We present the results of a lattice calculation of tetraquark states with quark contents q1q2QQ, q1, q2 ⊂ u, d, s, c and Q ≡ b, c in both spin zero (J = 0) and spin one (J = 1) sectors. This calculation is performed on three dynamical N f = 2 + 1 + 1 highly improved staggered quark ensembles at lattice spacings of about 0.12, 0.09 and 0.06 fm. We use the overlap action for light to charm quarks while a non-relativistic action with non-perturbatively improved coefficients with terms up to O(αsv 4 ) is employed for the bottom quark. While considering charm or bottom quarks as heavy, we calculate the energy levels of various four-quark configurations with light quark masses ranging from the physical strange quark mass to that of the corresponding physical pion mass. This enables us to explore the quark mass dependence of the extracted four-quark energy levels over a wide range of quark masses. The results of the spin one states show the presence of ground state energy levels which are below their respective thresholds for all the light flavor combinations. Further, we identify a trend that the energy splittings, defined as the energy difference between the ground state energy levels and their respective thresholds, increase with decreasing the light quark masses and are maximum at the physical point for all the spin one states. The rate of increase is however dependent on the light quark configuration of the particular spin one state. We also present a study of hadron mass relations involving tetraquarks, baryons and mesons arising in the limit of infinitely heavy quark and find that these relations are more compatible with the heavy quark limit in the bottom sector but deviate substantially in the charm sector. The ground state spectra of the spin zero tetraquark states with various flavor combinations are seen to lie above their respective thresholds.1 A diquark can be interpreted as a compact colored object inside a hadron and is made out of two quarks (or antiquarks) in the 3(3) or 6(6) irrep of SU(3) and can have spin zero (scalar) or spin one (vector). With this model one can build rich phenomenology for mesons, baryons, as well as multiquark states.

The spectrum of excitations of triply-charmed baryons is computed using lattice QCD including dynamical light quark fields. Calculations are performed on anisotropic lattices with temporal and spatial spacings at = 0.0351(2) fm and as ∼ 0.12 fm respectively and with pion mass of about 390 MeV. The spectrum obtained has baryonic states with well-defined total spin up to 7 2 and the lowlying states closely resemble the expectation from models with an SU (6) × O(3) symmetry. Energy splittings between extracted states, including those due to spin-orbit coupling in the heavy quark limit are computed and compared against data at other quark masses.

We present the ground and excited state spectra of doubly charmed baryons from lattice QCD with dynamical quark fields. Calculations are performed on anisotropic lattices of size 16 3 ×128, with inverse spacing in temporal direction a −1 t = 5.67(4) GeV and with a pion mass of about 390 MeV. A large set of baryonic operators that respect the symmetries of the lattice yet which retain a memory of their continuum analogues are used. These operators transform as irreducible representations of SU(3)F symmetry for flavor, SU(4) symmetry for Dirac spins of quarks and O(3) for spatial symmetry. The distillation method is utilized to generate baryon correlation functions which are analysed using the variational fitting method to extract excited states. The lattice spectra obtained have baryonic states with well-defined total spins up to 7 2 and the pattern of low lying states does not support the diquark picture for doubly charmed baryons. On the contrary the calculated spectra are remarkably similar to the expectations from models with an SU(6)× O(3) symmetry. Various spin dependent energy splittings between the extracted states are also evaluated.

We perform a lattice study of charmonium-like mesons with J P C = 1 ++ and three quark contents ccdu,cc(ūu +dd) andccss, where the later two can mix withcc. This simulation with N f = 2 and mπ ≃ 266 MeV aims at the possible signatures of four-quark exotic states. We utilize a large basis ofcc, two-meson and diquark-antidiquark interpolating fields, with diquarks in both antitriplet and sextet color representations. A lattice candidate for X(3872) with I = 0 is observed very close to the experimental state only if bothcc and DD * interpolators are included; the candidate is not found if diquark-antidiquark and DD * are used in the absence ofcc. 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 exoticccss candidates below 4.2 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 report the ground state masses of hadrons containing at least one charm and one bottom quark using lattice quantum chromodynamics. These include mesons with spin (J)-parity (P ) quantum numbers (J P ): 0 − , 1 − , 1 + and 0 + and the spin-1/2 and 3/2 baryons. Among these hadrons only the ground state of 0 − is known experimentally and therefore our predictions provide important information for the experimental discovery of all other hadrons with these quark contents. PACS numbers: 12.38.Gc, 14.20.Lq Recently heavy hadron physics has attracted huge scientific interests mainly due to the prospects of studying new physics beyond the Standard Model at the intensity frontier [1][2][3][4][5], and to study various newly discovered subatomic particles to better understand the confining nature of strong interactions [6][7][8][9][10][11][12]. From the perspective of newly found hadrons itself, a large number of discoveries over the past decade ranging from usual mesons [13][14][15][16][17][18][19][20], baryons [21] along with their excited states [22][23][24][25], to new exotic particles like tetraquarks [26-28] and pentaquarks [29], as well as hadrons whose structures are still elusive [6][7][8][30][31][32][33], have proliferated interests in the study of heavy hadrons. Furthermore, it is envisaged that the large data already collected or to be obtained at different laboratories, particularly at LHCb and Belle II, will further unravel many other hadrons. One variety of such theorized but as yet essentially unobserved (except one) subatomic particles are hadrons made of at least a charm and a bottom quarks, the charmed-bottom (bc) hadrons.Investigations of such hadrons are highly appealing, as they provide a unique laboratory to explore the heavy quark dynamics at multiple scales: 1/m b , 1/m c and 1/Λ QCD . Decay constants and form factors of bc mesons are still unknown but are quite important because of their relevance to investigate physics beyond the standard model, particularly in view of the recent measurement of R(J/ψ) [34]. The information on spin splittings and decay constants can shed light on their structures and help us to understand the nature of strong interactions at multiple scales. Moreover, bc baryon decays can aid in studying b → c transition and |V cb | element of the CKM matrix.However, to date the discovery of these hadrons is limited to only two observations: B c (0 − ) with mass 6275(1) MeV [35] and B c (2S)(0 − ) at 6842(6) MeV [36] while the latter has not yet been confirmed [37]. On the other hand, LHC being an efficient factory for producing bc hadrons [38,39], one would envisage for their discovery and study their decays in near future. Precise theoretical predictions related to the energy spectra and decay of these hadrons are thus utmost essential to guide their discovery.In fact various model calculations exist in literatures on bc mesons [40][41][42][43][44][45][46] and baryons [47][48][49][50][51][52][53]. However, those predictions vary widely, e.g. 1S-hyperfine splitting in B c (bc...