We perform a lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $bar cc bar du$, $bar cc(bar uu+bar dd)$ and $bar cc bar ss$, where the later two can mix with $bar cc$. This simulation with $N_f=2$ and $m_pi=266$ Me
V aims at the possible signatures of four-quark exotic states. We utilize a large basis of $bar cc$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both anti-triplet and sextet color representations. A lattice candidate for X(3872) with I=0 is observed very close to the experimental state only if both $bar cc$ and $Dbar D^*$ interpolators are included; the candidate is not found if diquark-antidiquark and $Dbar D^*$ are used in the absence of $bar cc$. No candidate for neutral or charged X(3872), or any other exotic candidates are found in the I=1 channel. We also do not find signatures of exotic $bar ccbar ss$ candidates below 4.3 GeV, such as Y(4140). Possible physics and methodology related reasons for that are discussed. Along the way, we present the diquark-antidiquark operators as linear combinations of the two-meson operators via the Fierz transformations.
We determine the spectrum of $B_s$ 1P states using lattice QCD. For the $B_{s1}(5830)$ and $B_{s2}^*(5840)$ mesons, the results are in good agreement with the experimental values. Two further mesons are expected in the quantum channels $J^P=0^+$ and
$1^+$ near the $BK$ and $B^{*}K$ thresholds. A combination of quark-antiquark and $B^{(*)}$ meson-Kaon interpolating fields are used to determine the mass of two QCD bound states below the $B^{(*)}K$ threshold, with the assumption that mixing with $B_s^{(*)}eta$ and isospin-violating decays to $B_s^{(*)}pi$ are negligible. We predict a $J^P=0^+$ bound state $B_{s0}$ with mass $m_{B_{s0}}=5.711(13)(19)$ GeV. With further assumptions motivated theoretically by the heavy quark limit, a bound state with $m_{B_{s1}}= 5.750(17)(19)$ GeV is predicted in the $J^P=1^+$ channel. The results from our first principles calculation are compared to previous model-based estimates.
We study the three $D_s$ quantum channels $J^P = 0^+$, $1^+$ and $2^+$ where experiments have identified the charm-strange states $D^*_{s0} (2317)$, $D_{s1}(2460)$, $D_{s1}(2536)$ near the $DK$ and $D^*K$ thresholds, and $D^*_{s2}(2573)$. We consider
correlation functions for sets of $overline q q$ operators and, for $J^P = 0^+$, $1^+$, also the $DK$ and $D^*K$ meson-meson interpolators and determine for these cases values of the elastic scattering amplitude. Constructing the full set of correlators requires propagators which connect any pair of lattice sites. For one ensemble of gauge configurations ($32^3times 64$, $m_piapprox 156$ MeV) a stochastic distillation variant is employed and for another ensemble ($16^3times 32$, $m_piapprox 266$ MeV) we use the full distillation method. Both, $D^*_{s0} (2317)$ and $D_{s1}(2460)$, are found as bound states below threshold, whereas $D_{s1}(2536)$, and $D^*_{s2}(2573)$ are identified as narrow resonances close to the experimental masses.
Recently experimentalists have discovered several charged charmonium-like hadrons $Z_c^+$ with unconventional quark content $bar ccbar d u$. We perform a search for $Z_c^+$ with mass below $4.2~$GeV in the channel $I^G(J^{PC})=1^+(1^{+-})$ using latt
ice QCD. The major challenge is presented by the two-meson states $J/psi, pi$, $psi_{2S}pi$, $psi_{1D}pi$, $Dbar D^*$, $D^*bar D^*$, $eta_crho$ that are inevitably present in this channel. The spectrum of eigenstates is extracted using a number of meson-meson and diquark-antidiquark interpolating fields. For our pion mass of 266~MeV we find all the expected two-meson states but no additional candidate for $Z_c^+$ below $4.2~$GeV. Possible reasons for not seeing an additional eigenstate related to $Z_c^+$ are discussed. We also illustrate how a simulation incorporating interpolators with a structure resembling low-lying two-mesons states seems to render a $Z_c^+$ candidate, which is however not robust after further two-meson states around $4.2~$GeV are implemented.
$D_s$ mesons are studied in three quantum channels ($J^P=0^+$, $1^+$ and $2^+$), where experiments have identified the very narrow $D_{s0}^*(2317)$, $D_{s1}(2460)$ and narrow $D_{s1}(2536)$, $D_{s2}^*(2573)$. We explore the effect of nearby $DK$ and
$D^*K$ thresholds on the subthreshold states using lattice QCD. Our simulation is done on two very different ensembles of gauge configurations (2 or 2+1 dynamical quarks, Pion mass of 266 or 156 MeV, lattice size $16^3times 32$ or $32^3times 64$). In addition to $bar{q}q$ operators we also include meson-meson interpolators in the correlation functions. This clarifies the identification of the states above and below the scattering thresholds. The ensemble with $m_pi simeq 156~$MeV renders the $D_{s1}(2460)$ as a strong interaction bound state 44(10)MeV below $D^*K$ threshold, which is in agreement with the experiment. The $D_{s0}^*(2317)$ is found 37(17)MeV below $DK$ threshold, close to experiment value of 45MeV. The narrow resonances $D_{s1}(2536)$ and $D_{s2}^*(2573)$ are also found close to the experimental masses.
We extend our study of the $Kpi$ system to moving frames and present an exploratory extraction of the masses and widths for the $K^*$ resonances by simulating $Kpi$ scattering in p-wave with $I=1/2$ on the lattice. Using $Kpi$ systems with non-vanish
ing total momenta allows the extraction of phase shifts at several values of $Kpi$ relative momenta. A Breit-Wigner fit of the phase renders a $K^*(892)$ resonance mass and $K^*to K pi $ coupling compatible with the experimental numbers. We also determine the $K^*(1410)$ mass assuming the experimental $K^*(1410)$ width. We contrast the resonant $I=1/2$ channel with the repulsive non-resonant $I=3/2$ channel, where the phase is found to be negative and small, in agreement with experiment.
Including the meson-baryon (5 quark) intermediate states in a lattice simulation is challenging. However, it is important in order to obtain the correct energy eigenstates and to relate them to scattering phase shifts. Recent results for the negative
parity nucleon channel and the problem of baryonic resonances in lattice calculations are discussed.
The scalar meson $D_{s0}^*(2317)$ is found 37(17)MeV below DK threshold in a lattice simulation of the $J^P=0^+$ channel using, for the first time, both DK as well as $bar sc$ interpolating fields. The simulation is done on $N_f=2+1$ gauge configurat
ions with $m_pisimeq 156 $MeV, and the resulting $M_{D_{s0}^*}-tfrac{1}{4}(M_{D_s}+3M_{D_s^*})=266(16)$ MeV is close to the experimental value 241.5(0.8)MeV. The energy level related to the scalar meson is accompanied by additional discrete levels due to DK scattering states. The levels near threshold lead to the negative DK scattering length $a_0=-1.33(20)$ fm that indicates the presence of a state below threshold.
We study the coupled pion-nucleon system (negative parity, isospin 1/2) based on a lattice QCD simulation for nf=2 mass degenerate light quarks. Both, standard 3-quarks baryon operators as well as meson-baryon (4+1)-quark operators are included. This
is an exploratory study for just one lattice size and lattice spacing and at a pion mass of 266 MeV. Using the distillation method and variational analysis we determine energy levels of the lowest eigenstates. Comparison with the results of simple 3-quark correlation studies exhibits drastic differences and a new level appears. A clearer picture of the negative parity nucleon spectrum emerges. For the parameters of the simulation we may assume elastic s-wave scattering and can derive values of the phase shift.
We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution
of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the Delta - N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.
