We perform a calculation of the mass distribution in the $$\psi (3770) \rightarrow \gamma D {\bar{D}}$$ decay, studying both the $$D^+ D^- $$ and $$D^0 {\bar{D}}^0 $$ decays. The electromagnetic interaction is such that the tree level amplitude is null for the neutral channel, which forces the $$\psi (3770) \rightarrow \gamma D^0 {\bar{D}}^0$$ transition to go through a loop involving the $$D^+ D^- \rightarrow D^0 {\bar{D}}^0$$ scattering amplitude. We take the results for this amplitude from a theoretical model that predicts a $$D {\bar{D}}$$ bound state and find a $$D^0 {\bar{D}}^0 $$ mass distribution in the decay drastically different than phase space. The rates obtained are relatively large and the experiment is easily feasible in the present BESIII facility. The performance of this experiment could provide an answer to the issue of this much searched for state, which is the analogue of the $$f_0(980)$$ resonance.
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"title": "Searching for a $$D {\\bar{D}}$$ <math><mrow><mi>D</mi><mover><mrow><mi>D</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow></math> bound state with the $$\\psi (3770) \\rightarrow \\gamma D^0 {\\bar{D}}^0$$ <math><mrow><mi>\u03c8</mi><mrow><mo>(</mo><mn>3770</mn><mo>)</mo></mrow><mo>\u2192</mo><mi>\u03b3</mi><msup><mi>D</mi><mn>0</mn></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mn>0</mn></msup></mrow></math> decay"
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"source": "Springer",
"value": "We perform a calculation of the mass distribution in the $$\\psi (3770) \\rightarrow \\gamma D {\\bar{D}}$$ <math><mrow><mi>\u03c8</mi><mo>(</mo><mn>3770</mn><mo>)</mo><mo>\u2192</mo><mi>\u03b3</mi><mi>D</mi><mover><mrow><mi>D</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow></math> decay, studying both the $$D^+ D^- $$ <math><mrow><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>-</mo></msup></mrow></math> and $$D^0 {\\bar{D}}^0 $$ <math><mrow><msup><mi>D</mi><mn>0</mn></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mn>0</mn></msup></mrow></math> decays. The electromagnetic interaction is such that the tree level amplitude is null for the neutral channel, which forces the $$\\psi (3770) \\rightarrow \\gamma D^0 {\\bar{D}}^0$$ <math><mrow><mi>\u03c8</mi><mrow><mo>(</mo><mn>3770</mn><mo>)</mo></mrow><mo>\u2192</mo><mi>\u03b3</mi><msup><mi>D</mi><mn>0</mn></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mn>0</mn></msup></mrow></math> transition to go through a loop involving the $$D^+ D^- \\rightarrow D^0 {\\bar{D}}^0$$ <math><mrow><msup><mi>D</mi><mo>+</mo></msup><msup><mi>D</mi><mo>-</mo></msup><mo>\u2192</mo><msup><mi>D</mi><mn>0</mn></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mn>0</mn></msup></mrow></math> scattering amplitude. We take the results for this amplitude from a theoretical model that predicts a $$D {\\bar{D}}$$ <math><mrow><mi>D</mi><mover><mrow><mi>D</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow></math> bound state and find a $$D^0 {\\bar{D}}^0 $$ <math><mrow><msup><mi>D</mi><mn>0</mn></msup><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mn>0</mn></msup></mrow></math> mass distribution in the decay drastically different than phase space. The rates obtained are relatively large and the experiment is easily feasible in the present BESIII facility. The performance of this experiment could provide an answer to the issue of this much searched for state, which is the analogue of the $$f_0(980)$$ <math><mrow><msub><mi>f</mi><mn>0</mn></msub><mrow><mo>(</mo><mn>980</mn><mo>)</mo></mrow></mrow></math> resonance."
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