Production of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi mathvariant="normal">Ξ</mml:mi> <mml:mo>(</mml:mo> <mml:mn>1530</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> in the <mml:math xmlns:mml="http://www.w3.o

In the present work, we examine the production of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi mathvariant="normal">Ξ</a:mi> <a:mo>(</a:mo> <a:mn>1530</a:mn> <a:mo>)</a:mo> </a:mrow> </a:math> in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msup> <c:mi>K</c:mi> <c:mo>−</c:mo> </c:msup> <c:mi>p</c:mi> <c:mo>→</c:mo> <c:msup> <c:mi>K</c:mi> <c:mo>+</c:mo> </c:msup> <c:mi mathvariant="normal">Ξ</c:mi> <c:msup> <c:mrow> <c:mo>(</c:mo> <c:mn>1530</c:mn> <c:mo>)</c:mo> </c:mrow> <c:mo>−</c:mo> </c:msup> </c:mrow> </c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mrow> <e:msup> <e:mi>K</e:mi> <e:mo>−</e:mo> </e:msup> <e:mi>p</e:mi> <e:mo>→</e:mo> <e:msup> <e:mi>K</e:mi> <e:mn>0</e:mn> </e:msup> <e:mi mathvariant="normal">Ξ</e:mi> <e:msup> <e:mrow> <e:mo>(</e:mo> <e:mn>1530</e:mn> <e:mo>)</e:mo> </e:mrow> <e:mn>0</e:mn> </e:msup> </e:mrow> </e:math> reactions utilizing an effective Lagrangian approach. To accurately fit the cross sections for both processes, we include nine <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi mathvariant="normal">Λ</g:mi> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi mathvariant="normal">Σ</i:mi> </i:math> hyperons and their resonances in both <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi>s</k:mi> </k:math> - and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mi>u</l:mi> </l:math> -channel processes. Considering the discrepancy of the measured cross sections for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msup> <m:mi>K</m:mi> <m:mo>−</m:mo> </m:msup> <m:mi>p</m:mi> <m:mo>→</m:mo> <m:msup> <m:mi>K</m:mi> <m:mo>+</m:mo> </m:msup> <m:mi mathvariant="normal">Ξ</m:mi> <m:msup> <m:mrow> <m:mo>(</m:mo> <m:mn>1530</m:mn> <m:mo>)</m:mo> </m:mrow> <m:mo>−</m:mo> </m:msup> </m:mrow> </m:math> within the range <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:mrow> <o:msqrt> <o:mi>s</o:mi> </o:msqrt> <o:mo>=</o:mo> <o:mrow> <o:mo>[</o:mo> <o:mn>2.087</o:mn> <o:mo>,</o:mo> <o:mn>2.168</o:mn> <o:mo>]</o:mo> </o:mrow> <o:mspace width="4pt"/> <o:mi>GeV</o:mi> </o:mrow> </o:math> , we employ two distinct fitting strategies: a uniform weighting scheme (Model A) and a different weighting approach (Model B). A comparative analysis suggests that Model A yields a superior global agreement with experimental data compared to Model B. Beyond fitting the cross sections, we also estimate the individual contributions from various intermediate states. Our results reveal that the cross section arising from the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:mi mathvariant="normal">Σ</q:mi> <q:mo>(</q:mo> <q:mn>1193</q:mn> <q:mo>)</q:mo> </q:mrow> </q:math> intermediate process is dominant. Furthermore, we predict different cross sections for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:mrow> <s:msup> <s:mi>K</s:mi> <s:mo>−</s:mo> </s:msup> <s:mi>p</s:mi> <s:mo>→</s:mo> <s:msup> <s:mi>K</s:mi> <s:mo>+</s:mo> </s:msup> <s:mi mathvariant="normal">Ξ</s:mi> <s:msup> <s:mrow> <s:mo>(</s:mo> <s:mn>1530</s:mn> <s:mo>)</s:mo> </s:mrow> <s:mo>−</s:mo> </s:msup> </s:mrow> </s:math> and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:mrow> <u:msup> <u:mi>K</u:mi> <u:mo>−</u:mo> </u:msup> <u:mi>p</u:mi> <u:mo>→</u:mo> <u:msup> <u:mi>K</u:mi> <u:mn>0</u:mn> </u:msup> <u:mi mathvariant="normal">Ξ</u:mi> <u:msup> <u:mrow> <u:mo>(</u:mo> <u:mn>1530</u:mn> <u:mo>)</u:mo> </u:mrow> <u:mn>0</u:mn> </u:msup> </u:mrow> </u:math> at several representative center-of-mass energies, providing testable predictions for forthcoming J-PARC experiments.