Nonrelativistic Potential Model Research Articles

Charmed-strange tetraquarks and their decays in the potential quark model

In the framework of a nonrelativistic potential quark model, we investigate the mass spectrum of the $1S$-wave charmed-strange tetraquark states of $cn\overline{s}\overline{n}$ and $cs\overline{n}\overline{n}$ ($n=u$ or $d$) systems. The tetraquark system is solved by a correlated Gaussian method. With the same parameters fixed by the meson spectra, we obtained the mass spectra for the $1S$-wave tetraquark states. Furthermore, based on the predicted tetraquark spectra we estimate their rearrangement decays in a quark-exchange model. We find that the rearrangement decays of the tetraquarks may be mainly driven by the spin-spin interactions. The resonances ${X}_{0}(2900{)}^{0}$ and ${T}_{c\overline{s}0}^{a}(2900{)}^{++/0}$ reported from LHCb may be assigned to be the lowest $1S$-wave tetraquark states ${\overline{T}}_{cs0}^{f}(2818)$ and ${T}_{c\overline{s}0}^{a}(2828)$ classified in the quark model, respectively. It also allows us to extract the couplings for the initial tetraquark states to their nearby $S$-wave interaction channels. We find that some of these couplings turn out to be sizeable. Following the picture of the wave function renormalization for the near-threshold strong $S$-wave interactions, the sizeable coupling strengths can be regarded as an indication of their dynamic origins as candidates for hadronic molecules. Furthermore, our predictions suggest that signals for the $1S$-wave charmed-strange tetraquark states can also be searched in the other channels, such as ${D}^{0}{K}^{+}$, ${D}^{+}{K}^{+}$, ${D}^{*+}{K}^{\ensuremath{-}}$, ${D}^{*+}{K}^{+}$, ${D}^{*0}{K}^{+}$, ${D}^{0}{\overline{K}}^{*0}$, ${D}_{s}^{+}{\ensuremath{\rho}}^{0}$, etc.

Spectroscopy of Heavy–Heavy Flavour Mesons and Annihilation Widths of Quarkonia

Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into digluon, dilepton, $3\gamma$, $3g$ and $\gamma gg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schr\"odinger wave function at zero quark-antiquark separation for heavy quarkonia and $B_c$ mesons.

Coupled channel effects for the charmed-strange mesons

We make a systematic calculation of the spectra and hadronic decays of the ${D}_{s}$ system in a coupled channel framework, where the unquenched effects are induced by the $^{3}{P}_{0}$ model. In the calculation, the wave functions are obtained by using a nonrelativistic potential model and are handled precisely with Gaussian expansion method. Even though the fitting mainly focuses on the spectrum, our model agrees well with the experiments on both the spectra and the hadronic decays, suggesting that the coupled channel effect could result in a reasonable and coherent description of the ${D}_{s}$ mesons. Based on the calculation, we give a detailed analysis on various aspects of the excited states, especially ${D}_{s0}^{*}(2317),\phantom{\rule{0ex}{0ex}}{D}_{s1}(2460),{D}_{s1}(2536),{D}_{s1}^{*}(2860),{D}_{s0}(2590)$, and ${D}_{sJ}^{*}(3040)$. We also predict that ${D}_{s0}^{*}({2}^{3}{P}_{0})$ should be a ${D}^{*}{K}^{*}$ dominant molecule with mass 2894 MeV, which is only 5 MeV below the ${D}^{*}{K}^{*}$ threshold.

The low-lying hidden- and double-charm tetraquark states in a constituent quark model with instanton-induced interaction

Spectrum of the low-lying hidden- and double-charm tetraquark states are investigated in a nonrelativistic quark potential model, where the instanton-induced interaction is taken as the residual spin-dependent hyperfine interaction between quarks. The model parameters are fixed by fitting the spectrum of the ground hadron states. Our numerical results show that masses of several presently studied tetraquark states are close to those of the experimentally observed candidates of exotic meson, which indicates that the corresponding compact tetraquark components may take considerable probabilities in those observed exotic states.

Properties of B and Bs meson states in a nonrelativistic quark model with the inclusion of coupled channel effects

The mass spectra and decay properties of [Formula: see text] and [Formula: see text] mesons are obtained using the nonrelativistic potential model by applying the variational approach. The quark–anti-quark potential used in our model consists of a Hulthen potential and a confining linear potential. The hyper-fine interaction is introduced to obtain the splittings of the spin-singlet and triplet states, while the spin–orbit and tensor interactions provide the fine structure splittings. The model parameters and the wave functions that reproduce the mass spectra are used to investigate the decay properties of [Formula: see text] and [Formula: see text] mesons. The mass spectra of [Formula: see text] and [Formula: see text] mesons have been enhanced using coupled channel effects.

Masses, Radii and Regge Trajectories of $$\Sigma _{u}^{-}$$ State Hybrid Charmonium

In this paper, masses, radii and $$E_1$$ radiative transitions of $$\Sigma ^-_u$$ state hybrid charmonium mesons for radial and orbital excitations are calculated by numerically solving the Schrödinger equation with non-relativistic potential model. Results for calculated masses of $$\Sigma ^-_{u}$$ states charmonium hybrid mesons are found to be close to the results obtained through lattice simulations. Calculated masses are used to construct Regge trajectories. It is found that the trajectories are almost linear and parallel.

Higher mass spectra of the fully-charmed and fully-bottom tetraquarks

In this work, we calculate the higher mass spectra for the $2S$- and $1D$-wave fully-charmed and fully-bottom tetraquark states in a nonrelativistic potential quark model. The $2S$-wave fully-charmed/bottom tetraquark states lie in the mass range of $\ensuremath{\sim}(6.9,7.1)/(19.7,19.9)\text{ }\mathrm{GeV}$, apart from the highest ${0}^{++}$ state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)/{T}_{(bb\overline{b}\overline{b}){0}^{++}}(19976)$. Most of the $2S$-wave states highly overlap with the high-lying $1P$-wave states. The masses for the $1D$-wave fully-charmed/bottom tetraquark states are predicted to be in the range of $\ensuremath{\sim}(6.7,7.2)/(19.5,20.0)\text{ }\text{ }\mathrm{GeV}$. The mass range for the $D$-wave tetraquark states cover most of the mass range of the $P$-wave states and the whole mass range of the $2S$-wave states. The narrow structure $X(6900)$ recently observed at LHCb in the di-$J/\ensuremath{\psi}$ invariant mass spectrum may be caused by the $1P$-, or $2S$-, or $1D$-wave ${T}_{(cc\overline{c}\overline{c})}$ states. The vague structure $X(7200)$ may be caused by the highest $2S$-wave state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)$, two low-lying $3S$-wave states ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7240)$ and ${T}_{(cc\overline{c}\overline{c}){2}^{++}}(7248)$, and/or the high-lying $1D$-wave states with masses around 7.2 GeV and ${J}^{PC}={0}^{++},{1}^{++},{2}^{++},{3}^{++}$, or ${4}^{++}$. While it is apparent that the potential quark model calculations predict more states than the structures observed in the di-$J/\ensuremath{\psi}$ invariant mass spectrum, our calculations will help further understanding of the properties of these fully-heavy tetraquark states in their strong and magnetic interactions with open channels based on explicit quark model wave functions.

Mass Spectrum and Decay Constants of Heavy Quarkonia

In this paper, a non-relativistic potential model is used to find the solution of radial Schrodinger wave equation by using Crank Nicolson discretization for heavy quarkonia ( ̅, ̅). After solving the Schrodinger radial wave equation, the mass spectrum and hyperfine splitting of heavy quarkonia are calculated with and without relativistic corrections. The root means square radii and decay constants for S and P states of c ̅ and ̅ mesons by using the realistic and simple harmonic oscillator wave functions. The calculated results of mass, hyperfine splitting, root means square radii and decay constants agreed with experimental and theoretically calculated results in the literature.

Mass-spectroscopy of [$$bb][{\bar{b}}{\bar{b}}$$] and [$$bq][{\bar{b}}{\bar{q}}$$] tetraquark states in a diquark–antidiquark formalism

In this article, we utilise the non-relativistic potential model to calculate the mass-spectra of all bottom [ $$bb][{\bar{b}}{\bar{b}}$$ ] and heavy-light bottom [ $$bq][{\bar{b}}{\bar{q}}$$ ] (q = u,d) tetraquark states in diquark–antidiquark approximation. The four-body problem is reduced into two body problem by numerically solving the $$Schr\ddot{o}dinger$$ equation using a Cornell-inspired potential along with relativistic correction term. The splitting structure of the tetraquark spectrum is described using spin-dependent terms (spin-spin, spin-orbit, and tensor). We have successfully calculated and predicted the masses of bottom mesons, diquarks and tetraquarks. The masses of S and P-wave tetraquark states [ $$bb][{\bar{b}}{\bar{b}}$$ ] and [ $$bq][{\bar{b}}{\bar{q}}$$ ], respectively, are found to be between 18.7–19.4 GeV and 10.4–11.3 GeV, in which the masses of S-wave [ $$bb][{\bar{b}}{\bar{b}}$$ ] states are less than the 2 $$\eta _{b}$$ , $$\eta _{b}\Upsilon $$ , and 2 $$\Upsilon $$ threshold. Additionally, we have investigated the $$Z_b(10610)$$ and $$Z_ b(10650)$$ states in the current model and found that they are 150 MeV below the $$BB^{*}$$ and $$B^{*}B^{*}$$ thresholds.

Mass spectra of one or two heavy quark mesons and diquarks within a nonrelativistic potential model

In this paper, the mass spectra of mesons with one or two heavy quarks and their diquarks partners are estimated within a nonrelativistic framework by solving Schrödinger equation with an effective potential inspired by a symmetry preserving Poincaré covariant vector–vector contact interaction model of quantum chromodynamics. Matrix Numerov method is implemented for this purpose. In our survey of mesons with heavy quarks, we fix the model parameter to the masses of groundstates and then extend our calculations for radial excitations and diquarks. The potential model used in this work gives results which are in good agreement with experimental data and other theoretical calculations.

Electron-impact excitation of the (4d105s)S1/22→(4d95s2)D3/22 and (4d105s)S1/22→(4d106s)S1/22 transitions in silver: Experiment and theory

We present angle-differential and angle-integrated cross sections for electron-impact excitation of the ($4{d}^{10}5s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}(4{d}^{9}5{s}^{2})\phantom{\rule{0.16em}{0ex}}^{2}D_{3/2}$ and $(4{d}^{10}5s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}(4{d}^{10}6s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ transitions in atomic silver. Experimental data for four incident electron energies between 10 and 60 eV are compared with predictions from our relativistic distorted wave (RDW) and nonrelativistic atomic optical potential models. Agreement between our measured and calculated data is only fair, although in the case of the RDW it is seen to improve with increasing incident electron energy. However, only for the $(4{d}^{10}6s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ excitation process, agreement of our measured data with earlier relativistic convergent close coupling results from McNamara et al. [J. Phys. B 51, 085203 (2018)] was, with a few exceptions, typically observed to be very good, to within the uncertainties on the data.

Calculation of the Top-Quark Yukawa coupling constant

In this work, we study meson systems consisting of quark–antiquark. We solve Lippman–Schwinger equation numerically for heavy meson systems. We attempt to find a nonrelativistic potential model through which we can solve the quark–antiquark bound state problem. The coefficients obtained are in agreement with Martin potential coefficients. Via this method we also determine the strong coupling constant of Cornell and Yukawa potentials for the heavy meson.

Test of the nonrelativistic $$c\bar{c}$$ potential

We analyze the charmonium states by testing a phenomenological nonrelativistic potential and propose a new set of parameters. This new set of parameters is fixed using only the lowest lying S-wave states of charmonia where the spin-orbit and the tensor interactions will not contribute. After fitting the parameters, we analyze the whole fine structure of charmonium states taking into account the spin-orbit and the tensor interactions. Calculations showed that the nonrelativistic potential model with a phenomenologically defined parameters was indeed a good approximation for describing the charmonium states.

Pair structure of heavy tetraquark systems

We study the pair description of heavy tetraquark systems $|QQ\bar Q \bar Q\rangle$ in the frame of a non-relativistic potential model. By taking the two heavy quark pairs $(Q\bar Q)$ as colored clusters, the four-quark Schr\"odinger equation is reduced to a two-pair equation, when the inner motion inside the pairs can be neglected. Taking into account all the Casimir scaling potentials between two quarks and using the lattice QCD simulated mixing angle between the two color-singlet states for the tetraquark system, we extracted a detailed pair potential between the two heavy quark pairs.

Analyticity properties of scattering amplitude in theories with compactified space dimensions: The proof of dispersion relations

The analyticity properties of the scattering amplitude for a massive scalar field are reviewed in this paper where the space–time geometry is [Formula: see text], i.e. one spatial dimension is compact. Khuri investigated the analyticity of scattering amplitude in a nonrelativistic potential model in three dimensions with an additional compact dimension. He showed that under certain circumstances, the forward amplitude is nonanalytic. He argued that in high energy scattering if such a behavior persists it would be in conflicts with the established results of quantum field theory and LHC might observe such behaviors. We envisage a real scalar massive field in flat Minkowski space–time in five dimensions. The Kaluza–Klein (KK) compactification is implemented on a circle. The resulting four-dimensional manifold is [Formula: see text]. The LSZ formalism is adopted to study the analyticity of the scattering amplitude. The nonforward dispersion relation is proved. In addition the Jin–Martin bound and an analog of the Froissart–Martin bound are proved. A novel proposal is presented to look for evidence of the large-radius-compactification scenario. A seemingly violation of Froissart–Martin bound at LHC energy might hint that an extra dimension might be decompactified. However, we find no evidence for violation of the bound in our analysis.

Fully strange tetraquark sss¯s¯ spectrum and possible experimental evidence

In this work we construct 36 tetraquark configurations for the $1S$-, $1P$-, and $2S$-wave states, and make a prediction of the mass spectrum for the tetraquark $ss\bar{s}\bar{s}$ system in the framework of a nonrelativistic potential quark model without the diquark-antidiquark approximation. The model parameters are well determined by our previous study of the strangeonium spectrum. We find that the resonances $f_0(2200)$ and $f_2(2340)$ may favor the assignments of ground states $T_{(ss\bar{s}\bar{s})0^{++}}(2218)$ and $T_{(ss\bar{s}\bar{s})2^{++}}(2378)$, respectively, and the newly observed $X(2500)$ at BESIII may be a candidate of the lowest mass $1P$-wave $0^{-+}$ state $T_{(ss\bar{s}\bar{s})0^{-+}}(2481)$. Signals for the other $0^{++}$ ground state $T_{(ss\bar{s}\bar{s})0^{++}}(2440)$ may also have been observed in the $\phi\phi$ invariant mass spectrum in $J/\psi\to\gamma\phi\phi$ at BESIII. The masses of the $J^{PC}=1^{--}$ $T_{ss\bar{s}\bar{s}}$ states are predicted to be in the range of $\sim 2.44-2.99$ GeV, which indicates that the $\phi(2170)$ resonance may not be a good candidate of the $T_{ss\bar{s}\bar{s}}$ state. This study may provide a useful guidance for searching for the $T_{ss\bar{s}\bar{s}}$ states in experiments.

Bethe-Salpeter amplitudes of Upsilons

Based on lattice non-relativistic QCD (NRQCD) studies we present results for Bethe-Salpeter amplitudes for $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ in vacuum as well as in quark-gluon plasma. Our study is based on 2+1 flavor $48^3 \times 12$ lattices generated using the Highly Improved Staggered Quark (HISQ) action and with a pion mass of $161$ MeV. At zero temperature the Bethe-Salpeter amplitudes follow the expectations based on non-relativistic potential models. At non-zero temperatures, the interpretation of Bethe-Salpeter amplitudes turns out to be more nuanced, but consistent with our previous lattice QCD study of excited Upsilons in quark-gluon plasma.

2S and 3S State Masses and decay constants of heavy-flavour mesons in a non-relativistic QCD potential model with three-loop effects in V-scheme

We make an analysis of three -loop effects of the strong coupling constant in the study of masses and decay constants of the heavy-flavour pseudo-scalar mesons (PSM) D, D_s , B, B_s,B_c, eta _c and eta _b in a non-relativistic QCD potential model using Dalgarno’s perturbation theory (DPT). The first order mesonic wavefunction is obtained using Dalgarno’s perturbation theory. The three-loop effects of strong coupling constant are included in the wave function in co-ordinate space and then used to examine the static and dynamic properties of the heavy-flavour mesons for 2S and 3S higher states. The results are compared with the other models available and are found to be compatible with available experimental values. In V-scheme, the three-loop effects on masses and decay constants of heavy-flavour mesons show a significant result.

Next-to-next-to-leading-order radiative corrections to e+e\u2212\u2192 \u03c7cJ + \u03b3 at B factory

Within the nonrelativistic QCD (NRQCD) factorization framework, we have computed the mathcal{O}left({alpha}_s^2right) corrections to the exclusive production of P-wave spin-triplet charmonia χcJ (J = 0, 1, 2) accompanied with a hard photon at B factory. For the first time, we have explicitly verified the validity of NRQCD factorization for exclusive P-wave quarkonium production to two-loop order. Unlike the χcJ electromagnetic decays, the mathcal{O}left({alpha}_s^2right) corrections are found to be smaller than the mathcal{O} (αs) corrections in all three channels e+e− → χc0,1,2 + γ. In particular, the mathcal{O}left({alpha}_s^2right) corrections appear moderate for χc1 + γ case, and marginal for χc0 + γ. Moreover, the predictions in next-to-next-to-leading order (NNLO) accuracy for the production rates of χc0,1 + γ are insensitive to the renormalization and factorization scales. All these features may indicate that perturbative expansion in these two channels exhibits a decent convergence behavior. By contrast, both the mathcal{O} (αs) and mathcal{O}left({alpha}_s^2right) corrections to the χc2 + γ production rate are sizable, which reduce the Born order cross section by one order of magnitude after including the NNLO perturbative corrections. Taking the values of the long-distance NRQCD matrix elements from nonrelativistic potential model, our prediction to χc1 + γ production rate is consistent with the recent Belle measurement. The NNLO predictions to the χc0,2 + γ production rates are much smaller than that for χc1 + γ, which seems to naturally explain why the e+e− → χc0,2 + γ channels have escaped experimental detection to date.

Magnetoexcitons in monolayer transition-metal dichalcogenides

We study the magnetoexciton Rydberg states in MoS2, MoSe2, WS2, and WSe2 monolayers encapsulated by hexagonal boron nitride. Excitons in the magnetic field are described in the framework of the nonrelativistic potential model. We use the Rytova-Keldysh potential to calculate the energies of the magnetoexcitons. Our calculations use as inputs the effective masses of electron and hole obtained in the framework of the density functional theory. The binding energies of A and B magnetoexcitons are calculated by numerical integration of the Schrödinger equation. We report the energy contribution from the magnetic field to the binding energy and its dependence on the magnetic field. The diamagnetic coefficients are calculated. The reasonable agreement for diamagnetic coefficients and experimental data is obtained.