Doubly charm tetraquark channel with isospin 1 from lattice QCD
Lu Meng, Emmanuel Ortiz-Pacheco, V. Baru, E. Epelbaum, M. Padmanath, Saša Prelovšek
Abstract
Experimentally, the doubly charm tetraquark channel <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>c</a:mi> <a:mi>c</a:mi> <a:mover accent="true"> <a:mi>q</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> <a:mover accent="true"> <a:mi>q</a:mi> <a:mo stretchy="false">¯</a:mo> </a:mover> </a:math> with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mi>q</g:mi> <g:mo>=</g:mo> <g:mi>u</g:mi> </g:mrow> </g:math> , <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:mi>d</i:mi> </i:mrow> </i:math> features an exotic hadron, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>T</k:mi> <k:mrow> <k:mi>c</k:mi> <k:mi>c</k:mi> </k:mrow> </k:msub> </k:math> , with isospin <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>I</m:mi> <m:mo>=</m:mo> <m:mn>0</m:mn> </m:math> near the <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>D</o:mi> <o:msup> <o:mi>D</o:mi> <o:mo>*</o:mo> </o:msup> </o:math> threshold, while no peak was observed for <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>I</q:mi> <q:mo>=</q:mo> <q:mn>1</q:mn> </q:math> . We present a lattice QCD study of this channel with <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>I</s:mi> <s:mo>=</s:mo> <s:mn>1</s:mn> </s:math> , <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msup> <u:mi>J</u:mi> <u:mi>P</u:mi> </u:msup> <u:mo>=</u:mo> <u:msup> <u:mn>1</u:mn> <u:mo>+</u:mo> </u:msup> </u:math> , and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:msub> <w:mi>m</w:mi> <w:mi>π</w:mi> </w:msub> <w:mo>≃</w:mo> <w:mn>280</w:mn> <w:mtext> </w:mtext> <w:mtext> </w:mtext> <w:mi>MeV</w:mi> </w:math> . Finite-volume energies calculated across five charm quark masses consistently feature a positive energy shift with respect to noninteracting energies, indicating repulsive interaction at energies near the threshold. These energies are used to compute the <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mi>D</y:mi> <y:msup> <y:mi>D</y:mi> <y:mo>*</y:mo> </y:msup> </y:math> scattering amplitude using both the standard Lüscher method and the recently proposed effective field theory-based approach in the plane wave basis, which incorporates the long-range interactions and the left-hand cut. Both analyses render a small negative scattering length and a scattering amplitude that does not feature any poles in the energy region near the <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> threshold, in line with the LHCb results. We identify that the Wick contraction, resembling <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mi>t</cb:mi> </cb:math> -channel isovector-vector meson exchanges between <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:mi>D</eb:mi> </eb:math> and <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"> <gb:msup> <gb:mi>D</gb:mi> <gb:mo>*</gb:mo> </gb:msup> </gb:math> , plays a key role in distinguishing between the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi>I</ib:mi> <ib:mo>=</ib:mo> <ib:mn>0</ib:mn> </ib:math> and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"> <kb:mi>I</kb:mi> <kb:mo>=</kb:mo> <kb:mn>1</kb:mn> </kb:math> channels, leading to repulsion in the <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi>I</mb:mi> <mb:mo>=</mb:mo> <mb:mn>1</mb:mn> </mb:math> and attraction in the <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"> <ob:mi>I</ob:mi> <ob:mo>=</ob:mo> <ob:mn>0</ob:mn> </ob:math> channel.