Strong decays of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>2910</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>2940</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:msup><mml:mi>D</mml:mi><mml:mo>*</mml:mo></mml:msup></mml:math> molecular frame

Abstract

Stimulated by the observation of a new structure, named <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi mathvariant="normal">Λ</a:mi><a:mi>c</a:mi></a:msub><a:mo stretchy="false">(</a:mo><a:mn>2910</a:mn><a:mo stretchy="false">)</a:mo></a:math>, in the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:msub><f:mrow><f:mi mathvariant="normal">Σ</f:mi></f:mrow><f:mrow><f:mi>c</f:mi></f:mrow></f:msub><f:mo stretchy="false">(</f:mo><f:mn>2455</f:mn><f:msup><f:mrow><f:mo stretchy="false">)</f:mo></f:mrow><f:mrow><f:mn>0</f:mn><f:mo>,</f:mo><f:mo>+</f:mo><f:mo>+</f:mo></f:mrow></f:msup><f:msup><f:mrow><f:mi>π</f:mi></f:mrow><f:mrow><f:mo>+</f:mo><f:mo>,</f:mo><f:mo>−</f:mo></f:mrow></f:msup></f:mrow></f:math> decay channel from B meson decay process by the Belle Collaboration, and the similarity of the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:msub><k:mrow><k:mi mathvariant="normal">Λ</k:mi></k:mrow><k:mrow><k:mi>c</k:mi></k:mrow></k:msub><k:mo stretchy="false">(</k:mo><k:mn>2910</k:mn><k:mo stretchy="false">)</k:mo><k:mo>/</k:mo><k:msub><k:mrow><k:mi mathvariant="normal">Λ</k:mi></k:mrow><k:mrow><k:mi>c</k:mi></k:mrow></k:msub><k:mo stretchy="false">(</k:mo><k:mn>2940</k:mn><k:mo stretchy="false">)</k:mo></k:mrow></k:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>P</s:mi><s:mi>c</s:mi></s:msub></s:math> states, we investigate the decay behavior of the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi mathvariant="normal">Λ</u:mi><u:mi>c</u:mi></u:msub><u:mo stretchy="false">(</u:mo><u:mn>2910</u:mn><u:mo stretchy="false">)</u:mo></u:math> and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msub><z:mi mathvariant="normal">Λ</z:mi><z:mi>c</z:mi></z:msub><z:mo stretchy="false">(</z:mo><z:mn>2940</z:mn><z:mo stretchy="false">)</z:mo></z:math> in the <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:mi>N</eb:mi><eb:msup><eb:mi>D</eb:mi><eb:mo>*</eb:mo></eb:msup></eb:math> molecular frame with the possible <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msup><gb:mi>J</gb:mi><gb:mi>P</gb:mi></gb:msup></gb:math> quantum numbers to be <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mn>1</ib:mn><ib:mo>/</ib:mo><ib:msup><ib:mn>2</ib:mn><ib:mo>−</ib:mo></ib:msup></ib:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mn>3</kb:mn><kb:mo>/</kb:mo><kb:msup><kb:mn>2</kb:mn><kb:mo>−</kb:mo></kb:msup></kb:math>. We employ an effective Lagrangian approach to evaluate the partial widths of <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:mi>N</mb:mi><mb:mi>D</mb:mi></mb:math>, <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi mathvariant="normal">Σ</ob:mi><ob:mi>c</ob:mi></ob:msub><ob:mi>π</ob:mi></ob:math>, and <rb:math xmlns:rb="http://www.w3.org/1998/Math/MathML" display="inline"><rb:msubsup><rb:mi mathvariant="normal">Σ</rb:mi><rb:mi>c</rb:mi><rb:mo>*</rb:mo></rb:msubsup><rb:mi>π</rb:mi></rb:math> channels. The estimations in the present work indicate that the <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:msup><ub:mi>J</ub:mi><ub:mi>P</ub:mi></ub:msup></ub:math> quantum numbers of <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:msub><wb:mi mathvariant="normal">Λ</wb:mi><wb:mi>c</wb:mi></wb:msub><wb:mo stretchy="false">(</wb:mo><wb:mn>2910</wb:mn><wb:mo stretchy="false">)</wb:mo></wb:math> and <bc:math xmlns:bc="http://www.w3.org/1998/Math/MathML" display="inline"><bc:msub><bc:mi mathvariant="normal">Λ</bc:mi><bc:mi>c</bc:mi></bc:msub><bc:mo stretchy="false">(</bc:mo><bc:mn>2940</bc:mn><bc:mo stretchy="false">)</bc:mo></bc:math> are preferred to be <gc:math xmlns:gc="http://www.w3.org/1998/Math/MathML" display="inline"><gc:mn>1</gc:mn><gc:mo>/</gc:mo><gc:msup><gc:mn>2</gc:mn><gc:mo>−</gc:mo></gc:msup></gc:math> and <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"><ic:mn>3</ic:mn><ic:mo>/</ic:mo><ic:msup><ic:mn>2</ic:mn><ic:mo>−</ic:mo></ic:msup></ic:math>, respectively. From the present estimations, we also find the branching ratio of <kc:math xmlns:kc="http://www.w3.org/1998/Math/MathML" display="inline"><kc:mrow><kc:msub><kc:mrow><kc:mi mathvariant="normal">Λ</kc:mi></kc:mrow><kc:mrow><kc:mi>c</kc:mi></kc:mrow></kc:msub><kc:mo stretchy="false">(</kc:mo><kc:mn>3</kc:mn><kc:mo>/</kc:mo><kc:mn>2</kc:mn><kc:mo stretchy="false">)</kc:mo><kc:mo stretchy="false">→</kc:mo><kc:msubsup><kc:mrow><kc:mi mathvariant="normal">Σ</kc:mi></kc:mrow><kc:mrow><kc:mi>c</kc:mi></kc:mrow><kc:mrow><kc:mo>*</kc:mo></kc:mrow></kc:msubsup><kc:mi>π</kc:mi></kc:mrow></kc:math> is much larger than that of <rc:math xmlns:rc="http://www.w3.org/1998/Math/MathML" display="inline"><rc:mrow><rc:msub><rc:mrow><rc:mi mathvariant="normal">Λ</rc:mi></rc:mrow><rc:mrow><rc:mi>c</rc:mi></rc:mrow></rc:msub><rc:mo stretchy="false">(</rc:mo><rc:mn>1</rc:mn><rc:mo>/</rc:mo><rc:mn>2</rc:mn><rc:mo stretchy="false">)</rc:mo><rc:mo stretchy="false">→</rc:mo><rc:msubsup><rc:mrow><rc:mi mathvariant="normal">Σ</rc:mi></rc:mrow><rc:mrow><rc:mi>c</rc:mi></rc:mrow><rc:mrow><rc:mo>*</rc:mo></rc:mrow></rc:msubsup><rc:mi>π</rc:mi></rc:mrow></rc:math>, thus <yc:math xmlns:yc="http://www.w3.org/1998/Math/MathML" display="inline"><yc:msubsup><yc:mi mathvariant="normal">Σ</yc:mi><yc:mi>c</yc:mi><yc:mo>*</yc:mo></yc:msubsup><yc:mi>π</yc:mi></yc:math> could be a good channel to distinguish the <bd:math xmlns:bd="http://www.w3.org/1998/Math/MathML" display="inline"><bd:msup><bd:mi>J</bd:mi><bd:mi>P</bd:mi></bd:msup></bd:math> quantum numbers of <dd:math xmlns:dd="http://www.w3.org/1998/Math/MathML" display="inline"><dd:msub><dd:mi mathvariant="normal">Λ</dd:mi><dd:mi>c</dd:mi></dd:msub><dd:mo stretchy="false">(</dd:mo><dd:mn>2910</dd:mn><dd:mo stretchy="false">)</dd:mo></dd:math> and <id:math xmlns:id="http://www.w3.org/1998/Math/MathML" display="inline"><id:msub><id:mi mathvariant="normal">Λ</id:mi><id:mi>c</id:mi></id:msub><id:mo stretchy="false">(</id:mo><id:mn>2940</id:mn><id:mo stretchy="false">)</id:mo></id:math>. Therefore, we suggest searching for the structure in <nd:math xmlns:nd="http://www.w3.org/1998/Math/MathML" display="inline"><nd:msubsup><nd:mi mathvariant="normal">Σ</nd:mi><nd:mi>c</nd:mi><nd:mo>*</nd:mo></nd:msubsup><nd:mi>π</nd:mi></nd:math> invariant mass distribution in Belle II. Published by the American Physical Society 2024

Topics & Concepts