The effects of polarization on the observables in the decay Ξ cc⁺⁺→ Ξ c⁺ ̄ν

We investigate the effects of polarization on several physical observables in the semileptonic decay Ξ cc⁺⁺ → Ξ c⁺ ̄ν Ξ cc + + → Ξ c + ℓ ¯ ν ℓ . We analyze the polarization effects of the particles involved in the decay, namely Ξ cc⁺⁺ Ξ cc + + , Ξ c⁺ Ξ c + , and the charged muon ℓ . Using the form factors obtained from QCD sum rules, we compute the q² q 2 -dependent observables including the differential branching ratio, forward–backward asymmetry, and polarization asymmetries for both longitudinal and transverse polarization states. We also define and examine several polarization ratios and discuss correlations among different observables. In addition, we evaluate the lepton flavor universality ratio defined as RΞ c⁺(μ /e) ≡ D(Ξ cc⁺⁺→ Ξ c⁺μ ⁺ν _μ )/D(Ξ cc⁺⁺→ Ξ c⁺e⁺ν ₑ) R Ξ c + ( μ / e ) ≡ D ( Ξ cc + + → Ξ c + μ + ν μ ) / D ( Ξ cc + + → Ξ c + e + ν e ) and analyze its behavior over the available dynamical range. Our results show that these observables are quite sensitive to polarization effects, and can provide suitable probes for testing Standard Model predictions.