Studying the KΛ strong interaction using femtoscopic correlation functions and the N*(1535)

We investigate the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>K</a:mi><a:mi mathvariant="normal">Λ</a:mi></a:math> strong interaction dynamics around the energy region of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msup><d:mi>N</d:mi><d:mo>*</d:mo></d:msup><d:mo stretchy="false">(</d:mo><d:mn>1535</d:mn><d:mo stretchy="false">)</d:mo></d:math> resonance through femtoscopic correlation functions within the Koonin-Pratt formalism, where coupled-channel effects of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>π</h:mi><h:mi>N</h:mi></h:math>, <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>K</j:mi><j:mi mathvariant="normal">Λ</j:mi></j:math>, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>K</m:mi><m:mi mathvariant="normal">Σ</m:mi></m:math> and <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>η</p:mi><p:mi>N</p:mi></p:math> channels are taken into account, by means of which the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msup><r:mi>N</r:mi><r:mo>*</r:mo></r:msup><r:mo stretchy="false">(</r:mo><r:mn>1535</r:mn><r:mo stretchy="false">)</r:mo></r:math> resonance can be dynamically generated in the chiral unitary approach. Two-body scattering amplitudes are calculated using the chiral unitary approach, and the corresponding wave functions and correlation functions are obtained. Our analysis shows that the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>π</v:mi><v:mi>N</v:mi></v:math> channel becomes important to the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:msup><x:mi>K</x:mi><x:mo>+</x:mo></x:msup><x:mi mathvariant="normal">Λ</x:mi></x:math> correlation function through coupled channel effects, even if its mass threshold is far from the energy region of the <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msup><ab:mi>N</ab:mi><ab:mo>*</ab:mo></ab:msup><ab:mo stretchy="false">(</ab:mo><ab:mn>1535</ab:mn><ab:mo stretchy="false">)</ab:mo></ab:math>. Furthermore, with the picture that the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mi>N</eb:mi><eb:mo>*</eb:mo></eb:msup><eb:mo stretchy="false">(</eb:mo><eb:mn>1535</eb:mn><eb:mo stretchy="false">)</eb:mo></eb:math> is a dynamically generated state, we can get a good reproduction of the experimental data on the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msup><ib:mi>K</ib:mi><ib:mo>+</ib:mo></ib:msup><ib:mi mathvariant="normal">Λ</ib:mi></ib:math> correlation function. This work establishes femtoscopic correlation functions as a sensitive probe for coupled-channel dynamics and validates the Koonin-Pratt framework in multichannel hadronic systems, offering critical insights into some exotic hadron states and strong interaction mechanisms.