Exclusive decays of fully heavy tetraquarks into light mesons

In this work, we investigate the exclusive decays of the fully-heavy tetraquark states <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>T</a:mi> <a:mrow> <a:mn>4</a:mn> <a:mi>c</a:mi> <a:mo>,</a:mo> <a:mi>b</a:mi> </a:mrow> </a:msub> </a:math> into light mesons, specifically <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>π</c:mi> </c:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>K</e:mi> </e:math> , using the framework of nonrelativistic quantum chromodynamics (NRQCD) and collinear QCD factorization for hard exclusive processes. We estimate the decay widths to be <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msup> <g:mn>10</g:mn> <g:mrow> <g:mo>−</g:mo> <g:mn>9</g:mn> </g:mrow> </g:msup> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>GeV</g:mi> </g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msup> <i:mn>10</i:mn> <i:mrow> <i:mo>−</i:mo> <i:mn>14</i:mn> </i:mrow> </i:msup> <i:mtext> </i:mtext> <i:mtext> </i:mtext> <i:mi>GeV</i:mi> </i:math> for the decays <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>T</k:mi> <k:mrow> <k:mn>4</k:mn> <k:mi>c</k:mi> </k:mrow> </k:msub> <k:mo stretchy="false">→</k:mo> <k:msup> <k:mi>π</k:mi> <k:mo>+</k:mo> </k:msup> <k:msup> <k:mi>π</k:mi> <k:mo>−</k:mo> </k:msup> </k:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi>T</n:mi> <n:mrow> <n:mn>4</n:mn> <n:mi>b</n:mi> </n:mrow> </n:msub> <n:mo stretchy="false">→</n:mo> <n:msup> <n:mi>π</n:mi> <n:mo>+</n:mo> </n:msup> <n:msup> <n:mi>π</n:mi> <n:mo>−</n:mo> </n:msup> </n:math> (and similarly for <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msup> <q:mi>K</q:mi> <q:mo>+</q:mo> </q:msup> <q:msup> <q:mi>K</q:mi> <q:mo>−</q:mo> </q:msup> </q:math> ), respectively. The branching ratio for <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msub> <s:mi>T</s:mi> <s:mrow> <s:mn>4</s:mn> <s:mi>c</s:mi> </s:mrow> </s:msub> <s:mo stretchy="false">→</s:mo> <s:msup> <s:mi>π</s:mi> <s:mo>+</s:mo> </s:msup> <s:msup> <s:mi>π</s:mi> <s:mo>−</s:mo> </s:msup> <s:mo stretchy="false">(</s:mo> <s:msup> <s:mi>K</s:mi> <s:mo>+</s:mo> </s:msup> <s:msup> <s:mi>K</s:mi> <s:mo>−</s:mo> </s:msup> <s:mo stretchy="false">)</s:mo> </s:math> is on the order of <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msup> <x:mn>10</x:mn> <x:mrow> <x:mo>−</x:mo> <x:mn>8</x:mn> </x:mrow> </x:msup> </x:math> , making it currently unobservable in existing experiments. The factorization of <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msub> <z:mi>T</z:mi> <z:mrow> <z:mn>4</z:mn> <z:mi>c</z:mi> <z:mo>,</z:mo> <z:mi>b</z:mi> </z:mrow> </z:msub> </z:math> into light hadrons shares similarities with the decay <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>J</bb:mi> <bb:mo>/</bb:mo> <bb:mi>ψ</bb:mi> <bb:mo stretchy="false">→</bb:mo> <bb:mi>p</bb:mi> <bb:mover accent="true"> <bb:mi>p</bb:mi> <bb:mo stretchy="false">¯</bb:mo> </bb:mover> </bb:math> . However, unlike the latter process, the decay <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msub> <gb:mi>T</gb:mi> <gb:mrow> <gb:mn>4</gb:mn> <gb:mi>c</gb:mi> <gb:mo>,</gb:mo> <gb:mi>b</gb:mi> </gb:mrow> </gb:msub> <gb:mo stretchy="false">→</gb:mo> <gb:msup> <gb:mi>π</gb:mi> <gb:mo>+</gb:mo> </gb:msup> <gb:msup> <gb:mi>π</gb:mi> <gb:mo>−</gb:mo> </gb:msup> <gb:mo stretchy="false">(</gb:mo> <gb:msup> <gb:mi>K</gb:mi> <gb:mo>+</gb:mo> </gb:msup> <gb:msup> <gb:mi>K</gb:mi> <gb:mo>−</gb:mo> </gb:msup> <gb:mo stretchy="false">)</gb:mo> </gb:math> exhibits unique features that arise only in processes involving multiple incoming or outgoing particles. One such feature is the necessity of maintaining the <lb:math xmlns:lb="http://www.w3.org/1998/Math/MathML" display="inline"> <lb:mi>i</lb:mi> <lb:mi>ϵ</lb:mi> </lb:math> -prescription for the denominators or propagators due to the divergences in the kinematic region of interest. Employing the sector decomposition method, along with the aid of the Cheng-Wu theorem and the program, we present a systematic approach to handle the convolutions and phase-space integrations. This method can also be extended to similar processes, such as <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"> <nb:msub> <nb:mi>T</nb:mi> <nb:mrow> <nb:mn>4</nb:mn> <nb:mi>c</nb:mi> <nb:mo>,</nb:mo> <nb:mi>b</nb:mi> </nb:mrow> </nb:msub> <nb:mo stretchy="false">→</nb:mo> <nb:mi>p</nb:mi> <nb:mover accent="true"> <nb:mi>p</nb:mi> <nb:mo stretchy="false">¯</nb:mo> </nb:mover> </nb:math> , as well as to phase-space integrations where each denominator is a linear combination of integration variables.