New approach to finding invisible states in e+e− annihilation and application to BESIII data

We compare precision <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi>e</a:mi><a:mo>+</a:mo></a:msup><a:msup><a:mi>e</a:mi><a:mo>−</a:mo></a:msup><a:mo stretchy="false">→</a:mo><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> cross section measurements by BESIII in the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi>E</d:mi><d:mi>cm</d:mi></d:msub><d:mo>=</d:mo><d:mn>3.8</d:mn><d:mi>–</d:mi><d:mn>4.6</d:mn><d:mtext> </d:mtext><d:mtext> </d:mtext><d:mi>GeV</d:mi></d:math> range, to predictions based on measured <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msub><f:mi>R</f:mi><f:mrow><f:mi>had</f:mi></f:mrow></f:msub></f:math> data. The consistency is poor (p-value <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mo><</h:mo><h:mn>0.012</h:mn></h:math>). Allowing for resonance contributions not seen in <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi>R</j:mi><j:mrow><j:mi>had</j:mi></j:mrow></j:msub></j:math> gives an excellent fit. The <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mn>4.6</l:mn><l:mi>σ</l:mi></l:math> state required at 4421 MeV suggests that a substantial portion of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>ψ</n:mi><n:mo stretchy="false">(</n:mo><n:mn>4415</n:mn><n:mo stretchy="false">)</n:mo></n:math> decays are not identified, while the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mn>3.2</r:mn><r:mi>σ</r:mi></r:math> structure at 4211 MeV, if confirmed, points to a new, very narrow resonance. This analysis shows the power of precision <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msup><t:mi>e</t:mi><t:mo>+</t:mo></t:msup><t:msup><t:mi>e</t:mi><t:mo>−</t:mo></t:msup><t:mo stretchy="false">→</t:mo><t:msup><t:mi>μ</t:mi><t:mo>+</t:mo></t:msup><t:msup><t:mi>μ</t:mi><t:mo>−</t:mo></t:msup></t:math> measurements to uncover or probe otherwise difficult to access states.