Production of Xb via radiative transition of ϒ(10753)

We studied the radiative transitions between the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">ϒ</a:mi><a:mo stretchy="false">(</a:mo><a:mn>10753</a:mn><a:mo stretchy="false">)</a:mo></a:math>, the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mrow><f:mi>S</f:mi><f:mtext>−</f:mtext><f:mi>D</f:mi></f:mrow></f:math> mixed state of the <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi mathvariant="normal">ϒ</h:mi><h:mo stretchy="false">(</h:mo><h:mn>4</h:mn><h:mi>S</h:mi><h:mo stretchy="false">)</h:mo></h:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msub><m:mrow><m:mi mathvariant="normal">ϒ</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub><m:mo stretchy="false">(</m:mo><m:mn>3</m:mn><m:mmultiscripts><m:mrow><m:msub><m:mrow><m:mi>D</m:mi></m:mrow><m:mrow><m:mn>1</m:mn></m:mrow></m:msub></m:mrow><m:mprescripts/><m:none/><m:mrow><m:mn>3</m:mn></m:mrow></m:mmultiscripts><m:mo stretchy="false">)</m:mo></m:mrow></m:math>, and the <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mi>X</r:mi><r:mi>b</r:mi></r:msub></r:math>, the heavy quark flavor symmetry counterpart of the <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi>X</t:mi><t:mo stretchy="false">(</t:mo><t:mn>3782</t:mn><t:mo stretchy="false">)</t:mo></t:math> in the bottomonium sector. The radiative transition was assumed to occur through the intermediate bottom mesons, including <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"><x:mi>P</x:mi></x:math>-wave <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:msubsup><z:mi>B</z:mi><z:mn>1</z:mn><z:mrow><z:mo stretchy="false">(</z:mo><z:mo>′</z:mo><z:mo stretchy="false">)</z:mo></z:mrow></z:msubsup></z:math> mesons as well as the <db:math xmlns:db="http://www.w3.org/1998/Math/MathML" display="inline"><db:mi>S</db:mi></db:math>-wave <fb:math xmlns:fb="http://www.w3.org/1998/Math/MathML" display="inline"><fb:msup><fb:mi>B</fb:mi><fb:mrow><fb:mo stretchy="false">(</fb:mo><fb:mo>*</fb:mo><fb:mo stretchy="false">)</fb:mo></fb:mrow></fb:msup></fb:math> ones. The consideration of the <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:msubsup><jb:mi>B</jb:mi><jb:mn>1</jb:mn><jb:mrow><jb:mo stretchy="false">(</jb:mo><jb:mo>′</jb:mo><jb:mo stretchy="false">)</jb:mo></jb:mrow></jb:msubsup></jb:math> mesons leads to the couplings to be in <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>S</nb:mi></nb:math>-wave, and hence enhances the contributions of the intermediate meson loops. The radiative decay width for the <pb:math xmlns:pb="http://www.w3.org/1998/Math/MathML" display="inline"><pb:mi mathvariant="normal">ϒ</pb:mi><pb:mo stretchy="false">(</pb:mo><pb:mn>10753</pb:mn><pb:mo stretchy="false">)</pb:mo><pb:mo stretchy="false">→</pb:mo><pb:mi>γ</pb:mi><pb:msub><pb:mi>X</pb:mi><pb:mi>b</pb:mi></pb:msub></pb:math> is predicted to be order of 10 keV, corresponding to a branching fraction of <vb:math xmlns:vb="http://www.w3.org/1998/Math/MathML" display="inline"><vb:msup><vb:mn>10</vb:mn><vb:mrow><vb:mo>−</vb:mo><vb:mn>4</vb:mn></vb:mrow></vb:msup></vb:math>. Based on the theoretical results, we strongly suggest to search for the <xb:math xmlns:xb="http://www.w3.org/1998/Math/MathML" display="inline"><xb:msub><xb:mi>X</xb:mi><xb:mi>b</xb:mi></xb:msub></xb:math> in the <zb:math xmlns:zb="http://www.w3.org/1998/Math/MathML" display="inline"><zb:msup><zb:mi>e</zb:mi><zb:mo>+</zb:mo></zb:msup><zb:msup><zb:mi>e</zb:mi><zb:mo>−</zb:mo></zb:msup><zb:mo stretchy="false">→</zb:mo><zb:mi>γ</zb:mi><zb:msub><zb:mi>X</zb:mi><zb:mi>b</zb:mi></zb:msub></zb:math> with <cc:math xmlns:cc="http://www.w3.org/1998/Math/MathML" display="inline"><cc:msub><cc:mi>X</cc:mi><cc:mi>b</cc:mi></cc:msub><cc:mo stretchy="false">→</cc:mo><cc:mi>π</cc:mi><cc:mi>π</cc:mi><cc:msub><cc:mi>χ</cc:mi><cc:mrow><cc:mi>b</cc:mi><cc:mn>1</cc:mn></cc:mrow></cc:msub></cc:math> near <fc:math xmlns:fc="http://www.w3.org/1998/Math/MathML" display="inline"><fc:msqrt><fc:mi>s</fc:mi></fc:msqrt><fc:mo>=</fc:mo><fc:mn>10.754</fc:mn><fc:mtext> </fc:mtext><fc:mtext> </fc:mtext><fc:mi>GeV</fc:mi></fc:math>, and it is hoped that the calculations here could be tested by the future Belle II experiments. Published by the American Physical Society 2024