Theoretical study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>N</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1535</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi mathvariant="normal">Σ</mml:mi> <mml:mo>*</mml:mo> </mml:msup> <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> in the Cabibbo-favored process <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msubsup> <mml:mi mathvariant="normal">Λ</mml:mi> <mml:mi>c</mml:mi> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo stretchy="false">→</mml:mo> <mml:mi>p</mml:mi> <mml:msup> <mml:mover accent="true"> <mml:mi>K</mml:mi> <mml:mo stretchy="false">¯</mml:mo> </mml:mover> <mml:mn>0</mml:mn> </mml:msup> <mml:mi>η</mml:mi> </mml:math>

Abstract

Motivated by the recent experimental measurements, we have investigated the Cabibbo-favored process <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msubsup> <a:mi mathvariant="normal">Λ</a:mi> <a:mi>c</a:mi> <a:mo>+</a:mo> </a:msubsup> <a:mo stretchy="false">→</a:mo> <a:mi>p</a:mi> <a:msup> <a:mover accent="true"> <a:mi>K</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mn>0</a:mn> </a:msup> <a:mi>η</a:mi> </a:math> , where the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>N</g:mi> <g:mo stretchy="false">(</g:mo> <g:mn>1535</g:mn> <g:mo stretchy="false">)</g:mo> </g:math> resonance is dynamically generated from the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>S</k:mi> </k:math> -wave pseudoscalar meson-octet baryon interactions within the chiral unitary approach. The contributions from the intermediate <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>N</m:mi> <m:mo stretchy="false">(</m:mo> <m:mn>1650</m:mn> <m:mo stretchy="false">)</m:mo> </m:math> and the predicted low-lying baryon <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msup> <q:mi mathvariant="normal">Σ</q:mi> <q:mo>*</q:mo> </q:msup> <q:mo stretchy="false">(</q:mo> <q:mn>1</q:mn> <q:mo>/</q:mo> <q:msup> <q:mn>2</q:mn> <q:mo>−</q:mo> </q:msup> <q:mo stretchy="false">)</q:mo> </q:math> are also considered. In addition, a Breit-Wigner amplitude for the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:mi>N</v:mi> <v:mo stretchy="false">(</v:mo> <v:mn>1535</v:mn> <v:mo stretchy="false">)</v:mo> </v:math> resonance is checked. By comparing with the measured <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:mi>η</z:mi> <z:mi>p</z:mi> </z:math> , <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:msup> <bb:mover accent="true"> <bb:mi>K</bb:mi> <bb:mo stretchy="false">¯</bb:mo> </bb:mover> <bb:mn>0</bb:mn> </bb:msup> <bb:mi>η</bb:mi> </bb:math> , and <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"> <fb:mi>p</fb:mi> <fb:msup> <fb:mover accent="true"> <fb:mi>K</fb:mi> <fb:mo stretchy="false">¯</fb:mo> </fb:mover> <fb:mn>0</fb:mn> </fb:msup> </fb:math> invariant mass squared distributions, our results support the interpretation of <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi>N</jb:mi> <jb:mo stretchy="false">(</jb:mo> <jb:mn>1535</jb:mn> <jb:mo stretchy="false">)</jb:mo> </jb:math> as a dynamically generated state. Furthermore, we demonstrate that, with the contribution from <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:msup> <nb:mi mathvariant="normal">Σ</nb:mi> <nb:mo>*</nb:mo> </nb:msup> <nb:mo stretchy="false">(</nb:mo> <nb:mn>1</nb:mn> <nb:mo>/</nb:mo> <nb:msup> <nb:mn>2</nb:mn> <nb:mo>−</nb:mo> </nb:msup> <nb:mo stretchy="false">)</nb:mo> </nb:math> taken into account, the calculated invariant mass distributions agree with the Belle measurements. Future precise measurements of the <sb:math xmlns:sb="http://www.w3.org/1998/Math/MathML" display="inline"> <sb:msubsup> <sb:mi mathvariant="normal">Λ</sb:mi> <sb:mi>c</sb:mi> <sb:mo>+</sb:mo> </sb:msubsup> <sb:mo stretchy="false">→</sb:mo> <sb:mi>p</sb:mi> <sb:msup> <sb:mover accent="true"> <sb:mi>K</sb:mi> <sb:mo stretchy="false">¯</sb:mo> </sb:mover> <sb:mn>0</sb:mn> </sb:msup> <sb:mi>η</sb:mi> </sb:math> process can further elucidate the existence of the low-lying baryon <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:msup> <yb:mi mathvariant="normal">Σ</yb:mi> <yb:mo>*</yb:mo> </yb:msup> <yb:mo stretchy="false">(</yb:mo> <yb:mn>1</yb:mn> <yb:mo>/</yb:mo> <yb:msup> <yb:mn>2</yb:mn> <yb:mo>−</yb:mo> </yb:msup> <yb:mo stretchy="false">)</yb:mo> </yb:math> . Published by the American Physical Society 2024

Topics & Concepts