Analysis of hidden-charm pentaquark molecular states with and without strangeness via the QCD sum rules

In this study, we investigate the \begin{document}$\bar{D}\Sigma_c$\end{document}, \begin{document}$\bar{D}\Xi^\prime_c$\end{document}, \begin{document}$\bar{D}\Sigma_c^*$\end{document}, \begin{document}$\bar{D}\Xi_c^*$\end{document}, \begin{document}$\bar{D}^{*}\Sigma_c$\end{document}, \begin{document}$\bar{D}^{*}\Xi^\prime_c$\end{document}, \begin{document}$\bar{D}^{*}\Sigma_c^*$\end{document}, and \begin{document}$\bar{D}^{*}\Xi_c^*$\end{document} pentaquark molecular states with and without strangeness via the QCD sum rules in detail, focusing on the light flavor, \begin{document}$SU(3)$\end{document} , breaking effects, and make predictions for new pentaquark molecular states besides assigning \begin{document}$P_c(4312)$\end{document}, \begin{document}$P_c(4380)$\end{document}, \begin{document}$P_c(4440)$\end{document}, \begin{document}$P_c(4457)$\end{document} , and \begin{document}$P_{cs}(4459)$\end{document} self-consistently. In the future, we can search for these pentaquark molecular states in the decay of \begin{document}$\Lambda_b^0$\end{document}, \begin{document}$\Xi_b^0$\end{document} , and \begin{document}$\Xi_b^-$\end{document} . Furthermore, we discuss high-dimensional vacuum condensates in detail.     

Study of C parity violating and strangeness changing J/ψ→PP weak decays

Although J/ψ weak decays are rare,they are possible within the standard model of elementary particles.Inspired by the potential prospects of the future intensity frontier,the C parity violating J/ψ→πη~((')),ηη' decays and the strangeness changing J/ψ→πK,Kη~((')) decays are studied via the perturbative QCD approach.It is determined that the J/ψ→ηη' decays have relatively large branching ratios,approximately on the order of 10~(-11),which might be within the measurement capability and sensitivity of the future STCF experiment.     

Analysis of Pcs(4338) and related pentaquark molecular states via QCD sum rules

In this study, we tentatively identify \begin{document}$ P_{cs}(4338) $\end{document} as the \begin{document}$ \bar{D}\Xi_c $\end{document}molecular state and distinguish the isospins of current operators to explore in detail the\begin{document}$ \bar{D}\Xi_c $\end{document}, \begin{document}$ \bar{D}\Lambda_c $\end{document}, \begin{document}$ \bar{D}_s\Xi_c $\end{document}, \begin{document}$ \bar{D}_s\Lambda_c $\end{document}, \begin{document}$ \bar{D}^*\Xi_c $\end{document}, \begin{document}$ \bar{D}^*\Lambda_c $\end{document}, \begin{document}$ \bar{D}^*_s\Xi_c $\end{document}, and \begin{document}$ \bar{D}^*_s\Lambda_c $\end{document} molecular states without strange, with strange, and with double strange in the framework of QCD sum rules. The present exploration favors identifying \begin{document}$ P_{cs}(4338) $\end{document} (\begin{document}$ P_{cs}(4459) $\end{document}) as the \begin{document}$ \bar{D}\Xi_c $\end{document} (\begin{document}$ \bar{D}^*\Xi_c $\end{document}) molecular state with the spin-parity \begin{document}$ J^P={\dfrac{1}{2}}^- $\end{document} (\begin{document}$ {\dfrac{3}{2}}^- $\end{document}) and isospin \begin{document}$ (I,I_3)=(0,0) $\end{document}, and the observation of their cousins with the isospin \begin{document}$ (I,I_3)=(1,0) $\end{document} in the \begin{document}$ J/\psi\Sigma^0/\eta_c\Sigma^0 $\end{document} invariant mass distributions would decipher their inner structures.     

P-wave ?b states: masses and pole residues

In this study, we consider all P-wave \begin{document}$\Omega_{b}$\end{document} states represented by interpolating currents with a derivative and calculate the corresponding masses and pole residues using the QCD sum rule method. Because of the large uncertainties in our calculation compared with the small difference in the masses of the excited \begin{document}$\Omega_{b}$\end{document} states observed by the LHCb collaboration, it is necessary to study other properties of the P-wave \begin{document}$\Omega_{b}$\end{document} states represented by the interpolating currents investigated in the present work to gain a better understanding of the four excited \begin{document}$\Omega_{b}$\end{document} states observed by the LHCb collaboration.     

Impact of lepton p_T threshold on charge asymmetry predictions for inclusive W boson production in pp collisions at 13 TeV

This paper presents the impact of the lepton transverse momentum p_T~l threshold on the W boson charge asymmetry predictions in perturbative QCD for the inclusive W~++X→l~±v+X production in proton-proton(pp)collisions.The predictions are obtained at various low-p_T~l thresholds p_T~l 20,25,30,and 40 GeV in a fiducial region encompassing both the central and forward detector acceptances in terms of the lepton pseudorapidity0 ≤η_l≤4.5.The predicted distributions for the lepton charge asymmetry,which is defined by η_l(A_(η_l)),at the nextto-next-to-leading order(NNLO) accuracy are compared with the CMS and LHCb data at 8 TeV center-of-mass collision energy.The 8 TeV predictions reproduce the data fairly well within the quoted uncertainties.The predictions from the CT14 parton distribution function(PDF) model are in a slightly better agreement with the data over the other PDF sets that are tested.The 13 TeV predictions using various p_T~l thresholds are reported for A_(η_l) and the charge asymmetries that are defined in terms of the differential cross sections in bins of the W boson rapidity yw(A_(y_w)) and transverse momentum p_T~W(A_(p_T~W)).The NNLO predictions for the A_(η_l),A_(y_w).and A_(p_T~W) distributions are assessed to be in close correlation with the p_T~l value.The A_(η_l) and A_(y_w) distributions are particularly shown to be more correlated at a higher p_T~l threshold.The A_(p_T~W) distributions are also reported from the merged predictions with improved accuracy by the inclusion of the next-to-next-to-next-to-leading logarithm(N'LL) corrections,i.e.,at NNLO+N~3 LL.The predicted distributions from various p_T~l thresholds represent a finer probe in terms of the capability to provide more constraints on the ratio of u and d quark distribution functions in the parton momentum fraction range 10~(-4) x1.     

First lattice QCD calculation of semileptonic decays of charmed-strange baryonsΞc

While the standard model is the most successful theory to describe all the interactions and constituents of elementary particle physics,it has been constantly scrutinized for over four decades.Weak decays of charm quarks can be used to measure the coupling strength between quarks in different families and serve as an ideal probe for CP violation.As the lowest charm-strange baryons with three different flavors,Ξ;baryons(composed of csu or csd)have been extensively studied in experiments.In this study,we use state-of-the-art lattice QCD techniques to generate 2+1 clover fermion ensembles with two lattice spacings,a=(0.108,0.080 fm).Then,we present the first ab-initio lattice QCD calculation of the Ξ;→Ξ form factors.Our theoretical results for the Ξc→Ξl;v;decay widths are consistent with and approximately two times more precise than the latest measurements by the ALICE and Belle collaborations.Based on the latest experimental measurements,we independently obtain the quark-mixing matrix element |V;|,which is in good agreement with results from other theoretical approaches.     

Analysis of the strong decays of Pc(4312) as a pentaquark molecular state with QCD sum rules

In this article, we tentatively assign \begin{document}$P_c(4312)$\end{document} to be the \begin{document}$\bar{D}\Sigma_c$\end{document} pentaquark molecular state with the spin-parity \begin{document}$J^P={\frac{1}{2}}^-$\end{document} , and discuss the factorizable and non-factorizable contributions in the two-point QCD sum rules for the \begin{document}$\bar{D}\Sigma_c$\end{document} molecular state in detail to prove the reliability of the single pole approximation in the hadronic spectral density. We study its two-body strong decays with the QCD sum rules, and special attention is paid to match the hadron side with the QCD side of the correlation functions to obtain solid duality. We obtain the partial decay widths \begin{document}$\Gamma\left(P_c(4312)\to \eta_c p\right)=0.255\,\,{\rm{MeV}}$\end{document} and \begin{document}$\Gamma\left(P_c(4312)\to J/\psi p\right)=9.296^{+19.542}_{-9.296}\,\,{\rm{MeV}}$\end{document} , which are compatible with the experimental value of the total width, and support assigning \begin{document}$P_c(4312)$\end{document} to be the \begin{document}$\bar{D}\Sigma_c$\end{document} pentaquark molecular state.     

Some remarks on X(6900)

The analysis of the LHCb data on \begin{document}$X(6900)$\end{document} found in the di-\begin{document}$J/\psi$\end{document} system was performed using a momentum-dependent Flatté-like parameterization. The use of the pole counting rule and spectral density function sum rule provides consistent evidence that both confining and molecular states are possible. Alternatively, the nature of \begin{document}$X(6900)$\end{document} cannot be distinguished if only the di-\begin{document}$J/\psi$\end{document} experimental data with current statistics are available. Nevertheless, we found that the lowest state in the di-\begin{document}$J/\psi$\end{document} system likely has the same quantum numbers as \begin{document}$X(6900)$\end{document}, and \begin{document}$X(6900)$\end{document} is probably not interpreted as a \begin{document}$J/\psi-\psi(2S)$\end{document} molecular state.     

Revisiting radiative leptonic B decay

In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist \begin{document}$B$\end{document}-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors \begin{document}$F_{A,V}$\end{document} in the \begin{document}$B \to \gamma \ell\nu$\end{document} decay at leading power in \begin{document}$\Lambda/m_b$\end{document}. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by \begin{document}$1/E_\gamma$\end{document} and \begin{document}$1/m_b$\end{document}), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data.     

New behaviors of α-particle preformation factors near doubly magic 100Sn

The \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei above doubly magic nuclei \begin{document}$ ^{100} $\end{document}Sn and \begin{document}$ ^{208} $\end{document}Pb are investigated within the generalized liquid drop model. The results show that the \begin{document}$ \alpha $\end{document}-particle preformation factors of nuclei near self-conjugate doubly magic \begin{document}$ ^{100} $\end{document}Sn are significantly larger than those of analogous nuclei just above \begin{document}$ ^{208} $\end{document}Pb, and they will be enhanced as the nuclei move towards the \begin{document}$ N = Z $\end{document} line. The proton–neutron correlation energy \begin{document}$ E_{p-n} $\end{document} and two protons–two neutrons correlation energy \begin{document}$ E_{2p-2n} $\end{document} of nuclei near \begin{document}$ ^{100} $\end{document}Sn also exhibit a similar situation, indicating that the interactions between protons and neutrons occupying similar single-particle orbitals could enhance the \begin{document}$ \alpha $\end{document}-particle preformation factors and result in superallowed \begin{document}$ \alpha $\end{document} decay. This also provides evidence of the significant role of the proton–neutron interaction on \begin{document}$ \alpha $\end{document}-particle preformation. Also, the linear relationship between \begin{document}$ \alpha $\end{document}-particle preformation factors and the product of valence protons and valence neutrons for nuclei around \begin{document}$ ^{208} $\end{document}Pb is broken in the \begin{document}$ ^{100} $\end{document}Sn region because the \begin{document}$ \alpha $\end{document}-particle preformation factor is enhanced when a nucleus near \begin{document}$ ^{100} $\end{document}Sn moves towards the \begin{document}$ N = Z $\end{document} line. Furthermore, the calculated \begin{document}$ \alpha $\end{document} decay half-lives fit well with the experimental data, including the recent observed self-conjugate nuclei \begin{document}$ ^{104} $\end{document}Te and \begin{document}$ ^{108} $\end{document}Xe [Phys. Rev. Lett. 121, 182501 (2018)].     

QCD sum rule study for hidden-strange pentaquarks

Inspired by the LHCb observations of hidden-charm \begin{document}$ P_{c(s)} $\end{document} states, we study their hidden-strange analog\begin{document}$ P_s $\end{document} states in both the \begin{document}$ [udu][\bar ss] $\end{document} and \begin{document}$ [uds][\bar su] $\end{document} configurations. We investigate \begin{document}$ P_s $\end{document} pentaquark states in the \begin{document}$ p\eta^\prime $\end{document}, \begin{document}$ p\phi $\end{document}, \begin{document}$ \Lambda K $\end{document}, \begin{document}$ \Sigma K $\end{document}, and \begin{document}$ \Sigma^\ast K^\ast $\end{document} structures with \begin{document}$J^P ={1}/{2}^-$\end{document} and \begin{document}$ \Sigma ^\ast K $\end{document} and \begin{document}$ \Sigma K^\ast $\end{document} with \begin{document}$J^P = {3}/{2}^-$\end{document} and calculate their masses in the framework of QCD sum rules. Our numerical results show that the extracted hadron masses for all the \begin{document}$ p\eta^\prime $\end{document}, \begin{document}$ p\phi $\end{document}, \begin{document}$ \Lambda K $\end{document}, \begin{document}$ \Sigma K $\end{document}, and \begin{document}$ \Sigma^\ast K^\ast $\end{document} structures are significantly higher than the \begin{document}$ \Sigma K $\end{document} mass threshold, and the masses for \begin{document}$ \Sigma ^\ast K $\end{document} and \begin{document}$ \Sigma K^\ast $\end{document}are also higher than the threshold of the corresponding hadron; hence, no bound state exists in such channels, which is consistent with the current experimental status.     

Revisiting D-meson twist-2, 3 distribution amplitudes

Owing to the significant difference between the experimental measurements and the theoretical predictions of the standard model (SM) for the value of \begin{document}$ {\cal{R}}(D) $\end{document} of the semileptonic decay \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}, researchers speculate that this decay may be evidence of new physics beyond the SM. Usually, the D-meson twist-2, 3 distribution amplitudes (DAs) \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document} , and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document} are the main error sources when perturbative QCD factorization and light-cone QCD sum rules are used to study \begin{document}$ B\to D\ell\bar{\nu}_{\ell} $\end{document}. Therefore, it is important to obtain more reasonable and accurate behaviors for these DAs. Motivated by our previous work [Phys. Rev. D 104, no.1, 016021 (2021)] on pionic leading-twist DA, we revisit D-meson twist-2, 3 DAs \begin{document}$ \phi_{2;D}(x,\mu) $\end{document}, \begin{document}$ \phi_{3;D}^p(x,\mu) $\end{document}, and \begin{document}$ \phi_{3;D}^\sigma(x,\mu) $\end{document}. New sum rule formulae for the \begin{document}$\xi $\end{document}-moments of these three DAs are suggested for obtaining more accurate values. The light-cone harmonic oscillator models for the DAs are improved, and their parameters are determined by fitting the values of ξ-moments via the least squares method.     

Same-sign tetralepton signature in type-Ⅱ seesaw at lepton colliders

The same-sign tetralepton signature via the mixing of neutral Higgs bosons and their cascade decays to charged Higgs bosons is a unique signal in the type-Ⅱ seesaw model with the mass spectrum M_A⁰≈M_H⁰>M_H⁺>M_H^±±.In this study,we investigate this signature at future lepton colliders,such as the ILC,CLIC,and MuC.Direct searches for doubly charged scalar H^±±at the LHC have excluded MHg+t<350(870) GeV in the H^±±+W^±W(±)(l^±±)decay mode.Therefore,we choose M_A⁰=400,600,1000,1500 GeV as our benchmark scenarios.Constrained by direct search,H^±±+W^±W(±)(l^±±)d=is the only viable decay mode for Mρ=400 GeV at the √s=1 TeV ILC.With an integrated luminosity L=8 ab^-1,the promising region,with approximately 150 signal events,corresponds to a narrow band in the range of 10^-4 GeV≤v△≤10^-2GeV.Meanwhile,for Mpo=600 GeV at the √s=1.5 TeV CLIC,approximately 10 signal events can be produced with L=2.5 ab^-1.For heavier triplet scalars M_A⁰■870 GeV,although the H^±± decay mode is allowed,the cascade decays are suppressed.A maximum event number~16 can be obtained at approximately v△~4×10⁴GeV and λ₁₄~0.26 for M_A⁰=1000 GeV with L=5 ab^-1 at the √s=3 TeV CLIC.Finally,we find that this signature is not promising for M_A⁰= 1500 GeV at the √s=6 TeV MuC.Based on the benchmark scenarios,we also study the observability of this signature.In the H^±±+W^±W(±)(l^±±)d mode,one can probe MρS 800(1160) GeV at future lepton colliders.     

Toward discovering low-lying P-wave excited Σc baryon states

In this study, by combining the equal spacing rule with recent observations of \begin{document}$ \Omega_c(X) $\end{document} and \begin{document}$ \Xi_c(X) $\end{document} baryons, we predict the spectrum of the low-lying \begin{document}$ \lambda $\end{document}-mode \begin{document}$ 1P $\end{document}-wave excited \begin{document}$ \Sigma_c $\end{document} states. Furthermore, their strong decay properties are predicted using the chiral quark model and the nature of \begin{document}$ \Sigma_c(2800) $\end{document} is investigated by analyzing the \begin{document}$ \Lambda_c\pi $\end{document} invariant mass spectrum. The \begin{document}$ \Sigma_c(2800) $\end{document} structure observed in the \begin{document}$ \Lambda_c \pi $\end{document} mass spectrum was found to potentially arise from two overlapping \begin{document}$ P $\end{document}-wave \begin{document}$ \Sigma_c $\end{document} resonances, \begin{document}$ \Sigma_c(2813)3/2^- $\end{document} and \begin{document}$ \Sigma_c(2840)5/2^- $\end{document}. These resonances have similar decay widths of \begin{document}$ \Gamma\sim 40 $\end{document} MeV and predominantly decay into the \begin{document}$ \Lambda_c \pi $\end{document} channel. The \begin{document}$ \Sigma_c(2755)1/2^- $\end{document} state is likely to be a very narrow state with a width of \begin{document}$ \Gamma\sim 15 $\end{document} MeV, with its decays almost saturated by the \begin{document}$ \Lambda_c \pi $\end{document} channel. Additionally, evidence of the \begin{document}$\Sigma_c(2755) {1}/{2}^-$\end{document} resonance as a very narrow peak may be seen in the \begin{document}$ \Lambda_c\pi $\end{document} invariant mass spectrum. The other two \begin{document}$ P $\end{document}-wave states, \begin{document}$\Sigma_c(2746) {1}/{2}^-$\end{document} and \begin{document}$\Sigma_c(2796) {3}/{2}^-$\end{document}, are relatively narrow states with similar widths of \begin{document}$ \Gamma\sim 30 $\end{document} MeV and predominantly decay into \begin{document}$ \Sigma_c\pi $\end{document} and \begin{document}$ \Sigma^{*}_c\pi $\end{document}, respectively. This study can provide useful references for discovering these low-lying \begin{document}$ P $\end{document}-wave states in forthcoming experiments.     

Exploring HVV amplitudes with CP violation using decomposition and the on-shell scattering amplitude method

\begin{document}$ CP $\end{document} violation may play an important role in baryogenesis in the early universe and should be examined comprehensively at colliders. We study the \begin{document}$ CP $\end{document} properties of \begin{document}$ HVV $\end{document} vertexes between Higgs and gauge boson pairs by defining a \begin{document}$ CP $\end{document} violation phase angle ξ, which indicates the mixture of \begin{document}$ CP $\end{document}-even and \begin{document}$ CP $\end{document}-odd Higgs states in \begin{document}$ HVV $\end{document} in new physics. A series of \begin{document}$ HVV $\end{document} amplitudes, \begin{document}$ H\to\gamma\gamma, H\to\gamma V\to \gamma \ell\ell $\end{document}, and \begin{document}$ H\to VV\to 4\ell $\end{document}, with a \begin{document}$ CP $\end{document} phase angle are studied systematically to explicitly explain why \begin{document}$ CP $\end{document} violation can only be probed independently in the \begin{document}$ 4\ell $\end{document} process. We obtain a novel amplitude decomposition relation that illustrates that if two preconditions (multilinear momentum dependent vertexes, and the current \begin{document}$ J_\mu $\end{document} of \begin{document}$ V\to \ell^+ \ell^- $\end{document} is formally proportional to a photon's polarization vector) are satisfied, a higher-point amplitude can be decomposed into a summation of a series of lower-point amplitudes. As a practical example, the amplitude of the \begin{document}$ H\to\gamma V\to \gamma \ell\ell $\end{document} and \begin{document}$ H\to VV\to 4\ell $\end{document} processes can be decomposed into a summation of many \begin{document}$ H\to\gamma\gamma $\end{document} amplitudes. We calculate these amplitudes in the framework of the on-shell scattering amplitude method, considering both massless and massive vector gauge bosons with the \begin{document}$ CP $\end{document} violation phase angle. The above two approaches provide consistent results and clearly reveal the \begin{document}$ CP $\end{document} violation ξ dependence in the amplitudes.     

The effect of hadronic scatterings on the measurement of vector meson spin alignments in heavy-ion collisions

Spin alignments of vector mesons and hyperons in relativistic heavy-ion collisions have been proposed as signals of global polarization.The STAR experiment first observed the ∧ polarization.Recently,the ALICE collaboration measured the transverse momentum {PT) and the collision centrality dependence of K*,and Φ spin alignments during Pb-Pb collisions at ~(1/2)sNN=2.76 TeV.A large signal is observed in the low pT region of mid-central collisions for K~*,while the signal is much smaller for Φ,and these have not been understood yet.Since vector mesons have different lifetimes and their decay products have different scattering cross sections,they suffer from different hadronic effects.In this paper,we study the effect of hadronic interactions on the spin alignment of K~*,Φ,and p mesons in relativistic heavy-ion collisions with a multi-phase transport model.We find that hadronic scatterings lead to a deviation of the observed spin alignment matrix element p00 away from the true value for p and K*mesons(with a bigger effect on p) while the effect is negligible for the Φ meson.The effect depends on the kinematic acceptance:the observed p00 value is lower than the true value when the pseudorapidity(η) coverage is small,while there is little effect when the η coverage is large.Hence,this study provides valuable information to understand the vector meson spin alignment signals observed during the experiments.     

Linear seesaw model with T7 symmetry for neutrino mass and mixing

We propose a low-scale Standard Model extension with \begin{document}$T_7\times Z_4 \times Z_3\times Z_2$\end{document} symmetry that can successfully explain observed neutrino oscillation results within the \begin{document}$3 \sigma$\end{document} range. Small neutrino masses are obtained via the linear seesaw mechanism. Normal and inverted neutrino mass orderings are considered with three lepton mixing angles in their experimentally allowed \begin{document}$3\sigma$\end{document} ranges. The model provides a suitable correlation between the solar and reactor neutrino mixing angles, which is consistent with the \begin{document}${\rm{TM}}_2$\end{document} pattern. The prediction for the Dirac phase is \begin{document}$\delta_{\rm CP}\in (295.80, 330.0)^\circ$\end{document} for both normal and inverted orderings, including its experimentally maximum value, while those for the two Majorana phases are \begin{document}$\eta_1\in (349.60, 356.60)^\circ,\, \eta_2=0$\end{document} for normal ordering and \begin{document}$\eta_1\in (3.44, 10.37)^\circ, \, \eta_2=0$\end{document} for inverted ordering. In addition, the predictions for the effective neutrino masses are consistent with the present experimental bounds.     

Microscopic study of higher-order deformation effects on the ground states of superheavy nuclei around 270Hs

We investigate the effects of higher-order deformations \begin{document}$\beta_\lambda$\end{document} (\begin{document}$\lambda=4,6,8,$\end{document} and 10) on the ground state properties of superheavy nuclei (SHN) near the doubly magic deformed nucleus \begin{document}$^{270}{\rm{Hs}}$\end{document} using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model with five effective interactions: PC-PK1, PK1, NL3^*, DD-ME2, and PKDD. The doubly magic properties of \begin{document}$^{270}{\rm{Hs}}$\end{document} include large energy gaps at \begin{document}$N=162$\end{document} and \begin{document}$Z=108$\end{document} in the single-particle spectra. By investigating the binding energies and single-particle levels of \begin{document}$^{270}{\rm{Hs}}$\end{document} in the multidimensional deformation space, we find that, among these higher-order deformations, the deformation \begin{document}$\beta_6$\end{document} has the greatest impact on the binding energy and influences the shell gaps considerably. Similar conclusions hold for other SHN near \begin{document}$^{270}{\rm{Hs}}$\end{document}. Our calculations demonstrate that the deformation \begin{document}$\beta_6$\end{document} must be considered when studying SHN using MDC-RMF.     

Annihilation diagram contribution to charmonium masses

In this work, we generate gauge configurations with \begin{document}$ N_f = 2 $\end{document} dynamical charm quarks on anisotropic lattices. The mass shift of \begin{document}$ 1S $\end{document} and \begin{document}$ 1P $\end{document} charmonia due to the charm quark annihilation effect can be investigated directly in a manner of unitary theory. The distillation method is adopted to treat the charm quark annihilation diagrams at a very precise level. For \begin{document}$ 1S $\end{document} charmonia, the charm quark annihilation effect barely changes the \begin{document}$ J/\psi $\end{document} mass, but lifts the \begin{document}$ \eta_c $\end{document} mass by approximately 3–4 MeV. For \begin{document}$ 1P $\end{document} charmonia, this effect results in positive mass shifts of approximately 1 MeV for \begin{document}$ \chi_{c1} $\end{document} and \begin{document}$ h_c $\end{document}, but decreases the \begin{document}$ \chi_{c2} $\end{document} mass by approximately 3 MeV. We did not obtain a reliable result for the mass shift of \begin{document}$ \chi_{c0} $\end{document}. In addition, we observed that the spin averaged mass of the spin-triplet \begin{document}$ 1P $\end{document} charmonia is in good agreement with \begin{document}$ h_c $\end{document}, as expected by the non-relativistic quark model and measured by experiments.     

Discovery potentials of double-charm tetraquarks

In this study, we investigate the discovery potential of double-charm tetraquarks \begin{document}$ T^{\{cc\}}_{[\bar{q}\bar{q}']} $\end{document}. We find that their production cross sections at the LHCb with \begin{document}$ \sqrt{s} = 13 $\end{document} TeV reach \begin{document}$ \mathcal{O}(10^4) $\end{document} pb, which indicates that the LHCb has collected \begin{document}$ \mathcal{O}(10^8) $\end{document} such particles. Through the decay channels of \begin{document}$ T^{\{cc\}}_{[\bar{u}\bar{d}]}\to D^{+}K^{-}\pi^{+} $\end{document} or \begin{document}$ D^0D^+\gamma $\end{document} (if stable) or \begin{document}$ T^{\{cc\}}_{[\bar{u}\bar{d}]}\to D^0D^{*+}\to D^0D^0\pi^+ $\end{document} (if unstable), it is highly expected that they get discovered at the LHCb in the near future. We also discuss the productions and decays of the double-charm tetraquarks at future Tera-\begin{document}$ Z $\end{document} factories.