Modern Physics Letters A

This paper covers the recent experimental development on spin alignment measurements of $K^{\ast 0}$ and $\varphi$ vector mesons in heavy-ion and $pp$ collisions at RHIC and LHC energies. Measurements in $e^{+}{e}^{-}$ collisions at LEP energies are also discussed. Spin alignment of vector mesons is studied by measuring the second diagonal element ${\rho }_{00}$ of spin density matrix. The spin density matrix element ${\rho }_{00}$ is obtained by measuring the angular distribution of vector meson decay daughter with respect to the quantization axis in vector meson rest frame. Measured ${\rho }_{00}$ values for vector mesons are found to be larger than $1/3$ at high momentum in $e^{+}{e}^{-}$ collisions at LEP energies, suggesting the preferential production of vector meson with helicity zero state from the fragmentation process. The ${\rho }_{00}$ values are found to be smaller than $1/3$ (${\rho }_{00}=1/3$ implies no spin alignment) for $K^{\ast 0}$ and $\varphi$ vector mesons at low transverse momentum in Pb–Pb collisions at $\sqrt{s_{\mathrm{\text{NN}}}}=2.76$ TeV. These observations are qualitatively consistent with the expectation from models which attribute the spin alignment effect due to polarization of quarks in the presence of large initial angular momentum in noncentral heavy-ion collisions and its subsequent hadronization by the process of recombination. No significant spin alignment effect is observed for $K_S^0$ $(\mathrm{\text{spin}}=0)$ in mid-central Pb–Pb collisions and for vector mesons in $pp$ collisions. However, the preliminary results of ${\rho }_{00}$ for $\varphi$ mesons are larger than $1/3$ at intermediate $p_{\mathrm{\text{T}}}$ in Au–Au collisions at RHIC energies and can be attributed to the presence of $\varphi$ meson field. Although there is evidence of spin alignment effect of vector mesons in heavy-ion collisions but the measured effect is surprisingly larger in context of hyperon polarization. Therefore, these results will trigger further theoretical study.

The study of dibaryons has gained extensive attention both theoretically and experimentally since the confirmation of six-quark exotic $\mathrm{\Delta }\mathrm{\Delta }$ dibaryon (with spin 3 and isospin 0) by recent COSY experiment. We ever proposed the chiral SU(3) quark model and predicted the binding energy of the $\mathrm{\Delta }\mathrm{\Delta }$ system, in which the hidden-color channel was shown to play an important role in its structure. In this work, we further study the structure of ${\mathrm{\Sigma }}^{\ast }\mathrm{\Delta }$ dibaryon (with spin 0 and isospin $\frac{5}{2}$) and strangeness $S=-1$ under the chiral SU(3) quark model. The results show that hidden-color channel has an obvious influence on the binding energy of ${\mathrm{\Sigma }}^{\ast }\mathrm{\Delta }$ system.

The Gauß hypergeometric function shows a recursive structure which resembles those found in conformal blocks. We compare it with the recursive structure of the conformal block in boundary/crosscap conformal field theories that is obtained from the representation theory. We find that the pole structure perfectly agrees but the recursive structure in the Gauß hypergeometric function is slightly “off-shell”.

In this study, we consider baryons as three-body bound systems according to hypercentral constituent quark model in configuration space and solve three-body Klein–Gordon equation. Then we analyze perturbative spin-dependent and isospin-dependent interaction effects. To find the analytical solution, we used screened potential and calculate the eigenfunctions and eigenvalues of triply heavy baryons by using Nikiforov–Uvarov method. We compute the ground and excited state masses of triply heavy baryons with quantum numbers $J^P={\frac{1}{2}}^{\pm }$, ${\frac{3}{2}}^{\pm }$, ${\frac{5}{2}}^{\pm }$ via constituent quark model approach.

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in $(2+1$) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

In this paper, effects of Lorentz symmetry violation determined by a tensor field ${(K_F)}_{\mu \nu \alpha \beta }$ out of the Standard Model Extension on a modified quantum oscillator field in the presence of Cornell-type scalar potential are analyzed. We first introduced a scalar potential $S(r)=\left({\eta }_{L}r+\frac{{\eta }_c}{r}\right)$ by modifying the mass square term via transformation $M^2\to {(M+S(r))}^2$ in the Klein–Gordon equation, and then replace the momentum operator $\overrightarrow{p}\to (\overrightarrow{p}-iM\omega f(r)\widehat{r})$, where $f(r)$ is an arbitrary function other than $r$ to study the modified Klein–Gordon oscillator. We solve the wave equation and obtain the analytical bound-states solutions and see the dependence of oscillator frequency $(\omega )$ on the quantum numbers $\{n,l\}$ as well as on Lorentz-violating parameters with the potential which shows a quantum effect.