Two-lepton tales: Dalitz decays of heavy quarkonia

We study the Dalitz decays of heavy quarkonia, which result from the internal virtual photon conversion into an <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mo>ℓ</a:mo> <a:mo>+</a:mo> </a:msup> <a:msup> <a:mo>ℓ</a:mo> <a:mo>−</a:mo> </a:msup> </a:math> lepton pair. Heavy-quark symmetries allow us to establish systematic relations between transitions of different quarkonium states and to precisely determine the branching fractions for several charmonium and bottomonium decay modes. For charmonium, existing data on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>χ</c:mi> <c:mrow> <c:mi>c</c:mi> <c:mi>J</c:mi> </c:mrow> </c:msub> <c:mo stretchy="false">(</c:mo> <c:mn>1</c:mn> <c:mi>P</c:mi> <c:mo stretchy="false">)</c:mo> <c:mo stretchy="false">→</c:mo> <c:mi>J</c:mi> <c:mo>/</c:mo> <c:mi>ψ</c:mi> <c:msup> <c:mo>ℓ</c:mo> <c:mo>+</c:mo> </c:msup> <c:msup> <c:mo>ℓ</c:mo> <c:mo>−</c:mo> </c:msup> </c:math> and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>ψ</h:mi> <h:mo stretchy="false">(</h:mo> <h:mn>2</h:mn> <h:mi>S</h:mi> <h:mo stretchy="false">)</h:mo> <h:mo stretchy="false">→</h:mo> <h:msub> <h:mi>χ</h:mi> <h:mrow> <h:mi>c</h:mi> <h:mi>J</h:mi> </h:mrow> </h:msub> <h:mo stretchy="false">(</h:mo> <h:mn>1</h:mn> <h:mi>P</h:mi> <h:mo stretchy="false">)</h:mo> <h:msup> <h:mo>ℓ</h:mo> <h:mo>+</h:mo> </h:msup> <h:msup> <h:mo>ℓ</h:mo> <h:mo>−</h:mo> </h:msup> </h:math> enable us to determine the parameters of the transition form factors and to predict the rates of yet-unobserved modes. The Dalitz transitions of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>χ</o:mi> <o:mrow> <o:mi>c</o:mi> <o:mn>1</o:mn> </o:mrow> </o:msub> <o:mo stretchy="false">(</o:mo> <o:mn>3872</o:mn> <o:mo stretchy="false">)</o:mo> </o:math> are important, as they can help assessing the structure of this meson. For bottomonium, recent LHCb measurements allow us to predict the branching fractions of <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>χ</s:mi> <s:mrow> <s:mi>b</s:mi> <s:mi>J</s:mi> </s:mrow> </s:msub> <s:mo stretchy="false">(</s:mo> <s:mi>n</s:mi> <s:mi>P</s:mi> <s:mo stretchy="false">)</s:mo> <s:mo stretchy="false">→</s:mo> <s:mi mathvariant="normal">ϒ</s:mi> <s:mo stretchy="false">(</s:mo> <s:mn>1</s:mn> <s:mi>S</s:mi> <s:mo stretchy="false">)</s:mo> <s:msup> <s:mo>ℓ</s:mo> <s:mo>+</s:mo> </s:msup> <s:msup> <s:mo>ℓ</s:mo> <s:mo>−</s:mo> </s:msup> </s:math> and <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:msub> <ab:mi>h</ab:mi> <ab:mi>b</ab:mi> </ab:msub> <ab:mo stretchy="false">(</ab:mo> <ab:mi>n</ab:mi> <ab:mi>P</ab:mi> <ab:mo stretchy="false">)</ab:mo> <ab:mo stretchy="false">→</ab:mo> <ab:msub> <ab:mi>η</ab:mi> <ab:mi>b</ab:mi> </ab:msub> <ab:mo stretchy="false">(</ab:mo> <ab:mn>1</ab:mn> <ab:mi>S</ab:mi> <ab:mo stretchy="false">)</ab:mo> <ab:msup> <ab:mo>ℓ</ab:mo> <ab:mo>+</ab:mo> </ab:msup> <ab:msup> <ab:mo>ℓ</ab:mo> <ab:mo>−</ab:mo> </ab:msup> </ab:math> ( <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mi>n</hb:mi> <hb:mo>=</hb:mo> <hb:mn>1</hb:mn> </hb:math> , 2). We also investigate the sensitivity of heavy quarkonia Dalitz modes to the contribution of a new light vector mediator, such as the putative <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"> <jb:mi>X</jb:mi> <jb:mo stretchy="false">(</jb:mo> <jb:mn>17</jb:mn> <jb:mo stretchy="false">)</jb:mo> </jb:math> .