<p>Using the topological-diagram approach based on SU(3) flavor symmetry, we investigate two-body <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi mathvariant="normal">Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mi mathvariant="bold">B</mi> <mi>S</mi> </math></EquationSource> <EquationSource Format="TEX">\( {\Lambda}_c^{+}\to \textbf{B}S \)</EquationSource> </InlineEquation> decays, where <b>B</b> denotes the final-state baryon and <i>S</i> refers to a light scalar meson, such as <i>f</i><sub>0</sub>/<i>f</i><sub>0</sub>(980), <i>a</i><sub>0</sub>/<i>a</i><sub>0</sub>(980), <i>σ</i><sub>0</sub>/<i>f</i><sub>0</sub>(500), or <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <mi>κ</mi> <mo>/</mo> <msubsup> <mi>K</mi> <mn>0</mn> <mo>∗</mo> </msubsup> <mfenced close=")" open="("> <mn>700</mn> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \kappa /{K}_0^{\ast }(700) \)</EquationSource> </InlineEquation>. Our analysis indicates that interpreting the light scalar mesons as tetraquark states provides a more consistent description of the currently available experimental data. In particular, this framework naturally accommodates the experimentally observed branching fraction <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">B</mi> <mfenced close=")" open="("> <mrow> <msubsup> <mi mathvariant="normal">Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mi mathvariant="normal">Λ</mi> <msubsup> <mi>a</mi> <mn>0</mn> <mo>+</mo> </msubsup> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{B}\left({\Lambda}_c^{+}\to \Lambda {a}_0^{+}\right) \)</EquationSource> </InlineEquation>, which exceeds predictions based solely on long-distance effects by an order of magnitude. Within the tetraquark scenario, we predict <InlineEquation ID="IEq5"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">B</mi> <mfenced close=")" open="("> <mrow> <msubsup> <mi mathvariant="normal">Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi mathvariant="normal">Σ</mi> <mo>+</mo> </msup> <msub> <mi>f</mi> <mn>0</mn> </msub> </mrow> </mfenced> <mo>=</mo> <mfenced close=")" open="("> <mrow> <mn>4.9</mn> <mo>±</mo> <mn>1.9</mn> </mrow> </mfenced> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{B}\left({\Lambda}_c^{+}\to {\Sigma}^{+}{f}_0\right)=\left(4.9\pm 1.9\right)\times {10}^{-2} \)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">B</mi> <mfenced close=")" open="("> <mrow> <msubsup> <mi mathvariant="normal">Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mi>p</mi> <msub> <mi>f</mi> <mn>0</mn> </msub> </mrow> </mfenced> <mo>=</mo> <mfenced close=")" open="("> <mrow> <mn>3.6</mn> <mo>±</mo> <mn>1.4</mn> </mrow> </mfenced> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{B}\left({\Lambda}_c^{+}\to p{f}_0\right)=\left(3.6\pm 1.4\right)\times {10}^{-3} \)</EquationSource> </InlineEquation>. Owing to <i>f</i><sub>0</sub> − <i>σ</i><sub>0</sub> mixing, <InlineEquation ID="IEq7"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">B</mi> <mfenced close=")" open="("> <mrow> <msubsup> <mi mathvariant="normal">Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <msup> <mi mathvariant="normal">Σ</mi> <mo>+</mo> </msup> <msub> <mi>σ</mi> <mn>0</mn> </msub> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{B}\left({\Lambda}_c^{+}\to {\Sigma}^{+}{\sigma}_0\right) \)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">B</mi> <mfenced close=")" open="("> <mrow> <msubsup> <mi mathvariant="normal">Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mi>p</mi> <msub> <mi>σ</mi> <mn>0</mn> </msub> </mrow> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{B}\left({\Lambda}_c^{+}\to p{\sigma}_0\right) \)</EquationSource> </InlineEquation> are suppressed to the levels of 1 × 10<sup><i>−</i>3</sup> and 5 × 10<sup><i>−</i>5</sup>, respectively. These modes therefore provide sensitive probes of the internal structure of the light scalar mesons. More generally, the remaining branching ratios of <InlineEquation ID="IEq9"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi mathvariant="normal">Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mi mathvariant="bold">B</mi> <mi>S</mi> </math></EquationSource> <EquationSource Format="TEX">\( {\Lambda}_c^{+}\to \textbf{B}S \)</EquationSource> </InlineEquation> are found to be comparable to those of <InlineEquation ID="IEq10"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi mathvariant="normal">Λ</mi> <mi>c</mi> <mo>+</mo> </msubsup> <mo>→</mo> <mi mathvariant="bold">B</mi> <mi>M</mi> </math></EquationSource> <EquationSource Format="TEX">\( {\Lambda}_c^{+}\to \textbf{B}M \)</EquationSource> </InlineEquation>, where <i>M</i> denotes a pseudoscalar meson. Their predicted sizes suggest that these decay modes should be accessible to ongoing and near-future experimental studies at BESIII, Belle II, and LHCb.</p>

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Charmed \( {\Lambda}_c^{+} \) baryon decays into light scalar mesons in the topological SU(3)f framework

  • Y. L. Wang,
  • Y. K. Hsiao

摘要

Using the topological-diagram approach based on SU(3) flavor symmetry, we investigate two-body Λ c + B S \( {\Lambda}_c^{+}\to \textbf{B}S \) decays, where B denotes the final-state baryon and S refers to a light scalar meson, such as f0/f0(980), a0/a0(980), σ0/f0(500), or κ / K 0 700 \( \kappa /{K}_0^{\ast }(700) \) . Our analysis indicates that interpreting the light scalar mesons as tetraquark states provides a more consistent description of the currently available experimental data. In particular, this framework naturally accommodates the experimentally observed branching fraction B Λ c + Λ a 0 + \( \mathcal{B}\left({\Lambda}_c^{+}\to \Lambda {a}_0^{+}\right) \) , which exceeds predictions based solely on long-distance effects by an order of magnitude. Within the tetraquark scenario, we predict B Λ c + Σ + f 0 = 4.9 ± 1.9 × 10 2 \( \mathcal{B}\left({\Lambda}_c^{+}\to {\Sigma}^{+}{f}_0\right)=\left(4.9\pm 1.9\right)\times {10}^{-2} \) and B Λ c + p f 0 = 3.6 ± 1.4 × 10 3 \( \mathcal{B}\left({\Lambda}_c^{+}\to p{f}_0\right)=\left(3.6\pm 1.4\right)\times {10}^{-3} \) . Owing to f0σ0 mixing, B Λ c + Σ + σ 0 \( \mathcal{B}\left({\Lambda}_c^{+}\to {\Sigma}^{+}{\sigma}_0\right) \) and B Λ c + p σ 0 \( \mathcal{B}\left({\Lambda}_c^{+}\to p{\sigma}_0\right) \) are suppressed to the levels of 1 × 103 and 5 × 105, respectively. These modes therefore provide sensitive probes of the internal structure of the light scalar mesons. More generally, the remaining branching ratios of Λ c + B S \( {\Lambda}_c^{+}\to \textbf{B}S \) are found to be comparable to those of Λ c + B M \( {\Lambda}_c^{+}\to \textbf{B}M \) , where M denotes a pseudoscalar meson. Their predicted sizes suggest that these decay modes should be accessible to ongoing and near-future experimental studies at BESIII, Belle II, and LHCb.