Hadronic decays of possible pseudoscalar P -wave DD¯*/D¯D…

Recently, the new structure <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>G</a:mi><a:mo stretchy="false">(</a:mo><a:mn>3900</a:mn><a:mo stretchy="false">)</a:mo></a:math> observed by the BESIII Collaboration in the <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>D</e:mi><e:mover accent="true"><e:mi>D</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math> was identified to be the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>P</j:mi></j:math>-wave <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>D</l:mi><l:msup><l:mover accent="true"><l:mi>D</l:mi><l:mo stretchy="false">¯</l:mo></l:mover><l:mo>*</l:mo></l:msup><l:mo>/</l:mo><l:mover accent="true"><l:mi>D</l:mi><l:mo stretchy="false">¯</l:mo></l:mover><l:msup><l:mi>D</l:mi><l:mo>*</l:mo></l:msup></l:math> vector molecular resonance using a unified meson exchange model. Apart from the vector <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mi>P</r:mi></r:math>-wave state, a possible pseudoscalar <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>P</t:mi></t:math>-wave molecular state of the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mi>D</v:mi><v:msup><v:mover accent="true"><v:mi>D</v:mi><v:mo stretchy="false">¯</v:mo></v:mover><v:mo>*</v:mo></v:msup><v:mo>/</v:mo><v:mover accent="true"><v:mi>D</v:mi><v:mo stretchy="false">¯</v:mo></v:mover><v:msup><v:mi>D</v:mi><v:mo>*</v:mo></v:msup></v:math> [called <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:msub><bb:mi>G</bb:mi><bb:mn>0</bb:mn></bb:msub><bb:mo stretchy="false">(</bb:mo><bb:mn>3900</bb:mn><bb:mo stretchy="false">)</bb:mo></bb:math> for short] was also predicted, which is likely to be observed in future experiments. Within the molecular framework, we calculated the partial decay widths for a series of hadronic decays of the <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msub><fb:mi>G</fb:mi><fb:mn>0</fb:mn></fb:msub></fb:math>, including <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:msub><hb:mi>G</hb:mi><hb:mn>0</hb:mn></hb:msub><hb:mo stretchy="false">→</hb:mo><hb:mi>ω</hb:mi><hb:mo stretchy="false">(</hb:mo><hb:msup><hb:mi>ρ</hb:mi><hb:mn>0</hb:mn></hb:msup><hb:mo stretchy="false">)</hb:mo><hb:mi>J</hb:mi><hb:mo>/</hb:mo><hb:mi>ψ</hb:mi></hb:math>, <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msup><mb:mi>π</mb:mi><mb:mo>+</mb:mo></mb:msup><mb:msup><mb:mi>π</mb:mi><mb:mo>−</mb:mo></mb:msup><mb:msub><mb:mi>η</mb:mi><mb:mi>c</mb:mi></mb:msub><mb:mo stretchy="false">(</mb:mo><mb:mn>1</mb:mn><mb:mi>S</mb:mi><mb:mo stretchy="false">)</mb:mo></mb:math>, <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:msup><qb:mi>π</qb:mi><qb:mo>+</qb:mo></qb:msup><qb:msup><qb:mi>π</qb:mi><qb:mo>−</qb:mo></qb:msup><qb:msub><qb:mi>χ</qb:mi><qb:mrow><qb:mi>c</qb:mi><qb:mn>1</qb:mn></qb:mrow></qb:msub><qb:mo stretchy="false">(</qb:mo><qb:mn>1</qb:mn><qb:mi>P</qb:mi><qb:mo stretchy="false">)</qb:mo></qb:math>, and <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msup><ub:mi>D</ub:mi><ub:mn>0</ub:mn></ub:msup><ub:msup><ub:mover accent="true"><ub:mi>D</ub:mi><ub:mo stretchy="false">¯</ub:mo></ub:mover><ub:mn>0</ub:mn></ub:msup><ub:msup><ub:mi>π</ub:mi><ub:mn>0</ub:mn></ub:msup></ub:math>. Under present model parameters, the hidden-charm decay modes are dominated by the <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:msub><yb:mi>G</yb:mi><yb:mn>0</yb:mn></yb:msub><yb:mo stretchy="false">→</yb:mo><yb:mi>ω</yb:mi><yb:mi>J</yb:mi><yb:mo>/</yb:mo><yb:mi>ψ</yb:mi></yb:math> and <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:msub><bc:mi>G</bc:mi><bc:mn>0</bc:mn></bc:msub><bc:mo stretchy="false">→</bc:mo><bc:msup><bc:mi>π</bc:mi><bc:mo>+</bc:mo></bc:msup><bc:msup><bc:mi>π</bc:mi><bc:mo>−</bc:mo></bc:msup><bc:msub><bc:mi>η</bc:mi><bc:mi>c</bc:mi></bc:msub><bc:mo stretchy="false">(</bc:mo><bc:mn>1</bc:mn><bc:mi>S</bc:mi><bc:mo stretchy="false">)</bc:mo></bc:math>, and the partial widths can reach 1 MeV and 0.1 MeV, respectively. The open-charm channel <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:msub><gc:mi>G</gc:mi><gc:mn>0</gc:mn></gc:msub><gc:mo stretchy="false">→</gc:mo><gc:msup><gc:mi>D</gc:mi><gc:mn>0</gc:mn></gc:msup><gc:msup><gc:mover accent="true"><gc:mi>D</gc:mi><gc:mo stretchy="false">¯</gc:mo></gc:mover><gc:mn>0</gc:mn></gc:msup><gc:msup><gc:mi>π</gc:mi><gc:mn>0</gc:mn></gc:msup></gc:math> exhibits a rather small decay rate (<lc:math xmlns:lc="http://www.w3.org/1998/Math/MathML" display="inline"><lc:mo>∼</lc:mo><lc:mn>0.1</lc:mn><lc:mtext> </lc:mtext><lc:mtext> </lc:mtext><lc:mi>keV</lc:mi></lc:math>). In terms of our present predictions, we suggest BESIII and Belle II to search for the pseudoscalar <nc:math xmlns:nc="http://www.w3.org/1998/Math/MathML" display="inline"><nc:mi>P</nc:mi></nc:math>-wave <pc:math xmlns:pc="http://www.w3.org/1998/Math/MathML" display="inline"><pc:mi>D</pc:mi><pc:msup><pc:mover accent="true"><pc:mi>D</pc:mi><pc:mo stretchy="false">¯</pc:mo></pc:mover><pc:mo>*</pc:mo></pc:msup><pc:mo>/</pc:mo><pc:mover accent="true"><pc:mi>D</pc:mi><pc:mo stretchy="false">¯</pc:mo></pc:mover><pc:msup><pc:mi>D</pc:mi><pc:mo>*</pc:mo></pc:msup></pc:math> molecular state with <vc:math xmlns:vc="http://www.w3.org/1998/Math/MathML" display="inline"><vc:msup><vc:mi>J</vc:mi><vc:mrow><vc:mi>P</vc:mi><vc:mi>C</vc:mi></vc:mrow></vc:msup><vc:mo>=</vc:mo><vc:msup><vc:mn>0</vc:mn><vc:mrow><vc:mo>−</vc:mo><vc:mo>+</vc:mo></vc:mrow></vc:msup></vc:math> in the hidden-charm processes <xc:math xmlns:xc="http://www.w3.org/1998/Math/MathML" display="inline"><xc:msub><xc:mi>G</xc:mi><xc:mn>0</xc:mn></xc:msub><xc:mo stretchy="false">→</xc:mo><xc:mi>ω</xc:mi><xc:mi>J</xc:mi><xc:mo>/</xc:mo><xc:mi>ψ</xc:mi></xc:math> or <ad:math xmlns:ad="http://www.w3.org/1998/Math/MathML" display="inline"><ad:msub><ad:mi>G</ad:mi><ad:mn>0</ad:mn></ad:msub><ad:mo stretchy="false">→</ad:mo><ad:msup><ad:mi>π</ad:mi><ad:mo>+</ad:mo></ad:msup><ad:msup><ad:mi>π</ad:mi><ad:mo>−</ad:mo></ad:msup><ad:msub><ad:mi>η</ad:mi><ad:mi>c</ad:mi></ad:msub><ad:mo stretchy="false">(</ad:mo><ad:mn>1</ad:mn><ad:mi>S</ad:mi><ad:mo stretchy="false">)</ad:mo></ad:math>.