Phenomenological Analysis of Triply Heavy Pentaquarks with configurations $q\Bar{q}QQQ$ and $qqQQ\Bar{Q}$

We carried out the systematic analysis of the $s$-wave triply heavy pentaquarks with possible configurations like $q\Bar{q}QQQ$ and $qqQQ\Bar{Q}$, ($q = u, d, s$ and $Q = c, b$ quarks). Special unitary representations are utilized to study the classification scheme for triply heavy configurations like $q\Bar{q}QQQ$ and $qqQQ\Bar{Q}$. We classified the $q\Bar{q}QQQ$-type pentaquarks into an octet and $qqQQ\Bar{Q}$-type pentaquarks into sextet configurations with the help of SU(3) flavor representation. Also, with the help of SU(2) spin representation, we studied the possible spin assignments ($\frac{1}{2}^-$, $\frac{3}{2}^-$, and $\frac{5}{2}^-$) for ground state triply heavy pentaquarks. Furthermore, we used the formalism of the extended Gursey-Radicati mass formula and effective mass scheme to estimate the masses of triply heavy pentaquarks. Additionally, we calculated the magnetic moment assignments using the effective mass and screened charge schemes. The predicted outcomes align well with the existing theoretical data and benefit future studies. Our work provides a comprehensive framework that combines the theoretical aspects of SU(3) and SU(2) symmetries with practical predictions for observables, offering a strong foundation for experimental verification. This integrated approach enhances our understanding of the complex interactions within triply heavy pentaquarks and underscores their potential role in probing deeper into the dynamics of the strong force. These findings are crucial for designing future high-energy experiments that directly observe these exotic states and confirm their properties, paving the way for new insights into quantum chromodynamics.