Investigations of Λ states with spin-parity 32±

The present study provides spectroscopic investigations of spin-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mfrac><a:mn>3</a:mn><a:mn>2</a:mn></a:mfrac></a:math> <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi mathvariant="normal">Λ</c:mi></c:math> baryons with both positive and negative parities. The analysis mainly focuses on three states, namely <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mn>1</f:mn><f:mi>P</f:mi></f:math>, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mn>2</h:mn><h:mi>P</h:mi></h:math>, and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mn>2</j:mn><j:mi>S</j:mi></j:math>, and corresponding masses are calculated using the QCD sum rule method. To implement the method, we apply two types of interpolating currents with octet and singlet quantum numbers and compare the corresponding results with the reported masses of experimentally observed states. From the comparisons, it is extracted that the results of interpolating current with octet quantum numbers are in good agreement with the experimentally measured masses. The masses obtained with this interpolating current are <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mrow><l:mi>m</l:mi><l:mo>=</l:mo><l:mn>1513.64</l:mn><l:mo>±</l:mo><l:mn>8.76</l:mn><l:mtext> </l:mtext><l:mtext> </l:mtext><l:mi>MeV</l:mi></l:mrow></l:math> for <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mn>1</n:mn><n:mi>P</n:mi></n:math> state with <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msup><p:mi>J</p:mi><p:mi>P</p:mi></p:msup><p:mo>=</p:mo><p:msup><p:mfrac><p:mn>3</p:mn><p:mn>2</p:mn></p:mfrac><p:mo>−</p:mo></p:msup></p:math>, <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msup><r:mi>m</r:mi><r:mo>′</r:mo></r:msup><r:mo>=</r:mo><r:mn>1687.91</r:mn><r:mo>±</r:mo><r:mn>0.31</r:mn><r:mtext> </r:mtext><r:mtext> </r:mtext><r:mi>MeV</r:mi></r:math> for <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mn>2</t:mn><t:mi>P</t:mi></t:math> state with <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:msup><v:mi>J</v:mi><v:mi>P</v:mi></v:msup><v:mo>=</v:mo><v:msup><v:mfrac><v:mn>3</v:mn><v:mn>2</v:mn></v:mfrac><v:mo>−</v:mo></v:msup></v:math> and <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mover accent="true"><x:mi>m</x:mi><x:mo stretchy="false">˜</x:mo></x:mover><x:mo>=</x:mo><x:mn>1882.37</x:mn><x:mo>±</x:mo><x:mn>11.95</x:mn><x:mtext> </x:mtext><x:mtext> </x:mtext><x:mi>MeV</x:mi></x:math> for <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"><bb:mn>2</bb:mn><bb:mi>S</bb:mi></bb:math> state with <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:msup><db:mi>J</db:mi><db:mi>P</db:mi></db:msup><db:mo>=</db:mo><db:msup><db:mfrac><db:mn>3</db:mn><db:mn>2</db:mn></db:mfrac><db:mo>+</db:mo></db:msup></db:math> and they are consistent with the experimental masses of <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:mi mathvariant="normal">Λ</fb:mi><fb:mo stretchy="false">(</fb:mo><fb:mn>1520</fb:mn><fb:mo stretchy="false">)</fb:mo></fb:math>, <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi mathvariant="normal">Λ</kb:mi><kb:mo stretchy="false">(</kb:mo><kb:mn>1690</kb:mn><kb:mo stretchy="false">)</kb:mo></kb:math>, and <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:mi mathvariant="normal">Λ</pb:mi><pb:mo stretchy="false">(</pb:mo><pb:mn>1890</pb:mn><pb:mo stretchy="false">)</pb:mo></pb:math>, respectively, which confirm their spin-parity quantum numbers. Besides, we calculate the corresponding current coupling constants, which are utilized as inputs in the calculations of different form factors defining the widths of the states under study. Published by the American Physical Society 2024