Nonleptonic three-body charmed baryon weak decays with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>H</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>15</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>

Abstract

We study the nonleptonic three-body charmed baryon weak decays of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi mathvariant="bold">B</a:mi></a:mrow><a:mrow><a:mi>c</a:mi></a:mrow></a:msub><a:mo stretchy="false">→</a:mo><a:msub><a:mrow><a:mi mathvariant="bold">B</a:mi></a:mrow><a:mrow><a:mi>n</a:mi></a:mrow></a:msub><a:mi>P</a:mi><a:msup><a:mrow><a:mi>P</a:mi></a:mrow><a:mrow><a:mo>′</a:mo></a:mrow></a:msup></a:mrow></a:math> under the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>S</f:mi><f:mi>U</f:mi><f:mo stretchy="false">(</f:mo><f:mn>3</f:mn><f:msub><f:mo stretchy="false">)</f:mo><f:mi>F</f:mi></f:msub></f:math> flavor symmetry, where <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi mathvariant="bold">B</j:mi><j:mi>c</j:mi></j:msub></j:math> denotes the antitriplet charmed baryon, comprising <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mo stretchy="false">(</m:mo><m:msubsup><m:mrow><m:mi mathvariant="normal">Ξ</m:mi></m:mrow><m:mrow><m:mi>c</m:mi></m:mrow><m:mrow><m:mn>0</m:mn></m:mrow></m:msubsup><m:mo>,</m:mo><m:mo>−</m:mo><m:msubsup><m:mrow><m:mi mathvariant="normal">Ξ</m:mi></m:mrow><m:mrow><m:mi>c</m:mi></m:mrow><m:mrow><m:mo>+</m:mo></m:mrow></m:msubsup><m:mo>,</m:mo><m:msubsup><m:mrow><m:mi mathvariant="normal">Λ</m:mi></m:mrow><m:mrow><m:mi>c</m:mi></m:mrow><m:mrow><m:mo>+</m:mo></m:mrow></m:msubsup><m:mo stretchy="false">)</m:mo></m:mrow></m:math>, and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi mathvariant="bold">B</t:mi><t:mi>n</t:mi></t:msub></t:math> and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>P</w:mi><w:mo stretchy="false">(</w:mo><w:msup><w:mi>P</w:mi><w:mo>′</w:mo></w:msup><w:mo stretchy="false">)</w:mo></w:math> represent octet baryon and pseudoscalar meson states, respectively. In addition to 12 parameters from the contributions of the color-antisymmetric part of the effective Hamiltonian, denoted as <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mrow><ab:mi>H</ab:mi><ab:mo stretchy="false">(</ab:mo><ab:mover accent="true"><ab:mrow><ab:mn mathvariant="bold">6</ab:mn></ab:mrow><ab:mrow><ab:mo stretchy="false">¯</ab:mo></ab:mrow></ab:mover><ab:mo stretchy="false">)</ab:mo></ab:mrow></ab:math>, there are 4 parameters from the color-symmetric one, <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mi>H</hb:mi><hb:mo stretchy="false">(</hb:mo><hb:mn mathvariant="bold">15</hb:mn><hb:mo stretchy="false">)</hb:mo></hb:math>, which were not included in the previous study. With 16 parameters in total and 28 experimental data points, we obtain the minimal <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msup><mb:mi>χ</mb:mi><mb:mn>2</mb:mn></mb:msup></mb:math> over degree of freedom of <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msup><ob:mi>χ</ob:mi><ob:mn>2</ob:mn></ob:msup><ob:mo>/</ob:mo><ob:mi mathvariant="normal">d</ob:mi><ob:mo>.</ob:mo><ob:mi mathvariant="normal">o</ob:mi><ob:mo>.</ob:mo><ob:mi mathvariant="normal">f</ob:mi><ob:mo>=</ob:mo><ob:mn>1.5</ob:mn></ob:math>, which is a great improvement comparing to that without <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"><tb:mi>H</tb:mi><tb:mo stretchy="false">(</tb:mo><tb:mn mathvariant="bold">15</tb:mn><tb:mo stretchy="false">)</tb:mo></tb:math>. With the better fitting values, we evaluate the branching ratios and up-down asymmetries of <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"><yb:mrow><yb:msub><yb:mrow><yb:mi mathvariant="bold">B</yb:mi></yb:mrow><yb:mrow><yb:mi>c</yb:mi></yb:mrow></yb:msub><yb:mo stretchy="false">→</yb:mo><yb:msub><yb:mrow><yb:mi mathvariant="bold">B</yb:mi></yb:mrow><yb:mrow><yb:mi>n</yb:mi></yb:mrow></yb:msub><yb:mi>P</yb:mi><yb:msup><yb:mrow><yb:mi>P</yb:mi></yb:mrow><yb:mrow><yb:mo>′</yb:mo></yb:mrow></yb:msup></yb:mrow></yb:math>, which present some interesting results such as <dc:math xmlns:dc="http://www.w3.org/1998/Math/MathML" display="inline"><dc:mrow><dc:mi mathvariant="script">B</dc:mi><dc:mo stretchy="false">(</dc:mo><dc:msubsup><dc:mrow><dc:mi mathvariant="normal">Λ</dc:mi></dc:mrow><dc:mrow><dc:mi>c</dc:mi></dc:mrow><dc:mrow><dc:mo>+</dc:mo></dc:mrow></dc:msubsup><dc:mo stretchy="false">→</dc:mo><dc:mo stretchy="false">(</dc:mo><dc:mi mathvariant="normal">Ξ</dc:mi><dc:mo stretchy="false">(</dc:mo><dc:mn>1690</dc:mn><dc:msup><dc:mrow><dc:mo stretchy="false">)</dc:mo></dc:mrow><dc:mrow><dc:mn>0</dc:mn></dc:mrow></dc:msup><dc:mo stretchy="false">→</dc:mo><dc:msup><dc:mrow><dc:mi mathvariant="normal">Σ</dc:mi></dc:mrow><dc:mrow><dc:mo>+</dc:mo></dc:mrow></dc:msup><dc:msup><dc:mrow><dc:mi>K</dc:mi></dc:mrow><dc:mrow><dc:mo>−</dc:mo></dc:mrow></dc:msup><dc:mo stretchy="false">)</dc:mo><dc:msup><dc:mrow><dc:mi>K</dc:mi></dc:mrow><dc:mrow><dc:mo>+</dc:mo></dc:mrow></dc:msup><dc:mo stretchy="false">)</dc:mo><dc:mo>≡</dc:mo><dc:mo stretchy="false">(</dc:mo><dc:mn>1.5</dc:mn><dc:mo>±</dc:mo><dc:mn>0.4</dc:mn><dc:mo stretchy="false">)</dc:mo><dc:mo>×</dc:mo><dc:msup><dc:mrow><dc:mn>10</dc:mn></dc:mrow><dc:mrow><dc:mo>−</dc:mo><dc:mn>3</dc:mn></dc:mrow></dc:msup></dc:mrow></dc:math> and potential <tc:math xmlns:tc="http://www.w3.org/1998/Math/MathML" display="inline"><tc:mi>S</tc:mi><tc:mi>U</tc:mi><tc:mo stretchy="false">(</tc:mo><tc:mn>3</tc:mn><tc:mo stretchy="false">)</tc:mo></tc:math> breaking effects in <xc:math xmlns:xc="http://www.w3.org/1998/Math/MathML" display="inline"><xc:msubsup><xc:mi mathvariant="normal">Ξ</xc:mi><xc:mi>c</xc:mi><xc:mo>+</xc:mo></xc:msubsup><xc:mo stretchy="false">→</xc:mo><xc:mi>p</xc:mi><xc:msup><xc:mi>π</xc:mi><xc:mo>+</xc:mo></xc:msup><xc:msup><xc:mi>K</xc:mi><xc:mo>−</xc:mo></xc:msup></xc:math> and <bd:math xmlns:bd="http://www.w3.org/1998/Math/MathML" display="inline"><bd:mrow><bd:msubsup><bd:mrow><bd:mi mathvariant="normal">Λ</bd:mi></bd:mrow><bd:mrow><bd:mi>c</bd:mi></bd:mrow><bd:mrow><bd:mo>+</bd:mo></bd:mrow></bd:msubsup><bd:mo stretchy="false">→</bd:mo><bd:msup><bd:mrow><bd:mi mathvariant="normal">Σ</bd:mi></bd:mrow><bd:mrow><bd:mo>+</bd:mo></bd:mrow></bd:msup><bd:msup><bd:mrow><bd:mi>π</bd:mi></bd:mrow><bd:mrow><bd:mo>−</bd:mo></bd:mrow></bd:msup><bd:msup><bd:mrow><bd:mi>K</bd:mi></bd:mrow><bd:mrow><bd:mo>+</bd:mo></bd:mrow></bd:msup></bd:mrow></bd:math> to be verified by the experiments at BESIII, Belle-II, and LHCb. Published by the American Physical Society 2024

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