First Observation of a Three-Resonance Structure in e+e−→Nonopen Charm Hadrons

This is the authors' abstract. We don't add key points for this paper.

We report the measurement of the inclusive cross sections for <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msup><a:mrow><a:mi>e</a:mi></a:mrow><a:mrow><a:mo>+</a:mo></a:mrow></a:msup><a:msup><a:mrow><a:mi>e</a:mi></a:mrow><a:mrow><a:mo>−</a:mo></a:mrow></a:msup><a:mo stretchy="false">→</a:mo><a:mi>nOCH</a:mi></a:mrow></a:math> (where nOCH denotes non-open charm hadrons) with improved precision at center-of-mass (c.m.) energies from 3.645 to 3.871 GeV. We observe three resonances: <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:mi mathvariant="script">R</d:mi><d:mo stretchy="false">(</d:mo><d:mn>3760</d:mn><d:mo stretchy="false">)</d:mo></d:mrow></d:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="script">R</i:mi><i:mo stretchy="false">(</i:mo><i:mn>3780</i:mn><i:mo stretchy="false">)</i:mo></i:math>, and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi mathvariant="script">R</n:mi><n:mo stretchy="false">(</n:mo><n:mn>3810</n:mn><n:mo stretchy="false">)</n:mo></n:math> with significances of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mn>8.1</s:mn><s:mi>σ</s:mi></s:math>, <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mn>13.7</u:mn><u:mi>σ</u:mi></u:math>, and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mn>8.8</w:mn><w:mi>σ</w:mi></w:math>, respectively. The <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:mi mathvariant="script">R</y:mi><y:mo stretchy="false">(</y:mo><y:mn>3810</y:mn><y:mo stretchy="false">)</y:mo></y:math> state is observed for the first time, while the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi mathvariant="script">R</db:mi><db:mo stretchy="false">(</db:mo><db:mn>3760</db:mn><db:mo stretchy="false">)</db:mo></db:math> and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi mathvariant="script">R</ib:mi><ib:mo stretchy="false">(</ib:mo><ib:mn>3780</ib:mn><ib:mo stretchy="false">)</ib:mo></ib:math> states are observed for the first time in the nOCH cross sections. Two sets of resonance parameters describe the energy-dependent line shape of the cross sections well. In set I [set II], the <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi mathvariant="script">R</nb:mi><nb:mo stretchy="false">(</nb:mo><nb:mn>3810</nb:mn><nb:mo stretchy="false">)</nb:mo></nb:math> state has mass (<sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"><sb:mrow><sb:mn>3805.7</sb:mn><sb:mo>±</sb:mo><sb:mn>1.1</sb:mn><sb:mo>±</sb:mo><sb:mn>2.7</sb:mn></sb:mrow></sb:math>) <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mrow><ub:mo stretchy="false">[</ub:mo><ub:mo stretchy="false">(</ub:mo><ub:mn>3805.7</ub:mn><ub:mo>±</ub:mo><ub:mn>1.1</ub:mn><ub:mo>±</ub:mo><ub:mn>2.7</ub:mn><ub:mo stretchy="false">)</ub:mo><ub:mo stretchy="false">]</ub:mo><ub:mtext> </ub:mtext><ub:mtext> </ub:mtext><ub:mi>MeV</ub:mi><ub:mo>/</ub:mo><ub:msup><ub:mrow><ub:mi>c</ub:mi></ub:mrow><ub:mrow><ub:mn>2</ub:mn></ub:mrow></ub:msup></ub:mrow></ub:math>, total width (<ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mrow><ac:mn>11.6</ac:mn><ac:mo>±</ac:mo><ac:mn>2.9</ac:mn><ac:mo>±</ac:mo><ac:mn>1.9</ac:mn></ac:mrow></ac:math>) <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:mrow><cc:mo stretchy="false">[</cc:mo><cc:mo stretchy="false">(</cc:mo><cc:mn>11.5</cc:mn><cc:mo>±</cc:mo><cc:mn>2.8</cc:mn><cc:mo>±</cc:mo><cc:mn>1.9</cc:mn><cc:mo stretchy="false">)</cc:mo><cc:mo stretchy="false">]</cc:mo><cc:mtext> </cc:mtext><cc:mtext> </cc:mtext><cc:mi>MeV</cc:mi></cc:mrow></cc:math>, and an electronic width multiplied by the nOCH decay branching fraction of (<ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:mrow><ic:mn>10.9</ic:mn><ic:mo>±</ic:mo><ic:mn>3.8</ic:mn><ic:mo>±</ic:mo><ic:mn>2.5</ic:mn></ic:mrow></ic:math>) <kc:math xmlns:kc="http://www.w3.org/1998/Math/MathML" display="inline"><kc:mrow><kc:mo stretchy="false">[</kc:mo><kc:mo stretchy="false">(</kc:mo><kc:mn>11.0</kc:mn><kc:mo>±</kc:mo><kc:mn>3.4</kc:mn><kc:mo>±</kc:mo><kc:mn>2.5</kc:mn><kc:mo stretchy="false">)</kc:mo><kc:mo stretchy="false">]</kc:mo><kc:mtext> </kc:mtext><kc:mtext> </kc:mtext><kc:mi>eV</kc:mi></kc:mrow></kc:math>. In addition, we measure the branching fractions <qc:math xmlns:qc="http://www.w3.org/1998/Math/MathML" display="inline"><qc:mrow><qc:mi mathvariant="script">B</qc:mi><qc:mo stretchy="false">[</qc:mo><qc:mi mathvariant="script">R</qc:mi><qc:mo stretchy="false">(</qc:mo><qc:mn>3760</qc:mn><qc:mo stretchy="false">)</qc:mo><qc:mo stretchy="false">→</qc:mo><qc:mi>nOCH</qc:mi><qc:mo stretchy="false">]</qc:mo><qc:mo>=</qc:mo><qc:mo stretchy="false">(</qc:mo><qc:mn>25.2</qc:mn><qc:mo>±</qc:mo><qc:mn>16.1</qc:mn><qc:mo>±</qc:mo><qc:mn>30.4</qc:mn><qc:mo stretchy="false">)</qc:mo><qc:mo>%</qc:mo><qc:mo stretchy="false">[</qc:mo><qc:mo stretchy="false">(</qc:mo><qc:mn>6.4</qc:mn><qc:mo>±</qc:mo><qc:mn>4.8</qc:mn><qc:mo>±</qc:mo><qc:mn>7.7</qc:mn><qc:mo stretchy="false">)</qc:mo><qc:mo>%</qc:mo><qc:mo stretchy="false">]</qc:mo></qc:mrow></qc:math> and <fd:math xmlns:fd="http://www.w3.org/1998/Math/MathML" display="inline"><fd:mrow><fd:mi mathvariant="script">B</fd:mi><fd:mo stretchy="false">[</fd:mo><fd:mi mathvariant="script">R</fd:mi><fd:mo stretchy="false">(</fd:mo><fd:mn>3780</fd:mn><fd:mo stretchy="false">)</fd:mo><fd:mo stretchy="false">→</fd:mo><fd:mi>nOCH</fd:mi><fd:mo stretchy="false">]</fd:mo><fd:mo>=</fd:mo><fd:mo stretchy="false">(</fd:mo><fd:mn>12.3</fd:mn><fd:mo>±</fd:mo><fd:mn>6.6</fd:mn><fd:mo>±</fd:mo><fd:mn>8.3</fd:mn><fd:mo stretchy="false">)</fd:mo><fd:mo>%</fd:mo><fd:mo stretchy="false">[</fd:mo><fd:mo stretchy="false">(</fd:mo><fd:mn>10.4</fd:mn><fd:mo>±</fd:mo><fd:mn>4.8</fd:mn><fd:mo>±</fd:mo><fd:mn>7.0</fd:mn><fd:mo stretchy="false">)</fd:mo><fd:mo>%</fd:mo><fd:mo stretchy="false">]</fd:mo></fd:mrow></fd:math> for the first time. The <ud:math xmlns:ud="http://www.w3.org/1998/Math/MathML" display="inline"><ud:mi mathvariant="script">R</ud:mi><ud:mo stretchy="false">(</ud:mo><ud:mn>3760</ud:mn><ud:mo stretchy="false">)</ud:mo></ud:math> state can be interpreted as an open-charm (OC) molecular state, but containing a simple four-quark state component. The <zd:math xmlns:zd="http://www.w3.org/1998/Math/MathML" display="inline"><zd:mi mathvariant="script">R</zd:mi><zd:mo stretchy="false">(</zd:mo><zd:mn>3810</zd:mn><zd:mo stretchy="false">)</zd:mo></zd:math> state can be interpreted as a hadrocharmonium state.