Prompt diphoton production compared to measurements at 13 TeV in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mm

We perform an in-depth comparative analysis of unintegrated parton distribution function (UPDF) models for isolated prompt diphoton production in proton-proton collisions at <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msqrt> <a:mi>s</a:mi> </a:msqrt> <a:mo>=</a:mo> <a:mn>13</a:mn> <a:mtext> </a:mtext> <a:mtext> </a:mtext> <a:mi>TeV</a:mi> </a:math> within the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>k</c:mi> </c:mrow> <c:mrow> <c:mi>T</c:mi> </c:mrow> </c:msub> </c:mrow> </c:math> -factorization framework. Predictions are obtained with three UPDF approaches: parton branching (PB), NLO-MRW, and modified KMRW (MKMRW). Tree-level <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>q</e:mi> <e:mo>+</e:mo> <e:mover accent="true"> <e:mi>q</e:mi> <e:mo stretchy="false">¯</e:mo> </e:mover> <e:mo stretchy="false">→</e:mo> <e:mi>γ</e:mi> <e:mo>+</e:mo> <e:mi>γ</e:mi> </e:math> , <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mi>q</j:mi> <j:mo>+</j:mo> <j:mover accent="true"> <j:mi>q</j:mi> <j:mo stretchy="false">¯</j:mo> </j:mover> <j:mo stretchy="false">→</j:mo> <j:mi>γ</j:mi> <j:mo>+</j:mo> <j:mi>γ</j:mi> <j:mo>+</j:mo> <j:mi>g</j:mi> </j:math> , and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>q</o:mi> <o:mo>+</o:mo> <o:mi>g</o:mi> <o:mo stretchy="false">→</o:mo> <o:mi>γ</o:mi> <o:mo>+</o:mo> <o:mi>γ</o:mi> <o:mo>+</o:mo> <o:mi>q</o:mi> </o:math> subprocesses are generated with using off shell initial states; the loop-induced <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>g</r:mi> <r:mo>+</r:mo> <r:mi>g</r:mi> <r:mo stretchy="false">→</r:mo> <r:mi>γ</r:mi> <r:mo>+</r:mo> <r:mi>γ</r:mi> </r:math> channel is evaluated independently. We compare differential cross sections with ATLAS measurements across a broad set of observables, including the photon transverse momenta, diphoton invariant mass and transverse momentum, the Collins-Soper angle, acoplanarity, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msubsup> <u:mi>ϕ</u:mi> <u:mi>η</u:mi> <u:mo>*</u:mo> </u:msubsup> </u:math> , and a transverse thrust-related variable. This comparative study quantifies the impact of the UPDF choice on the diphoton spectra. We find that the PB model provides the most consistent agreement over all distributions, whereas NLO-MRW tends to overshoot in regions correlated with larger factorization scales and MKMRW generally undershoots due to stronger Sudakov suppression. With standard scale variations, our results indicate that <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>k</w:mi> <w:mi>t</w:mi> </w:msub> </w:math> -factorization with PB UPDFs can accurately describe diphoton production, while fixed-order collinear predictions typically require higher-order corrections together with parton-shower effects to achieve a comparable description.