi></b:math>-channel meson exchanges (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>π</c:mi><c:mo>,</c:mo><c:mo> </c:mo><c:mi>η</c:mi></c:math>, and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>f</d:mi><d:mn>2</d:mn></d:msub></d:math>), <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>s</e:mi></e:math>-channel nucleon (<f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>N</f:mi></f:math>) and nucleon resonance (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:msup><g:mi>N</g:mi><g:mo>*</g:mo></g:msup></g:math>) exchanges, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>u</h:mi></h:math>-channel <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>N</i:mi></i:math> exchange, and a generalized contact term to construct the scattering amplitudes. Regge propagators are employed for <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>t</j:mi></j:math>-channel amplitudes to incorporate the contributions from mesons with various spins lying on the same trajectories. The analysis shows that the background contributions, dominated by the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:msub><k:mi>f</k:mi><k:mn>2</k:mn></k:msub></k:math>-trajectory exchange, provide a satisfactory description of the data in the high-energy and forward-angle regions. The inclusion of specific nucleon resonances, such as <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mi>N</l:mi><l:mrow><l:mo>(</l:mo><l:mn>2100</l:mn><l:mo>)</l:mo></l:mrow><l:mn>1</l:mn><l:mo>/</l:mo><l:msup><l:mn>2</l:mn><l:mo>+</l:mo></l:msup></l:mrow><l:mo>,</l:mo><l:mo> </l:mo><l:mrow><l:mi>N</l:mi><l:mrow><l:mo>(</l:mo><l:mn>2060</l:mn><l:mo>)</l:mo></l:mrow><l:mn>5</l:mn><l:mo>/</l:mo><l:msup><l:mn>2</l:mn><l:mo>−</l:mo></l:msup></l:mrow></l:math>, or <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi mathvariant="normal">Δ</m:mi><m:mrow><m:mo>(</m:mo><m:mn>2000</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>, significantly improves the description of the differential cross-section data at near-perpendicular scattering angles in the low-energy region. Predictions of photon beam and target nucleon asymmetries are provided, offering valuable insights to discriminate reaction mechanisms when corresponding data become available in the future.