Charmonium-like resonances and bound states with isospin zero and
$J^{PC}=0^{++},~1^{--},~2^{++},~3^{--}$ are extracted on the lattice. Coupled
$D\bar D$ and $D_s\bar D_s$ scattering suggests three ...charmonium-like states
with $J^{PC}=0^{++}$ in addition to $\chi_{c0}(1P)$: a so far unobserved $D\bar
D$ bound state just below threshold, a conventional resonance likely related to
$\chi_{c0}(3860)/\chi_{c0}(2P)$ and a narrow resonance just below the $D_s\bar
D_s$ threshold with a large coupling to $D_s\bar D_s$ likely related to
$X(3915)/\chi_{c0}(3930)$. One-channel $D\bar D$ scattering renders resonances
and bound states with $J^{PC}= 1^{--},~2^{++},~3^{--}$ related to the observed
conventional charmonia. Lattice QCD ensembles from the CLS consortium with
$m_{\pi}\simeq 280$ MeV are utilized.
We study the
qq¯ singlet and non-singlet scalar-meson masses using domain wall fermions and the quenched approximation. The singlet mass is found to be smaller than the non-singlet mass and indicates ...that the lowest singlet meson state could be lighter than 1 GeV. The two-point functions for very small quark masses are compared with expectations from the small-volume chiral perturbation theory and the presence of fermionic zero modes.
We present the first lattice investigation of coupled-channel $D\bar D$ and
$D_s\bar D_s$ scattering in the $J^{PC}=0^{++}$ and $2^{++}$ channels. The
scattering matrix for partial waves $l=0,2$ and ...isospin zero is determined
using multiple volumes and inertial frames via L\"uscher's formalism. Lattice
QCD ensembles from the CLS consortium with $m_{\pi}\simeq280$ MeV, $a \simeq
0.09 $ fm and $L/a=24,~32$ are utilized. The resulting scattering matrix
suggests the existence of three charmonium-like states with $J^{PC}=0^{++}$ in
the energy region ranging from slightly below $2m_D$ up to 4.13 GeV. We find a
so far unobserved $D\bar D$ bound state just below threshold and a $D\bar D$
resonance likely related to $\chi_{c0}(3860)$, which is believed to be
$\chi_{c0}(2P)$. In addition, there is an indication for a narrow $0^{++}$
resonance just below the $D_s\bar D_s$ threshold with a large coupling to
$D_s\bar D_s$ and a very small coupling to $D\bar D$. This resonance is
possibly related to the narrow $X(3915)$/$\chi_{c0}(3930)$ observed in
experiment also just below $D_s\bar D_s$. The partial wave $l=2$ features a
resonance likely related to $\chi_{c2}(3930)$. We work with several
assumptions, such as the omission of $J/\psi\omega$, $\eta_c\eta$ and
three-particle channels. Only statistical uncertainties are quantified, while
the extrapolations to the physical quark-masses and the continuum limit are
challenges for the future.
Two tetraquark candidates \(Z_b(10610)\) and \(Z_b(10650)\) with flavor structure \(\bar bb\bar du\) were discovered by Belle experiment in 2011. We present a preliminary \(N_f=2\) lattice study of ...the \(\bar bb\bar du\) system in the approximation of static \(b\) quarks, where the total spin of heavy quarks is fixed to one. The ground and the excited eigen-energies are determined as a function of separation \(r\) between \(b\) and \(\bar b\). The lower eigenstates are related to a bottomonium and a pion. One of the higher eigenstates is dominated by \(B\bar B^*\): its energy is significantly below \(m_B+m_{B*}\) for r=0.1,0.4 fm, which suggests sizable attraction. The attractive potential \(V(r)\) between \(B\) and \(\bar B^*\) is extracted assuming that this eigenstate is related exclusively to \(B\bar B^*\). Assuming a certain form of the potential and solving non-relativistic Schrodinger equation, we find a bound state pole below \(B\bar B^*\) threshold. For certain parametrizations, the bound state is very close to the \(B\bar B^*\) threshold - this feature could be related to \(Z_b(10610)\) in the experiment.
Phys. Rev. D 100, 074505 (2019) We present a lattice QCD study of charmonium resonances and bound states with
$J^{PC}=1^{--}$ and $3^{--}$ near the open-charm threshold, taking into account
their ...strong transitions to $\bar DD$. Vector charmonia are the most abundant
in the experimentally established charmonium spectrum, while recently LHCb
reported also the first discovery of a charmonium with likely spin three. The
$\bar DD$ scattering amplitudes for partial waves $l=1$ and $l=3$ are extracted
on the lattice by means of the L\"uscher formalism, using multiple volumes and
inertial frames. Parameterizations of the scattering amplitudes provide masses
and widths of the resonances, as well as the masses of bound states. CLS
ensembles with 2+1 dynamical flavors of non-perturbatively $O(a)$ improved
Wilson quarks are employed with $m_\pi\simeq 280$ MeV, a single lattice spacing
of $a\simeq0.086$ fm and two lattice spatial extents of $L=24$ and $32$. Two
values of the charm quark mass are considered to examine the influence of the
position of the $\bar{D}D$ threshold on the hadron masses. For the lighter
charm quark mass we find the vector resonance $\psi(3770)$ with mass
$m=3780(7)$ MeV and coupling $g=16.0(^{+2.1}_{-0.2})$ (related to the width),
both consistent with their experimental values. The vector $\psi(2S)$ appears
as a bound state with $m=3666(10)$ MeV. The charmonium resonance with
$J^{PC}=3^{--}$ is found at $m=3831(^{+10}_{-16})$ MeV, consistent with the
$X(3842)$ recently discovered by LHCb. At our heavier charm-quark mass the
$\psi(2S)$ as well as the $\psi(3770)$ are bound states and the $X(3842)$
remains a resonance. We stress that all quoted uncertainties are only
statistical, while lattice spacing effects and the approach to the physical
point still need to be explored. This study of conventional charmonia sets the
stage for more challenging future studies of unconventional charmonium-like
states.
Phys. Rev. D 94, 074509 (2016) We investigate $B_s\pi^+$ scattering in s-wave using lattice QCD in order to
search for an exotic resonance X(5568) with flavor $\bar b s \bar d u$; such a
state was ...recently reported by D0 but was not seen by LHCb. If X(5568) with
$J^P=0^+$ exists, it can strongly decay only to $B_s\pi^+$ and lies
significantly below all other thresholds, which makes a lattice search for
X(5568) cleaner and simpler than for other exotic candidates. Both an elastic
resonance in $B_s\pi^+$ as well as a deeply bound $B^+\bar K^0$ would lead to
distinct signatures in the energies of lattice eigenstates, which are not seen
in our simulation. We therefore do not find a candidate for X(5568) with
$J^P=0^+$ in agreement with the recent LHCb result. The extracted $B_s\pi^+$
scattering length is compatible with zero within the error.
In this talk I present the results obtained using effective field theories in
a finite volume from a reanalysis of lattice data on the $KD^{(*)}$ systems,
where bound states of $KD$ and $KD^*$ are ...found and associated with the states
$D^*_{s0}(2317)$ and $D^*_{s1}(2460)$, respectively. We confirm the presence of
such states on the lattice data and determine the weight of the $KD$ channel in
the wave function of $D^*_{s0}(2317)$ and that of $KD^*$ in the wave function
of $D^*_{s1}(2460)$. Our results indicate a large meson-meson component in both
cases.
PDF
