Reanalysis of rare radiative Ξb−→Ξ−γ decay in QCD

The upper limit of the branching ratio of the rare <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi mathvariant="normal">Ξ</a:mi><a:mi>b</a:mi><a:mo>−</a:mo></a:msubsup><a:mo stretchy="false">→</a:mo><a:msup><a:mi mathvariant="normal">Ξ</a:mi><a:mo>−</a:mo></a:msup><a:mi>γ</a:mi></a:math> decay is obtained as <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>BR</f:mi><f:mo stretchy="false">(</f:mo><f:msubsup><f:mi mathvariant="normal">Ξ</f:mi><f:mi>b</f:mi><f:mo>−</f:mo></f:msubsup><f:mo stretchy="false">→</f:mo><f:msup><f:mi mathvariant="normal">Ξ</f:mi><f:mo>−</f:mo></f:msup><f:mi>γ</f:mi><f:mo stretchy="false">)</f:mo><f:mo><</f:mo><f:mn>1.3</f:mn><f:mo>×</f:mo><f:msup><f:mn>10</f:mn><f:mrow><f:mo>−</f:mo><f:mn>4</f:mn></f:mrow></f:msup></f:math> by the LHCb. In the present work we study this decay within the light cone QCD sum rules employing the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi mathvariant="normal">Ξ</m:mi><m:mi>b</m:mi></m:msub></m:math> distribution amplitudes. At the first stage, the form factors entering the <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msubsup><p:mi mathvariant="normal">Ξ</p:mi><p:mi>b</p:mi><p:mo>−</p:mo></p:msubsup><p:mo stretchy="false">→</p:mo><p:msup><p:mi mathvariant="normal">Ξ</p:mi><p:mo>−</p:mo></p:msup><p:mi>γ</p:mi></p:math> decay are obtained. Next, using the results for the form factors the corresponding branching ratio for this decay is estimated to be <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>BR</u:mi><u:mo stretchy="false">(</u:mo><u:msubsup><u:mi mathvariant="normal">Ξ</u:mi><u:mi>b</u:mi><u:mo>−</u:mo></u:msubsup><u:mo stretchy="false">→</u:mo><u:msup><u:mi mathvariant="normal">Ξ</u:mi><u:mo>−</u:mo></u:msup><u:mi>γ</u:mi><u:mo stretchy="false">)</u:mo><u:mo>=</u:mo><u:mo stretchy="false">(</u:mo><u:mn>4.8</u:mn><u:mo>±</u:mo><u:mn>1.3</u:mn><u:mo stretchy="false">)</u:mo><u:mo>×</u:mo><u:msup><u:mn>10</u:mn><u:mrow><u:mo>−</u:mo><u:mn>5</u:mn></u:mrow></u:msup></u:math>. This value lies below the upper limit established by the LHCb collaboration. Our finding for the branching ratio is also compared with the results of the other theoretical approaches existing in the literature.