Doubly heavy tetraquarks from lattice QCD: Incorporating diquark-antidiquark operators and the left-hand cut

Abstract

Lattice studies of the doubly charm tetraquark <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>T</a:mi> <a:mrow> <a:mi>c</a:mi> <a:mi>c</a:mi> </a:mrow> </a:msub> <a:mo>=</a:mo> <a:mi>c</a:mi> <a:mi>c</a:mi> <a:mover accent="true"> <a:mi>u</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mover accent="true"> <a:mi>d</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> require the determination of the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>D</g:mi> <g:msup> <g:mi>D</g:mi> <g:mo>*</g:mo> </g:msup> </g:math> scattering amplitude, which most often incorporate only meson-meson interpolators. We additionally incorporate diquark-antidiquark operators and find that these have some impact on certain eigenenergies. This study presents the first extraction of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>D</i:mi> <i:msup> <i:mi>D</i:mi> <i:mo>*</i:mo> </i:msup> </i:math> scattering amplitude based on the meson-meson as well as diquark antidiquark interpolators. The effect of the additional operators renders slightly smaller values of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mi>p</k:mi> </k:mrow> </k:math> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mi>cot</m:mi> <m:msub> <m:mrow> <m:mi>δ</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msub> </m:mrow> </m:math> and a <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>T</o:mi> <o:mrow> <o:mi>c</o:mi> <o:mi>c</o:mi> </o:mrow> </o:msub> </o:math> pole slightly closer to the threshold. The scattering amplitude is extracted from eigenenergies by adopting plane-wave and effective-field-theoretic methods, which also incorporate the left-hand cut and address the partial wave mixing. The <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>T</q:mi> <q:mrow> <q:mi>c</q:mi> <q:mi>c</q:mi> </q:mrow> </q:msub> </q:math> is found to be a subthreshold resonance with a pole at <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mrow> <s:msub> <s:mrow> <s:mi>m</s:mi> </s:mrow> <s:mrow> <s:msub> <s:mrow> <s:mi>T</s:mi> </s:mrow> <s:mrow> <s:mi>c</s:mi> <s:mi>c</s:mi> </s:mrow> </s:msub> </s:mrow> </s:msub> <s:mo>−</s:mo> <s:msub> <s:mrow> <s:mi>m</s:mi> </s:mrow> <s:mrow> <s:mi>D</s:mi> </s:mrow> </s:msub> <s:mo>−</s:mo> <s:msub> <s:mrow> <s:mi>m</s:mi> </s:mrow> <s:mrow> <s:msup> <s:mrow> <s:mi>D</s:mi> </s:mrow> <s:mrow> <s:mo>*</s:mo> </s:mrow> </s:msup> </s:mrow> </s:msub> <s:mo>=</s:mo> <s:mo>−</s:mo> <s:msubsup> <s:mrow> <s:mn>5.2</s:mn> </s:mrow> <s:mrow> <s:mo>−</s:mo> <s:mn>0.8</s:mn> </s:mrow> <s:mrow> <s:mo>+</s:mo> <s:mn>0.7</s:mn> </s:mrow> </s:msubsup> <s:mo>−</s:mo> <s:mi>i</s:mi> <s:mo>·</s:mo> <s:msubsup> <s:mrow> <s:mn>6.3</s:mn> </s:mrow> <s:mrow> <s:mo>−</s:mo> <s:mn>4.8</s:mn> </s:mrow> <s:mrow> <s:mo>+</s:mo> <s:mn>2.4</s:mn> </s:mrow> </s:msubsup> <s:mtext> </s:mtext> <s:mtext> </s:mtext> <s:mi>MeV</s:mi> </s:mrow> </s:math> , employing coordinated lattice simulations (CLS) ensembles with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>m</u:mi> <u:mi>π</u:mi> </u:msub> <u:mo>≃</u:mo> <u:mn>280</u:mn> <u:mtext> </u:mtext> <u:mtext> </u:mtext> <u:mi>MeV</u:mi> </u:math> and the distillation method. A more significant effect of diquark-antidiquark operators on eigen-energies is found for larger heavy quark masses relevant for <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>T</w:mi> <w:mrow> <w:mi>b</w:mi> <w:mi>b</w:mi> </w:mrow> </w:msub> </w:math> . We find that deeply bound <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msub> <y:mi>T</y:mi> <y:mrow> <y:mi>b</y:mi> <y:mi>b</y:mi> </y:mrow> </y:msub> </y:math> does not emerge when employing only meson-meson operators, where each meson is separately momentum projected, while the deeply bound state emerges after adding local diquark antidiquark operators.

Topics & Concepts