Feasibility study of true muonium discovery with the CERN-SPS H4 positron beam

True muonium (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>μ</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>μ</a:mi><a:mo>−</a:mo></a:msup></a:math>) is one of the heaviest and smallest electromagnetic bound states not containing hadrons, and has never been observed so far. In this work we show that the spin-1 TM state (ortho-TM) can be observed at a discovery level of significance in three months at the CERN SPS North-Area H4A beam line, using 43.7 GeV secondary positrons. In this way, by impinging the positrons on multiple thin low-Z targets, ortho-TM, which decays predominantly to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>e</c:mi><c:mo>+</c:mo></c:msup><c:msup><c:mi>e</c:mi><c:mo>−</c:mo></c:msup></c:math>, can be produced from <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>e</e:mi><e:mo>+</e:mo></e:msup><e:msup><e:mi>e</e:mi><e:mo>−</e:mo></e:msup><e:mo stretchy="false">→</e:mo><e:mi>TM</e:mi></e:math> interaction on resonance (<h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msqrt><h:mi>s</h:mi></h:msqrt><h:mo>∼</h:mo><h:mn>2</h:mn><h:msub><h:mi>m</h:mi><h:mi>μ</h:mi></h:msub></h:math>). Published by the American Physical Society 2024