Investigations of $\mathrm{\Lambda }$ states with spin-parity ${\frac{3}{2}}^{\pm }$

The present study provides spectroscopic investigations of spin-$\frac{3}{2}$ $\mathrm{\Lambda }$ baryons with both positive and negative parities. The analysis mainly focuses on three states, namely $1P$, $2P$, and $2S$, and corresponding masses are calculated using the QCD sum rule method. To implement the method, we apply two types of interpolating currents with octet and singlet quantum numbers and compare the corresponding results with the reported masses of experimentally observed states. From the comparisons, it is extracted that the results of interpolating current with octet quantum numbers are in good agreement with the experimentally measured masses. The masses obtained with this interpolating current are $m=1513.64\pm 8.76\mathrm{MeV}$ for $1P$ state with $J^P={\frac{3}{2}}^{-}$, $m^{\prime }=1687.91\pm 0.31\mathrm{MeV}$ for $2P$ state with $J^P={\frac{3}{2}}^{-}$ and $\tilde{m}=1882.37\pm 11.95\mathrm{MeV}$ for $2S$ state with $J^P={\frac{3}{2}}^{+}$ and they are consistent with the experimental masses of $\mathrm{\Lambda }(1520)$, $\mathrm{\Lambda }(1690)$, and $\mathrm{\Lambda }(1890)$, respectively, which confirm their spin-parity quantum numbers. Besides, we calculate the corresponding current coupling constants, which are utilized as inputs in the calculations of different form factors defining the widths of the states under study.

Figure 1

Left: the dependence of the mass of the ground state $\mathrm{\Lambda }$ on $M^2$ at different values of $s_0$. Right: the dependence of the mass of the ground state $\mathrm{\Lambda }$ on $s_0$ at different values of $M^2$.

Figure 2

Left: the dependence of the current coupling constant of the ground state $\mathrm{\Lambda }$ on $M^2$ at different values of $s_0$. Right: the dependence of the current coupling constant of the ground state $\mathrm{\Lambda }$ on $s_0$ at different values of $M^2$.

Figure 3

Left: the dependence of the mass of the $(2P)$ exited state of $\mathrm{\Lambda }$ on $M^2$ at different values of $s_0$. Right: the dependence of the mass of the $(2P)$ exited state of $\mathrm{\Lambda }$ on $s_0$ at different values of $M^2$.

Figure 4

Left: the dependence of the current coupling constant of the $(2P)$ exited state of $\mathrm{\Lambda }$ on $M^2$ at different values of $s_0$. Right: the dependence of the current coupling constant of the $(2P)$ exited state of $\mathrm{\Lambda }$ on $s_0$ at different values of $M^2$.

Figure 5

Left: the dependence of the mass of the $(2S)$ exited state of $\mathrm{\Lambda }$ on $M^2$ at different values of $s_0$. Right: the dependence of the mass of the $(2S)$ exited state of $\mathrm{\Lambda }$ on $s_0$ at different values of $M^2$.

Figure 6

Left: the dependence of the current coupling constant of the $(2S)$ exited state of $\mathrm{\Lambda }$ on $M^2$ at different values of $s_0$. Right: the dependence of the current coupling constant of the $(2S)$ exited state of $\mathrm{\Lambda }$ on $s_0$ at different values of $M^2$.