<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> </mml:math> -wave kaon-nucleon interactions from lattice QCD at the physical point

We investigate S-wave kaon-nucleon ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>K</a:mi> <a:mi>N</a:mi> </a:mrow> </a:math> ) interactions with strangeness <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>S</c:mi> <c:mo>=</c:mo> <c:mo>+</c:mo> <c:mn>1</c:mn> </c:math> in lattice QCD using the time-dependent HAL QCD method. Employing the ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mn>2</e:mn> <e:mo>+</e:mo> <e:mn>1</e:mn> </e:mrow> </e:math> )-flavor gauge configuration with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>m</g:mi> <g:mi>π</g:mi> </g:msub> <g:mo>≈</g:mo> <g:mn>137</g:mn> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>MeV</g:mi> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>m</i:mi> <i:mi>K</i:mi> </i:msub> <i:mo>≈</i:mo> <i:mn>502</i:mn> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>MeV</i:mi> </i:math> , we calculate the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi>K</k:mi> <k:mi>N</k:mi> </k:mrow> </k:math> potentials at the leading order in the derivative expansion. The potentials in both isospin channels ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>I</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>I</o:mi> <o:mo>=</o:mo> <o:mn>0</o:mn> </o:math> ) exhibit repulsion at short distances, while only the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>I</q:mi> <q:mo>=</q:mo> <q:mn>0</q:mn> </q:math> potential has a small attractive pocket at intermediate distances. The phase shifts computed from these potentials show no signals corresponding to resonances or bound states in both isospin channels, suggesting the absence of the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msup> <s:mi mathvariant="normal">Θ</s:mi> <s:mo>+</s:mo> </s:msup> <s:mo stretchy="false">(</s:mo> <s:mn>1540</s:mn> <s:mo stretchy="false">)</s:mo> </s:math> pentaquark in the S-wave <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mrow> <x:mi>K</x:mi> <x:mi>N</x:mi> </x:mrow> </x:math> systems. The scattering lengths result in <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mrow> <z:msubsup> <z:mrow> <z:mi>a</z:mi> </z:mrow> <z:mrow> <z:mn>0</z:mn> </z:mrow> <z:mrow> <z:mi>I</z:mi> <z:mo>=</z:mo> <z:mn>1</z:mn> </z:mrow> </z:msubsup> <z:mo>=</z:mo> <z:mo>−</z:mo> <z:mn>0.226</z:mn> <z:mo stretchy="false">(</z:mo> <z:mn>5</z:mn> <z:mo stretchy="false">)</z:mo> <z:msubsup> <z:mrow> <z:mo stretchy="false">(</z:mo> </z:mrow> <z:mrow> <z:mo>−</z:mo> <z:mn>0</z:mn> </z:mrow> <z:mrow> <z:mo>+</z:mo> <z:mn>5</z:mn> </z:mrow> </z:msubsup> <z:mo stretchy="false">)</z:mo> <z:mtext> </z:mtext> <z:mtext> </z:mtext> <z:mi>fm</z:mi> </z:mrow> </z:math> and <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:msubsup> <fb:mi>a</fb:mi> <fb:mn>0</fb:mn> <fb:mrow> <fb:mi>I</fb:mi> <fb:mo>=</fb:mo> <fb:mn>0</fb:mn> </fb:mrow> </fb:msubsup> <fb:mo>=</fb:mo> <fb:mo>+</fb:mo> <fb:mn>0.028</fb:mn> <fb:mo stretchy="false">(</fb:mo> <fb:mn>61</fb:mn> <fb:mo stretchy="false">)</fb:mo> <fb:msubsup> <fb:mo stretchy="false">(</fb:mo> <fb:mrow> <fb:mo>−</fb:mo> <fb:mn>26</fb:mn> </fb:mrow> <fb:mrow> <fb:mo>+</fb:mo> <fb:mn>3</fb:mn> </fb:mrow> </fb:msubsup> <fb:mo stretchy="false">)</fb:mo> <fb:mtext> </fb:mtext> <fb:mtext> </fb:mtext> <fb:mi>fm</fb:mi> </fb:math> . Our results of the S-wave cross sections for <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:mi>I</lb:mi> <lb:mo>=</lb:mo> <lb:mn>1</lb:mn> </lb:math> are consistent with some of the experimental data within <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:mn>2</nb:mn> <nb:mi>–</nb:mi> <nb:mn>3</nb:mn> <nb:mi>σ</nb:mi> </nb:math> , while they deviate from others. The results for <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"> <pb:mi>I</pb:mi> <pb:mo>=</pb:mo> <pb:mn>0</pb:mn> </pb:math> , combined with recent studies on chiral perturbation theory, suggest that the scattering amplitudes in this channel are dominated by P-wave components rather than S-wave.