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1. Diabatic dynamical diquark bound states: Mass corrections and widths

   https://doi.org/10.1103/PhysRevD.110.074002  

   Lebed, Richard F; Martinez, Steven R (October 2024, Physical Review D)

   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 $c\overline{c}q{\overline{q}}^{\prime }$ , $c\overline{c}s\overline{s}$ , and $c\overline{c}q\overline{s}$ 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 Society2024 

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2. Spin dependence of meson thresholds in the diabatic dynamical diquark model

   https://doi.org/10.1103/4sx7-rrdl  

   Lebed, Richard F (December 2025, Physical Review D)

   The diabatic dynamical diquark model is designed to unify diquark and molecular approaches for exotic hadrons by including the effects of dimeson thresholds on fundamental diquark-antidiquark states in order to form physical tetraquarks. We generalize this model by implementing the consequences of heavy-quark spin symmetry for each dimeson pair. We include the specific spin factors and mass differences associated with mesons related by this symmetry (such as $D,D^{*}$ ), both features being necessary for the systematic incorporation of effects beyond the static, heavy-source limit inherent to the (adiabatic) Born-Oppenheimer treatment. We obtain explicit interaction potentials for all $J=0$ , 1, 2 states, along the way deriving unusual variants of Fierz reordering identities, and discuss the application of the potentials to specific physical states such as ${\chi }_{c1}\left(3872\right)$ and $T_{c\overline{c}1}\left(3900\right)$ . 

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3. $\omega$ Meson from Lattice QCD

   https://doi.org/10.1103/PhysRevLett.133.211906  

   Yan, Haobo; Mai, Maxim; Garofalo, Marco; Meißner, Ulf-G; Liu, Chuan; Liu, Liuming; Urbach, Carsten (November 2024, Physical Review Letters)

   Many excited states in the hadron spectrum have large branching ratios to three-hadron final states. Understanding such particles from first principles QCD requires input from lattice QCD with one-, two-, and three-meson interpolators as well as a reliable three-body formalism relating finite-volume spectra at unphysical pion mass values to the scattering amplitudes at the physical point. In this work, we provide the first-ever calculation of the resonance parameters of the $\omega$ meson from lattice QCD, including an update of the formalism through matching to effective field theories. The main result of this pioneering study, the pole position of the $\omega$ meson at $\sqrt{s_{\omega }}=\left(778.0\right(11.2)-i3.0(5\left)\right)\mathrm{MeV}$ , agrees reasonably well with experiment. In addition we provide an estimate of the $\omega -\rho$ mass difference as 29(15) MeV. Published by the American Physical Society2024 

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4. Diabatic dynamical diquark model of hidden-strangeness tetraquarks

   https://doi.org/10.1103/vspf-jybk  

   Jafarzade, Shahriyar; Lebed, Richard F (December 2025, Physical Review D)

   We generalize our recent analysis of hidden-strangeness tetraquarks within the dynamical diquark model from its adiabatic form (in which each state is described solely by a diquark-antidiquark potential) to its diabatic form (which incorporates effects of dihadron thresholds upon the states). We tabulate all relevant thresholds and compute the dihadron content of each predicted state. Our results produce no particular hidden-strange tetraquark candidate whose structure is dominated by dihadron structure, in contrast to the charm sector, where many exotic states are strongly associated with such thresholds: The hidden-strange states tend to remain compact and less influenced by dihadron thresholds. Multiple states above 2 GeV with peculiar decay properties, including $\varphi \left(2170\right)$ , $f_2\left(2340\right)$ , and $\eta \left(2370\right)$ , continue to serve as excellent hidden-strange tetraquark candidates. 

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5. D meson -- pion scattering on CLS 2+1 flavor ensembles

   https://doi.org/10.22323/1.430.0068  

   Mohler, Daniel; Bulava, John; Hoerz, Ben; Johnson, Christopher; Morningstar, Colin; Hudspith, Renwick J. (February 2023, Proceedings of Science)

   We report progress on finite-volume determinations of heavy light-meson – Goldstone boson scattering phase shifts using the Luescher method on CLS 2+1 flavor gauge field ensembles. In a first iteration we will focus on D-meson – pion scattering in the elastic scattering region at various pion masses using ensembles with three lattice spacings. We employ ensembles on the CLS quark-mass trajectory with a fixed trace of the quark-mass matrix as well as ensembles with a strange-quark mass fixed close to its physical value, which will allow us to study both the light and the strange quark-mass dependence of positive parity heavy-light hadrons close to threshold. 

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