We calculated transitions of the higher radial excited charmonia $$ \psi (nS) ~ ( n=3,4,5 )$$ to the orbital excited charmonium $$ h_c(1P) $$ with emission of one pion or eta meson. In calculations, the intermediate S- and P-wave charmed meson loops were considered in terms of the nonrelativistic effective field theory. The results indicate that the transitions of interest are dominated by the loops involving the $$ s_l^P=(1/2)^+ $$ charmed mesons, whereas the $$ s_l^P=(1/2)^- $$ charmed meson loops are of minor contributions. The partial decay widths of $$ \psi (nS) \rightarrow h_c \pi ^0 $$ are of the order of 0.01–1 keV. For the case of $$ \psi (nS) \rightarrow h_c \eta $$ , the partial decay widths are from 0.1 to 100 keV, implying the branching ratios from $$ 10^{-5} $$ to $$ 10^{-3} $$ . Moreover, the partial decay widths for $$ \psi (nS) \rightarrow h_c \eta $$ are found to decrease as the $$ \eta $$ - $$ \eta ' $$ mixing angle increases. It is hoped that the present calculated results would be observed in the future experiments.
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"surname": "Zheng",
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"full_name": "Zheng, Yuanxin"
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"surname": "Li",
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"title": "Hidden charmonium decays of $$\\psi (nS)$$ <math> <mrow> <mi>\u03c8</mi> <mo>(</mo> <mi>n</mi> <mi>S</mi> <mo>)</mo> </mrow> </math> through charmed meson loops"
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"value": "We calculated transitions of the higher radial excited charmonia $$ \\psi (nS) ~ ( n=3,4,5 )$$ <math> <mrow> <mi>\u03c8</mi> <mo>(</mo> <mi>n</mi> <mi>S</mi> <mo>)</mo> <mspace width=\"3.33333pt\"></mspace> <mo>(</mo> <mi>n</mi> <mo>=</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>,</mo> <mn>5</mn> <mo>)</mo> </mrow> </math> to the orbital excited charmonium $$ h_c(1P) $$ <math> <mrow> <msub> <mi>h</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>1</mn> <mi>P</mi> <mo>)</mo> </mrow> </mrow> </math> with emission of one pion or eta meson. In calculations, the intermediate S- and P-wave charmed meson loops were considered in terms of the nonrelativistic effective field theory. The results indicate that the transitions of interest are dominated by the loops involving the $$ s_l^P=(1/2)^+ $$ <math> <mrow> <msubsup> <mi>s</mi> <mi>l</mi> <mi>P</mi> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>+</mo> </msup> </mrow> </math> charmed mesons, whereas the $$ s_l^P=(1/2)^- $$ <math> <mrow> <msubsup> <mi>s</mi> <mi>l</mi> <mi>P</mi> </msubsup> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>-</mo> </msup> </mrow> </math> charmed meson loops are of minor contributions. The partial decay widths of $$ \\psi (nS) \\rightarrow h_c \\pi ^0 $$ <math> <mrow> <mi>\u03c8</mi> <mrow> <mo>(</mo> <mi>n</mi> <mi>S</mi> <mo>)</mo> </mrow> <mo>\u2192</mo> <msub> <mi>h</mi> <mi>c</mi> </msub> <msup> <mi>\u03c0</mi> <mn>0</mn> </msup> </mrow> </math> are of the order of 0.01\u20131 keV. For the case of $$ \\psi (nS) \\rightarrow h_c \\eta $$ <math> <mrow> <mi>\u03c8</mi> <mrow> <mo>(</mo> <mi>n</mi> <mi>S</mi> <mo>)</mo> </mrow> <mo>\u2192</mo> <msub> <mi>h</mi> <mi>c</mi> </msub> <mi>\u03b7</mi> </mrow> </math> , the partial decay widths are from 0.1 to 100 keV, implying the branching ratios from $$ 10^{-5} $$ <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </math> to $$ 10^{-3} $$ <math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </math> . Moreover, the partial decay widths for $$ \\psi (nS) \\rightarrow h_c \\eta $$ <math> <mrow> <mi>\u03c8</mi> <mrow> <mo>(</mo> <mi>n</mi> <mi>S</mi> <mo>)</mo> </mrow> <mo>\u2192</mo> <msub> <mi>h</mi> <mi>c</mi> </msub> <mi>\u03b7</mi> </mrow> </math> are found to decrease as the $$ \\eta $$ <math> <mi>\u03b7</mi> </math> - $$ \\eta ' $$ <math> <msup> <mi>\u03b7</mi> <mo>\u2032</mo> </msup> </math> mixing angle increases. It is hoped that the present calculated results would be observed in the future experiments."
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