Near-threshold states in coupled <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>D</mml:mi> <mml:msup> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> <mml:mo>−</mml:mo> <mml:msup> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> <mml:msup> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> scattering from lattice QCD

Abstract

The first determination of doubly charmed isospin-0 coupled-channel <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>D</a:mi> <a:msup> <a:mi>D</a:mi> <a:mo>*</a:mo> </a:msup> <a:mo>−</a:mo> <a:msup> <a:mi>D</a:mi> <a:mo>*</a:mo> </a:msup> <a:msup> <a:mi>D</a:mi> <a:mo>*</a:mo> </a:msup> </a:math> scattering amplitudes from lattice quantum chromodynamics (QCD) is presented. The finite-volume spectrum is computed for three lattice volumes with a light-quark mass corresponding to <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>m</c:mi> </c:mrow> <c:mrow> <c:mi>π</c:mi> </c:mrow> </c:msub> <c:mo>≈</c:mo> <c:mn>391</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi>MeV</c:mi> </c:mrow> </c:math> and is used to extract the scattering amplitudes in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>J</e:mi> <e:mi>P</e:mi> </e:msup> <e:mo>=</e:mo> <e:msup> <e:mn>1</e:mn> <e:mo>+</e:mo> </e:msup> </e:math> via the Lüscher quantization condition. By analytically continuing the scattering amplitudes to complex energies, a <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>T</g:mi> <g:mrow> <g:mi>c</g:mi> <g:mi>c</g:mi> </g:mrow> </g:msub> </g:math> pole corresponding to a virtual bound state is found below <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> threshold. We also find a second pole, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msubsup> <k:mi>T</k:mi> <k:mrow> <k:mi>c</k:mi> <k:mi>c</k:mi> </k:mrow> <k:mo>′</k:mo> </k:msubsup> </k:math> , corresponding to a resonance pole below the kinematically closed <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msup> <m:mi>D</m:mi> <m:mo>*</m:mo> </m:msup> <m:msup> <m:mi>D</m:mi> <m:mo>*</m:mo> </m:msup> </m:math> channel, to which it has a strong coupling. A nonzero coupling is robustly found between the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>S</o:mi> </o:math> -wave <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>D</q:mi> <q:msup> <q:mi>D</q:mi> <q:mo>*</q:mo> </q:msup> </q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:msup> <s:mi>D</s:mi> <s:mo>*</s:mo> </s:msup> <s:msup> <s:mi>D</s:mi> <s:mo>*</s:mo> </s:msup> </s:math> channels producing a clear cusp in the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi>D</u:mi> <u:msup> <u:mi>D</u:mi> <u:mo>*</u:mo> </u:msup> </u:math> amplitude at the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msup> <w:mi>D</w:mi> <w:mo>*</w:mo> </w:msup> <w:msup> <w:mi>D</w:mi> <w:mo>*</w:mo> </w:msup> </w:math> threshold energy. This suggests that the experimental <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msubsup> <y:mi>T</y:mi> <y:mrow> <y:mi>c</y:mi> <y:mi>c</y:mi> </y:mrow> <y:mo>′</y:mo> </y:msubsup> </y:math> should be observable in <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>D</ab:mi> <ab:msup> <ab:mi>D</ab:mi> <ab:mo>*</ab:mo> </ab:msup> </ab:math> and <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msup> <cb:mi>D</cb:mi> <cb:mo>*</cb:mo> </cb:msup> <cb:msup> <cb:mi>D</cb:mi> <cb:mo>*</cb:mo> </cb:msup> </cb:math> final states at ongoing experiments.

Topics & Concepts