Effect of spin-spin interaction and fractional order on heavy pentaquark masses under topological defect space-times

Abstract In this paper, we investigate the masses of heavy pentaquark states under the influence of a spin-spin interaction term within a torsion-free fractal space-time with a point-like global monopole. The application and presence of fractional derivative is established from the outset. New operators are constructed using the definition of fractional derivative, and fractional-order Schrödinger equation is derived from these operators. The Hamiltonian operator is constructed with a two-part interaction potential: a spin-independent part containing Cornell potential, inversely quadratic and harmonic oscillator terms and a spin-dependent part containing a spin-spin interaction term to break the degeneracy between spin singlets and triplets. The spin dependence in our model arises from the harmonic approximation of the Gaussian function included in the spin-spin interaction term. This approximation facilitates obtaining analytical solutions for the bound states of heavy pentaquarks, expressed in terms of bi-confluent Heun functions. To achieve precise mass calculations for these pentaquarks using our model, various factors have been considered, including spin configurations, color and flavor combinations. Thus, we obtained the ground state masses for pentaquark containing two heavy quarks and having spin-parity $$\frac{1}{2}^{-}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>-</mml:mo> </mml:msup> </mml:math> , $$\frac{3}{2}^{-}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>-</mml:mo> </mml:msup> </mml:math> and $$\frac{5}{2}^{-}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mfrac> <mml:mn>5</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>-</mml:mo> </mml:msup> </mml:math> . Our results show consistency with previous calculations and are improved when experimental data are available, highlighting the relevance of fractional models and topological defects in heavy pentaquark mass calculations.