In addition to the strong and electromagnetic decay modes, the $$\psi (1S,2S)$$ and $$\eta _{c}(1S,2S)$$ can also decay via the weak interaction. Such weak decays can be detected by the high-luminosity heavy-flavor experiments. At present, some of the semileptonic and nonleptonic $$J/\Psi $$ weak decays have been measured at BESIII. Researching for these charmonium weak decays to $$D_{(s)}$$ meson can provide a platform to check of the standard model (SM) and probe new physics (NP). So we investigate the semileptonic and nonleptonic weak decays of $$\psi (1S,2S)$$ and $$\eta _{c}(1S,2S)$$ to $$D_{(s)}$$ within the covariant light-front quark model (CLFQM). With form factors of the transitions $$\psi (1S,2S)\rightarrow D_{(s)}$$ and $$\eta _{c}(1S,2S)\rightarrow D_{(s)}$$ calculated under the CLFQM, we predict and discuss some physical observables, such as the branching ratios, the longitudinal polarizations $$f_{L}$$ and the forward–backward asymmetries $$A_{FB}$$ . One can find that the Cabibbo-favored semi-leptonic decay channels $$\psi (1\,S,2\,S)\rightarrow D_{s}^{-}\ell ^{+}\nu _{\ell }$$ with $$\ell =e,\mu $$ and the nonleptonic decay modes $$\psi (1S,2S)\rightarrow D_{s}^{-}\rho ^{+}$$ have relatively large branching ratios of the order $$\mathcal {O}(10^{-9})$$ , which are most likely to be accessible at the future high-luminosity experiments.
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"title": "Semileptonic and nonleptonic weak decays of $$\\psi (1S,2S)$$ <math> <mrow> <mi>\u03c8</mi> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </math> and $$\\eta _{c}(1S,2S)$$ <math> <mrow> <msub> <mi>\u03b7</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </mrow> </math> to $$D_{(s)}$$ <math> <msub> <mi>D</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msub> </math> in the covariant light-front approach"
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"abstracts": [
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"source": "Springer",
"value": "In addition to the strong and electromagnetic decay modes, the $$\\psi (1S,2S)$$ <math> <mrow> <mi>\u03c8</mi> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </math> and $$\\eta _{c}(1S,2S)$$ <math> <mrow> <msub> <mi>\u03b7</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </mrow> </math> can also decay via the weak interaction. Such weak decays can be detected by the high-luminosity heavy-flavor experiments. At present, some of the semileptonic and nonleptonic $$J/\\Psi $$ <math> <mrow> <mi>J</mi> <mo>/</mo> <mi>\u03a8</mi> </mrow> </math> weak decays have been measured at BESIII. Researching for these charmonium weak decays to $$D_{(s)}$$ <math> <msub> <mi>D</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msub> </math> meson can provide a platform to check of the standard model (SM) and probe new physics (NP). So we investigate the semileptonic and nonleptonic weak decays of $$\\psi (1S,2S)$$ <math> <mrow> <mi>\u03c8</mi> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </math> and $$\\eta _{c}(1S,2S)$$ <math> <mrow> <msub> <mi>\u03b7</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> </mrow> </math> to $$D_{(s)}$$ <math> <msub> <mi>D</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msub> </math> within the covariant light-front quark model (CLFQM). With form factors of the transitions $$\\psi (1S,2S)\\rightarrow D_{(s)}$$ <math> <mrow> <mi>\u03c8</mi> <mrow> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> <mo>\u2192</mo> <msub> <mi>D</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msub> </mrow> </math> and $$\\eta _{c}(1S,2S)\\rightarrow D_{(s)}$$ <math> <mrow> <msub> <mi>\u03b7</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> <mo>\u2192</mo> <msub> <mi>D</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msub> </mrow> </math> calculated under the CLFQM, we predict and discuss some physical observables, such as the branching ratios, the longitudinal polarizations $$f_{L}$$ <math> <msub> <mi>f</mi> <mi>L</mi> </msub> </math> and the forward\u2013backward asymmetries $$A_{FB}$$ <math> <msub> <mi>A</mi> <mrow> <mi>FB</mi> </mrow> </msub> </math> . One can find that the Cabibbo-favored semi-leptonic decay channels $$\\psi (1\\,S,2\\,S)\\rightarrow D_{s}^{-}\\ell ^{+}\\nu _{\\ell }$$ <math> <mrow> <mi>\u03c8</mi> <mrow> <mo>(</mo> <mn>1</mn> <mspace width=\"0.166667em\"></mspace> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mspace width=\"0.166667em\"></mspace> <mi>S</mi> <mo>)</mo> </mrow> <mo>\u2192</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>-</mo> </msubsup> <msup> <mi>\u2113</mi> <mo>+</mo> </msup> <msub> <mi>\u03bd</mi> <mi>\u2113</mi> </msub> </mrow> </math> with $$\\ell =e,\\mu $$ <math> <mrow> <mi>\u2113</mi> <mo>=</mo> <mi>e</mi> <mo>,</mo> <mi>\u03bc</mi> </mrow> </math> and the nonleptonic decay modes $$\\psi (1S,2S)\\rightarrow D_{s}^{-}\\rho ^{+}$$ <math> <mrow> <mi>\u03c8</mi> <mrow> <mo>(</mo> <mn>1</mn> <mi>S</mi> <mo>,</mo> <mn>2</mn> <mi>S</mi> <mo>)</mo> </mrow> <mo>\u2192</mo> <msubsup> <mi>D</mi> <mrow> <mi>s</mi> </mrow> <mo>-</mo> </msubsup> <msup> <mi>\u03c1</mi> <mo>+</mo> </msup> </mrow> </math> have relatively large branching ratios of the order $$\\mathcal {O}(10^{-9})$$ <math> <mrow> <mi>O</mi> <mo>(</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>9</mn> </mrow> </msup> <mo>)</mo> </mrow> </math> , which are most likely to be accessible at the future high-luminosity experiments."
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