Study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="normal">Ξ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">→</mml:mo> <mml:mi mathvariant="normal">Λ</mml:mi> <mml:msup> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>K</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>π</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> and search for the low-lying baryons <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Ξ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mo>−</mml:mo> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Σ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mo>−</mml:mo> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math>

Abstract

Since searches for the low-lying excited baryons <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Ξ</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:msup> <a:mn>2</a:mn> <a:mo>−</a:mo> </a:msup> <a:mo stretchy="false">)</a:mo> </a:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mi mathvariant="normal">Σ</f:mi> <f:mo stretchy="false">(</f:mo> <f:mn>1</f:mn> <f:mo>/</f:mo> <f:msup> <f:mn>2</f:mn> <f:mo>−</f:mo> </f:msup> <f:mo stretchy="false">)</f:mo> </f:math> are crucial to deepening our understanding of the light baryon spectrum, we have investigated the Cabibbo-favored process <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msubsup> <k:mi mathvariant="normal">Ξ</k:mi> <k:mi>c</k:mi> <k:mo>+</k:mo> </k:msubsup> <k:mo stretchy="false">→</k:mo> <k:mi mathvariant="normal">Λ</k:mi> <k:msup> <k:mover accent="true"> <k:mi>K</k:mi> <k:mo stretchy="false">¯</k:mo> </k:mover> <k:mn>0</k:mn> </k:msup> <k:msup> <k:mi>π</k:mi> <k:mo>+</k:mo> </k:msup> </k:math> by taking into account the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mi>S</r:mi> </r:math> -wave pseudoscalar meson-octet baryon interactions within the chiral unitary approach, which could dynamically generate the resonances <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mi mathvariant="normal">Ξ</t:mi> <t:mo stretchy="false">(</t:mo> <t:mn>1</t:mn> <t:mo>/</t:mo> <t:msup> <t:mn>2</t:mn> <t:mo>−</t:mo> </t:msup> <t:mo stretchy="false">)</t:mo> </t:math> and <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi mathvariant="normal">Σ</y:mi> <y:mo stretchy="false">(</y:mo> <y:mn>1</y:mn> <y:mo>/</y:mo> <y:msup> <y:mn>2</y:mn> <y:mo>−</y:mo> </y:msup> <y:mo stretchy="false">)</y:mo> </y:math> . The contributions from the excited kaons are double Cabibbo suppressed, and the contribution from the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"> <db:mi mathvariant="normal">Σ</db:mi> <db:mo stretchy="false">(</db:mo> <db:mn>1385</db:mn> <db:mo stretchy="false">)</db:mo> </db:math> is also suppressed due to Korner-Pati-Woo theory; thus, those states are expected to play negligible contributions in this process. We have predicted the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:msup> <ib:mover accent="true"> <ib:mi>K</ib:mi> <ib:mo stretchy="false">¯</ib:mo> </ib:mover> <ib:mn>0</ib:mn> </ib:msup> <ib:mi mathvariant="normal">Λ</ib:mi> </ib:math> and <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:msup> <nb:mi>π</nb:mi> <nb:mo>+</nb:mo> </nb:msup> <nb:mi mathvariant="normal">Λ</nb:mi> </nb:math> invariant mass distributions, which have the clear signals of the <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:mi mathvariant="normal">Ξ</qb:mi> <qb:mo stretchy="false">(</qb:mo> <qb:mn>1</qb:mn> <qb:mo>/</qb:mo> <qb:msup> <qb:mn>2</qb:mn> <qb:mo>−</qb:mo> </qb:msup> <qb:mo stretchy="false">)</qb:mo> </qb:math> and <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"> <vb:mi mathvariant="normal">Σ</vb:mi> <vb:mo stretchy="false">(</vb:mo> <vb:mn>1</vb:mn> <vb:mo>/</vb:mo> <vb:msup> <vb:mn>2</vb:mn> <vb:mo>−</vb:mo> </vb:msup> <vb:mo stretchy="false">)</vb:mo> </vb:math> . Thus, the <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"> <ac:msubsup> <ac:mi mathvariant="normal">Ξ</ac:mi> <ac:mi>c</ac:mi> <ac:mo>+</ac:mo> </ac:msubsup> <ac:mo stretchy="false">→</ac:mo> <ac:mi mathvariant="normal">Λ</ac:mi> <ac:msup> <ac:mover accent="true"> <ac:mi>K</ac:mi> <ac:mo stretchy="false">¯</ac:mo> </ac:mover> <ac:mn>0</ac:mn> </ac:msup> <ac:msup> <ac:mi>π</ac:mi> <ac:mo>+</ac:mo> </ac:msup> </ac:math> is an ideal process to search for the low-lying baryons <hc:math xmlns:hc="http://www.w3.org/1998/Math/MathML" display="inline"> <hc:mi mathvariant="normal">Ξ</hc:mi> <hc:mo stretchy="false">(</hc:mo> <hc:mn>1</hc:mn> <hc:mo>/</hc:mo> <hc:msup> <hc:mn>2</hc:mn> <hc:mo>−</hc:mo> </hc:msup> <hc:mo stretchy="false">)</hc:mo> </hc:math> and <mc:math xmlns:mc="http://www.w3.org/1998/Math/MathML" display="inline"> <mc:mi mathvariant="normal">Σ</mc:mi> <mc:mo stretchy="false">(</mc:mo> <mc:mn>1</mc:mn> <mc:mo>/</mc:mo> <mc:msup> <mc:mn>2</mc:mn> <mc:mo>−</mc:mo> </mc:msup> <mc:mo stretchy="false">)</mc:mo> </mc:math> , and we make a call for a precise measurements of this process in experiments, such as Belle II, LHCb, and the proposed Super Tau-Charm Facility.

Topics & Concepts