We extend the chromomagnetic model by further considering the effect of color interaction. The effective mass parameters between quark pairs (m qq or m qq ) are introduced to account for both the effective quark masses and the color interaction between the two quarks. Using the experimental masses of hadrons, the quark pair parameters are determined between the light quark pairs and the light-heavy quark pairs. Then the parameters of heavy quark pairs (cc, cb, bb) are estimated based on simple quark model assumption. We calculate all masses of doubly and triply heavy-quark baryons. The newly discovered doubly charmed baryon Ξ cc fits into the model with an error of 12 MeV.

Recently, the LHCb Collaboration reported three Pc states in the J/ψp channel. We systematically study the mass spectrum of the hidden charm pentaquark in the framework of an extended chromomagnetic model. For the nnncc pentaquark with I = 1/2, we find that (i) the lowest state is Pc(4327.0, 1/2, 1/2 − ) [We use Pc(m, I, J P ) to denote the nnncc pentaquark], which corresponds to the Pc(4312). Its dominant decay mode is ΛcD * . (ii) We find two states in the vicinity of Pc(4380). The first one is Pc(4367.4, 1/2, 3/2 − ) and decays dominantly to N J/ψ and ΛcD * . The other one is Pc(4372.4, 1/2, 1/2 − ). Its dominant decay mode is ΛcD, and its partial decay width of N ηc channel is comparable to that of N J/ψ. (iii) In higher mass region, we find Pc(4476.3, 1/2, 3/2 − ) and Pc(4480.9, 1/2, 1/2 − ), which correspond to Pc(4440) and Pc (4457). In the open charm channels, both of them decay dominantly to the ΛcD * . (iv) We predict two states above 4.5 GeV, namely Pc(4524.5, 1/2, 3/2 − ) and Pc(4546.0, 1/2, 5/2 − ). The masses of the nnncc state with I = 3/2 are all over 4.6 GeV. Moreover, we use the model to explore the nnscc, ssncc, and ssscc pentaquark states. P c (4312) + : M = 4311.9 ± 0.7 +6.8 −0.6 MeV, Γ = 9.8 ± 2.7 +3.7 −4.5 MeV, P c (4440) + : M = 4440.3 ± 1.3 +4.1 −4.7 MeV, Γ = 20.6 ± 4.9 +8.7 −10.1 MeV, P c (4457) + : M = 4457.3 ± 0.6 +4.1 −1.7 MeV, Γ = 6.4 ± 2.0 +5.7 −1.9 MeV.Since their masses are slightly below the Σ cD , Σ * cD , and Σ cD * thresholds respectively, they can be interpreted as molecules composed of a charm baryon and an anticharm meson [37][38][39][40][41][42][43][44][45][46][47][48][49]. For example, Chen [46] interpreted them as bound states of Σ cD with J P = 1/2 − , Σ * cD with J P = 3/2 − , and Σ cD * with J P = 3/2 − , while Chen et al. [45], He [48], and Liu et al. [49] interpreted the P c (4312), P c (4440), and P c (4457) as loosely bound Σ cD with (I = 1/2, J P = 1/2 − ), Σ cD * with (I = 1/2, J P = 1/2 − ), and Σ cD * with (I = 1/2, J P = 3/2 − ). Another interesting possibility is that some of the P c states might be tightly bound pentaquark states. The light q 4q pentaquark states was first studied with the color-magnetic interaction among the quarks [9,10]. Later, Strottman used the MIT bag model to discuss this arXiv:1904.09891v3 [hep-ph] 26 Jul 2019 *

Both proper, red-shifting and improper, blue-shifting hydrogen bonds have been well-recognized with enormous experimental and computational studies. The current consensus is that there is no difference in nature between these two kinds of hydrogen bonds, where the electrostatic interaction dominates. Since most if not all the computational studies are based on molecular orbital theory, it would be interesting to gain insight into the hydrogen bonds with modern valence bond (VB) theory. In this work, we performed ab initio VBSCF computations on a series of hydrogen-bonding systems, where the sole hydrogen bond donor CF3H interacts with ten hydrogen bond acceptors Y (═NH2CH3, NH3, NH2Cl, OH(-), H2O, CH3OH, (CH3)2O, F(-), HF, or CH3F). This series includes four red-shifting and six blue-shifting hydrogen bonds. Consistent with existing findings in literature, VB-based energy decomposition analyses show that electrostatic interaction plays the dominating role and polarization plays the secondary role in all these hydrogen-bonding systems, and the charge transfer interaction, which denotes the hyperconjugation effect, contributes only slightly to the total interaction energy. As VB theory describes any real chemical bond in terms of pure covalent and ionic structures, our fragment interaction analysis reveals that with the approaching of a hydrogen bond acceptor Y, the covalent state of the F3C-H bond tends to blue-shift, due to the strong repulsion between the hydrogen atom and Y. In contrast, the ionic state F3C(-) H(+) leads to the red-shifting of the C-H vibrational frequency, owing to the attraction between the proton and Y. Thus, the relative weights of the covalent and ionic structures essentially determine the direction of frequency change. Indeed, we find the correlation between the structural weights and vibrational frequency changes.

Inspired by the recent measurement of the process , we calculate the mass spectrum of the meson with the GI model. For the excited vector strangeonium states and , we investigate the electronic decay width with the Van Royen-Weisskopf formula, and the partial widths of the , , and decay modes with the extended quark-pair creation model. We find that the electronic decay width of the -wave vector strangeonium is about times larger than of the -wave vector strangeonium. Around 2232 MeV, the partial decay width of the mode can be up to several MeV for , while the partial decay width of is keV. If the threshold enhancement reported by the BESIII collaboration arises from the strangeonium meson, this state is very likely the state. We also note that the and partial decay widths of the states and are several MeV, which is sufficient to be observed in future experiments.

We systematically study the mass spectra of the fully heavy dibaryons in an extended chromomagnetic model, which includes both the colorelectric and chromomagnetic interactions. We find no stable state below the corresponding baryon-baryon thresholds. Besides the masses, we also estimate the relative width ratios of the two-body decay channels. We hope our study will be of help for future experiments.