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The diquark-triquark model is used to explain charmonium-pentaquark states, i.e., Pc(4380) and Pc(4450), which were observed recently by the LHCb collaboration. For the first time, we investigate the properties of the color attractive configuration of a triquark and we define a nonlocal light cone distribution amplitude for pentaquark states, where both diquark and triquark are not pointlike, but they have nonzero size. We establish an effective diquark-triquark Hamiltonian based on spin-orbital interaction. According to the Hamiltonian, we show that the minimum mass splitting between 5 2 + and 3 2 − is around 100 MeV, which may naturally solve the challenging problem of small mass splitting between Pc(4450) and Pc (4380). This helps to understand the peculiarities of Pc(4380) with a broad decay width whereas Pc(4450) has a narrow decay width. Based on the diquark-triquark model, we predict more pentaquark states, which will hopefully be measured in future experiments.The hadron spectrum has played an important role in understanding the inner hadron structure and for testing various models of hadrons with fundamental freedom. The study of hadron physics is also crucial for understanding the dynamics of quark and strong interaction, according to quantum chromodynamics (QCD). Conventional hadrons can be understood well by using the naive constituent quark model, where a meson comprises two constituent quarks, qq , while a baryon is constructed from three constituent quarks, qq q , with all in a color singlet. This simple description has been highly successful in the past half century. However, the quark model and QCD do not include a rule that forbids the existence of other multiquark states [1], such as tetraquark or pentaquark states. In contrast to the conventional meson and baryon, finding the multiquark state, also known as the exotic state, has been a goal of particle physicists for many years.Recent developments in exotic heavy hadron research started with the discovery of X(3872) by the Belle Collaboration in 2003 [2], which is distinguished by its narrow decay width (Γ < 1.2MeV). Subsequently, a series of exotic states, XY Z, were determined experimentally, which are difficult to embed in the conventional meson and baryon spectra, and thus they have attracted much attention from both theoretical and experimental researchers (e.g., see [3] and the references therein). Recently, the LHCb Collaboration observed two exotic structures in the J/ψp channel of Λ b decay, which they † Corresponding author * Electronic address: rlzhu@sjtu.edu.cn ‡ Electronic address: qiaocf@ucas.ac.cn referred to as pentaquark-charmonium states, P c (4380) and P c (4450) [4]. One of these two structures has a mass of 4380 ± 8 ± 29MeV, a width of 205 ± 18 ± 86MeV, and a preferred spin-parity assignment of J P = 3 2 − , whereas arXiv:1510.08693v4 [hep-ph]

We study the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory. For the quark quasidistribution, power law ultraviolet divergences arise in the cut-off scheme and an important observation is that they all are subjected to Wilson lines. However for the gluon quasidistribution function, we first point out that the linear ultraviolet divergences also exist in the real diagram which is not connected to any Wilson line. We then study the one loop corrections to parton distribution functions in both cut-off scheme and dimensional regularization to deal with the ultraviolet divergences. In addition to the ordinary quark and gluon distributions, we also include the quark to gluon and gluon to quark splitting diagrams. The complete one-loop matching factors between the quasi and light cone parton distribution functions are presented in the cut-off scheme. We derive the P z evolution equation for quasi parton distribution functions, and find that the P z evolution kernels are identical to the DGLAP evolution kernels.

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We study the charmed and bottomed doubly strange baryons within the heavy-quark-light-diquark framework. The two strange quarks are assumed to lie in S wave and thus their total spin is 1. We calculate the mass spectra of the S and P wave orbitally excited states and find the Ω 0 c (

Motivated by the LHCb observation of exotic states $$X_{0,1}(2900)$$ X 0 , 1 ( 2900 ) with four open quark flavors in the $$D^- K^+$$ D - K + invariant mass distribution in the decay channel $$B^\pm \rightarrow D^+ D^- K^\pm $$ B ± → D + D - K ± , we study the spectrum and decay properties of the open charm tetraquarks. Using the two-body chromomagnetic interactions, we find that the two newly observed states can be interpreted as a radial excited tetraquark with $$J^P=0^+$$ J P = 0 + and an orbitally excited tetraquark with $$J^P=1^-$$ J P = 1 - , respectively. We then explore the mass and decays of the other flavor-open tetraquarks made of $$su {\bar{d}} {\bar{c}}$$ s u d ¯ c ¯ and $$ d s {\bar{u}} {\bar{c}}$$ d s u ¯ c ¯ , which are in the $${\bar{6}}$$ 6 ¯ or 15 representation of the flavor SU(3) group. We point that these two states can be found through the decays: $$X^{(\prime )}_{d s \bar{u}\bar{c}}\rightarrow (D^- K^-, D_s^- \pi ^-) $$ X d s u ¯ c ¯ ( ′ ) → ( D - K - , D s - π - ) , and $$X^{(\prime )}_{s u \bar{d}\bar{c}}\rightarrow D_s^-\pi ^+ $$ X s u d ¯ c ¯ ( ′ ) → D s - π + . We also apply our analysis to open bottom tetraquark $$X_b$$ X b and predict their masses. The open-flavored $$X_b$$ X b can be discovered through the following decays: $$X_{ud{\bar{s}}\bar{b}}\rightarrow B^0K^+$$ X u d s ¯ b ¯ → B 0 K + , $$X^{(\prime )}_{d s \bar{u}\bar{b}}\rightarrow (B^0 K^-, B_s^0 \pi ^-) $$ X d s u ¯ b ¯ ( ′ ) → ( B 0 K - , B s 0 π - ) , and $$X^{(\prime )}_{s u \bar{d}\bar{b}}\rightarrow B_s^0\pi ^+ $$ X s u d ¯ b ¯ ( ′ ) → B s 0 π + .

In this paper the next-to-leading order (NLO) corrections to B c meson exclusive decays to S-wave charmonia and light pseudoscalar or vector mesons, i.e. π, K, ρ, and K * , are performed within non-relativistic (NR) QCD approach. The non-factorizable contribution is included, which is absent in traditional naive factorization (NF). And the theoretical uncertainties for their branching ratios are reduced compared with that of direct tree level calculation. Numerical results show that NLO QCD corrections markedly enhance the branching ratio with a K factor of 1.75 for B ± c → η c π ± and 1.31 for B ± c → J/ψπ ± . In order to investigate the asymptotic behavior, the analytic form is obtained in the heavy quark limit, i.e. m b → ∞. We note that annihilation topologies contribute trivia in this limit, and the corrections at leading order in z = m c /m b expansion come from form factors and hard spectator interactions. At last, some related phenomenologies are also discussed.

Very recently, the D0 collaboration has reported the observation of a narrow structure, X(5568), in the decay process X(5568) → B 0 s π ± using the 10.4fb −1 data of pp collision at √ s = 1.96 TeV. This structure is of great interest since it is the first hadronic state with four different valence quark flavors, b, s, u, d. In this work, we investigate tetraquarks with four different quark flavors. Based on the diquark-antidiquark scheme, we study the spectroscopy of the tetraquarks with one heavy bottom/charm quark and three light quarks. We find that the lowest-lying S-wave state, a tetraquark with the flavor [su][bd] and the spin-parity J P = 0 + , is about 150 MeV higher than the X(5568). Further detailed experimental and theoretical studies of the spectrum, production and decays of tetraquark states with four different flavors in the future are severely needed towards a better understanding its nature and the classification of hadron exotic states.