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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.