Diabatic dynamical diquark bound states: Mass corrections and widths

Using the diabatic formalism, which generalizes the adiabatic approximation in the Born-Oppen-heimer formalism, we apply well-known Hamiltonian methods to calculate the effect of open di-meson thresholds that lie well below the mass of elementary <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>c</a:mi><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mi>q</a:mi><a:msup><a:mover accent="true"><a:mi>q</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mo>′</a:mo></a:msup></a:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>c</g:mi><g:mover accent="true"><g:mi>c</g:mi><g:mo stretchy="false">¯</g:mo></g:mover><g:mi>s</g:mi><g:mover accent="true"><g:mi>s</g:mi><g:mo stretchy="false">¯</g:mo></g:mover></g:math>, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>c</m:mi><m:mover accent="true"><m:mi>c</m:mi><m:mo stretchy="false">¯</m:mo></m:mover><m:mi>q</m:mi><m:mover accent="true"><m:mi>s</m:mi><m:mo stretchy="false">¯</m:mo></m:mover></m:math> tetraquark bound states. We compute the resulting mass shifts for these states, as well as their decay widths to the corresponding meson pairs. Each mass eigenstate, originally produced using a bound-state approximation under the diabatic formalism, consists of an admixture of a compact diquark-antidiquark configuration (an eigenstate of the original dynamical diquark model) with an extended di-meson configuration induced by the nearest threshold. We compare our results with those from our recent work that employs a scattering formalism, and find a great deal of agreement, but also comment upon interesting discrepancies between the two approaches. Published by the American Physical Society 2024