Color-allowed bottom baryon to s-wave and p-wave charmed baryon nonleptonic decays

Chua, Chun-Khiang

doi:10.1103/PhysRevD.100.034025

Color-allowed bottom baryon to $s$ -wave and $p$ -wave charmed baryon nonleptonic decays

Chun-Khiang Chua (Department of Physics and Center for High Energy Physics Chung Yuan Christian University Chung-Li, Taiwan 320, Republic of China)

We study color allowed bottom baryon to $s$ -wave and $p$ -wave charmed baryon nonleptonic decays in this work. The charmed baryons include $spin − 1 / 2$ and $spin − 3 / 2$ states. Explicitly, we consider $Λ_{b} \to Λ_{c}^{(*, * *)} M^{-}$ , $Ξ_{b} \to Ξ_{c}^{(* *)} M^{-}$ , and $Ω_{b} \to Ω_{c}^{(*, * *)} M^{-}$ decays with $M = π, K, ρ, K^{*}, a_{1}, D, D_{s}, D^{*}, D_{s}^{*}$ , $Λ_{c}^{(*, * *)} = Λ_{c}, Λ_{c} (2595), Λ_{c} (2625), Λ_{c} (2765), Λ_{c} (2940)$ , $Ξ_{c}^{(* *)} = Ξ_{c}, Ξ_{c} (2790), Ξ_{c} (2815)$ and $Ω_{c}^{(*, * *)} = Ω_{c}, Ω_{c} (2770), Ω_{c} (3050), Ω_{c} (3090), Ω_{c} (3120)$ . There are six types of transitions, namely, (i) $B_{b} ({\bar{3}}_{f}, 1 / 2^{+})$ to $B_{c} ({\bar{3}}_{f}, 1 / 2^{+})$ , (ii) $B_{b} (6_{f}, 1 / 2^{+})$ to $B_{c} (6_{f}, 1 / 2^{+})$ , (iii) $B_{b} (6_{f}, 1 / 2^{+})$ to $B_{c} (6_{f}, 3 / 2^{+})$ , (iv) $B_{b} (6_{f}, 1 / 2^{+})$ to $B_{c} (6_{f}, 3 / 2^{-})$ , (v) $B_{b} ({\bar{3}}_{f}, 1 / 2^{+})$ to $B_{c} ({\bar{3}}_{f}, 1 / 2^{-})$ , and (vi) $B_{b} (\bar{3_{f}}, 1 / 2^{+})$ to $B_{c} ({\bar{3}}_{f}, 3 / 2^{-})$ transitions. Types (i) to (iii) involve spin $1 / 2$ and $3 / 2$ $s$ -wave charmed baryons, while types (iv) to (vi) involve spin $1 / 2$ and $3 / 2$ $p$ -wave charmed baryons. The light diquarks are spectating in these transitions. The transition form factors are calculated in the light-front quark model approach. All of the form factors in the $1 / 2 \to 1 / 2$ and $1 / 2 \to 3 / 2$ transitions are extracted, and they are found to reasonably satisfy the relations obtained in the heavy quark limit, as we are using heavy but finite $m_{b}$ and $m_{c}$ . Using naïve factorization, decay rates and up-down asymmetries of the above modes are predicted and can be checked experimentally. We compare our results to data and other theoretical predictions. The study on these decay modes may shed light on the quantum numbers of $Λ_{c} (2765)$ , $Λ_{c} (2940) Ω_{c} (3050)$ , $Ω_{c} (3090)$ , and $Ω_{c} (3120)$ .

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  "abstracts": [
    {
      "source": "APS", 
      "value": "We study color allowed bottom baryon to <math><mi>s</mi></math>-wave and <math><mi>p</mi></math>-wave charmed baryon nonleptonic decays in this work. The charmed baryons include <math><mi>spin</mi><mtext>\u2212</mtext><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> and <math><mi>spin</mi><mtext>\u2212</mtext><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> states. Explicitly, we consider <math><msub><mi>\u039b</mi><mi>b</mi></msub><mo>\u2192</mo><msubsup><mi>\u039b</mi><mi>c</mi><mrow><mo>(</mo><mo>*</mo><mo>,</mo><mo>*</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mi>M</mi><mo>\u2212</mo></msup></math>, <math><mrow><msub><mrow><mi>\u039e</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>\u2192</mo><msubsup><mrow><mi>\u039e</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mrow><mi>M</mi></mrow><mrow><mo>\u2212</mo></mrow></msup></mrow></math>, and <math><mrow><msub><mrow><mi>\u03a9</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>\u2192</mo><msubsup><mrow><mi>\u03a9</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>,</mo><mo>*</mo><mo>*</mo><mo>)</mo></mrow></msubsup><msup><mrow><mi>M</mi></mrow><mrow><mo>\u2212</mo></mrow></msup></mrow></math> decays with <math><mi>M</mi><mo>=</mo><mi>\u03c0</mi><mo>,</mo><mi>K</mi><mo>,</mo><mi>\u03c1</mi><mo>,</mo><msup><mi>K</mi><mo>*</mo></msup><mo>,</mo><msub><mi>a</mi><mn>1</mn></msub><mo>,</mo><mi>D</mi><mo>,</mo><msub><mi>D</mi><mi>s</mi></msub><mo>,</mo><msup><mi>D</mi><mo>*</mo></msup><mo>,</mo><msubsup><mi>D</mi><mi>s</mi><mo>*</mo></msubsup></math>, <math><msubsup><mi>\u039b</mi><mi>c</mi><mrow><mo>(</mo><mo>*</mo><mo>,</mo><mo>*</mo><mo>*</mo><mo>)</mo></mrow></msubsup><mo>=</mo><mspace></mspace><msub><mi>\u039b</mi><mi>c</mi></msub><mo>,</mo><msub><mi>\u039b</mi><mi>c</mi></msub><mo>(</mo><mn>2595</mn><mo>)</mo><mo>,</mo><msub><mi>\u039b</mi><mi>c</mi></msub><mo>(</mo><mn>2625</mn><mo>)</mo><mo>,</mo><msub><mi>\u039b</mi><mi>c</mi></msub><mo>(</mo><mn>2765</mn><mo>)</mo><mo>,</mo><msub><mi>\u039b</mi><mi>c</mi></msub><mo>(</mo><mn>2940</mn><mo>)</mo></math>, <math><mrow><msubsup><mrow><mi>\u039e</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>*</mo><mo>)</mo></mrow></msubsup><mo>=</mo><msub><mrow><mi>\u039e</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msub><mrow><mi>\u039e</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>2790</mn><mo>)</mo><mo>,</mo><msub><mrow><mi>\u039e</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>2815</mn><mo>)</mo></mrow></math> and <math><mrow><msubsup><mrow><mi>\u03a9</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>,</mo><mo>*</mo><mo>*</mo><mo>)</mo></mrow></msubsup><mo>=</mo><mspace></mspace><msub><mrow><mi>\u03a9</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>,</mo><msub><mrow><mi>\u03a9</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>2770</mn><mo>)</mo><mo>,</mo><msub><mrow><mi>\u03a9</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>3050</mn><mo>)</mo><mo>,</mo><msub><mrow><mi>\u03a9</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>3090</mn><mo>)</mo><mo>,</mo><msub><mrow><mi>\u03a9</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mn>3120</mn><mo>)</mo></mrow></math>. There are six types of transitions, namely, (i) <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><msub><mrow><mover><mrow><mn>3</mn></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mi>f</mi></mrow></msub><mo>,</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></mrow></math> to <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><msub><mrow><mover><mrow><mn>3</mn></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mi>f</mi></mrow></msub><mo>,</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></mrow></math>, (ii) <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><msub><mrow><mn>6</mn></mrow><mrow><mi>f</mi></mrow></msub><mo>,</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>+</mo></mrow></msup><mo>)</mo></mrow></math> to <math><msub><mi>B</mi><mi>c</mi></msub><mo>(</mo><msub><mn>6</mn><mi>f</mi></msub><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>)</mo></math>, (iii) <math><msub><mi>B</mi><mi>b</mi></msub><mo>(</mo><msub><mn>6</mn><mi>f</mi></msub><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>)</mo></math> to <math><msub><mi>B</mi><mi>c</mi></msub><mo>(</mo><msub><mn>6</mn><mi>f</mi></msub><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>)</mo></math>, (iv) <math><msub><mi>B</mi><mi>b</mi></msub><mo>(</mo><msub><mn>6</mn><mi>f</mi></msub><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>)</mo></math> to <math><msub><mi>B</mi><mi>c</mi></msub><mo>(</mo><msub><mn>6</mn><mi>f</mi></msub><mo>,</mo><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>\u2212</mo></msup><mo>)</mo></math>, (v) <math><msub><mi>B</mi><mi>b</mi></msub><mo>(</mo><msub><mover><mn>3</mn><mo>\u00af</mo></mover><mi>f</mi></msub><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>)</mo></math> to <math><msub><mi>B</mi><mi>c</mi></msub><mo>(</mo><msub><mover><mn>3</mn><mo>\u00af</mo></mover><mi>f</mi></msub><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>\u2212</mo></msup><mo>)</mo></math>, and (vi) <math><msub><mi>B</mi><mi>b</mi></msub><mo>(</mo><mover><msub><mn>3</mn><mi>f</mi></msub><mo>\u00af</mo></mover><mo>,</mo><mn>1</mn><mo>/</mo><msup><mn>2</mn><mo>+</mo></msup><mo>)</mo></math> to <math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><msub><mrow><mover><mrow><mn>3</mn></mrow><mrow><mo>\u00af</mo></mrow></mover></mrow><mrow><mi>f</mi></mrow></msub><mo>,</mo><mn>3</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>\u2212</mo></mrow></msup><mo>)</mo></mrow></math> transitions. Types (i) to (iii) involve spin <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> and <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> <math><mi>s</mi></math>-wave charmed baryons, while types (iv) to (vi) involve spin <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> and <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math> <math><mi>p</mi></math>-wave charmed baryons. The light diquarks are spectating in these transitions. The transition form factors are calculated in the light-front quark model approach. All of the form factors in the <math><mn>1</mn><mo>/</mo><mn>2</mn><mo>\u2192</mo><mn>1</mn><mo>/</mo><mn>2</mn></math> and <math><mn>1</mn><mo>/</mo><mn>2</mn><mo>\u2192</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> transitions are extracted, and they are found to reasonably satisfy the relations obtained in the heavy quark limit, as we are using heavy but finite <math><msub><mi>m</mi><mi>b</mi></msub></math> and <math><msub><mi>m</mi><mi>c</mi></msub></math>. Using na\u00efve factorization, decay rates and up-down asymmetries of the above modes are predicted and can be checked experimentally. We compare our results to data and other theoretical predictions. The study on these decay modes may shed light on the quantum numbers of <math><msub><mi>\u039b</mi><mi>c</mi></msub><mo>(</mo><mn>2765</mn><mo>)</mo></math>, <math><msub><mi>\u039b</mi><mi>c</mi></msub><mo>(</mo><mn>2940</mn><mo>)</mo><msub><mi>\u03a9</mi><mi>c</mi></msub><mo>(</mo><mn>3050</mn><mo>)</mo></math>, <math><msub><mi>\u03a9</mi><mi>c</mi></msub><mo>(</mo><mn>3090</mn><mo>)</mo></math>, and <math><msub><mi>\u03a9</mi><mi>c</mi></msub><mo>(</mo><mn>3120</mn><mo>)</mo></math>."
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Published on:: 26 August 2019
Publisher:: APS
Published in:: Physical Review D , Volume 100 (2019)
Issue 3
DOI:: https://doi.org/10.1103/PhysRevD.100.034025
arXiv:: 1905.00153
Copyrights:: Published by the American Physical Society
Licence:: CC-BY-4.0

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