Search for a mirror hidden sector with neutral kaons at NA64

Mirror matter from the dark hidden sector with the same particle content and gauge interactions as in the standard model is still an interesting candidate for dark matter. Several experiments on the search for positronium and neutron oscillations into their mirror partner have been conducted recently. In this work, we consider the transitions <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mi>K</a:mi></a:mrow><a:mrow><a:mn>0</a:mn></a:mrow></a:msup><a:mo>−</a:mo><a:msubsup><a:mrow><a:mi>K</a:mi></a:mrow><a:mrow><a:mi>m</a:mi></a:mrow><a:mrow><a:mn>0</a:mn></a:mrow></a:msubsup></a:mrow></a:math> of a neutral kaon into a hidden mirror kaon. It is shown that their probability can be probed with the sensitivity of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mi>P</c:mi><c:mo stretchy="false">(</c:mo><c:msup><c:mrow><c:mi>K</c:mi></c:mrow><c:mrow><c:mn>0</c:mn></c:mrow></c:msup><c:mo>−</c:mo><c:msubsup><c:mrow><c:mi>K</c:mi></c:mrow><c:mrow><c:mi>m</c:mi></c:mrow><c:mrow><c:mn>0</c:mn></c:mrow></c:msubsup><c:mo stretchy="false">)</c:mo><c:mo>≲</c:mo><c:msup><c:mrow><c:mn>10</c:mn></c:mrow><c:mrow><c:mo>−</c:mo><c:mn>7</c:mn></c:mrow></c:msup></c:mrow></c:math> from the search for missing-energy events in the NA64 experiment at the CERN SPS with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo>∼</g:mo><g:msup><g:mn>10</g:mn><g:mn>11</g:mn></g:msup></g:math> <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>K</i:mi><i:mo>+</i:mo></i:msup></i:math> on target. This would result in a limit on the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msup><k:mi>K</k:mi><k:mn>0</k:mn></k:msup><k:mo>−</k:mo><k:msubsup><k:mi>K</k:mi><k:mi>m</k:mi><k:mn>0</k:mn></k:msubsup></k:math> mixing parameter much stronger than the similar bound estimated from the cosmological considerations.