Probing anomalous $Wtb$ couplings through $bW$ spin correlations in top-quark pair production at the HL-LHC

We propose a spin-density-matrix framework for probing anomalous $Wtb$ interactions in top-quark pair production by exploiting the polarizations of the $b$ quark and the $W$ boson and their spin correlations. The $b$-quark spin is analyzed through angular distributions in semileptonic ${\mathrm{\Lambda }}_b$ decay following fragmentation, while the leptonic $W$ decay serves as a $W$-polarization analyzer. We derive the $bW$ spin density matrix in the presence of anomalous $Wtb$ couplings and show that its polarization and spin-correlation parameters provide linear sensitivity to these couplings. We construct experimentally accessible angular observables associated with these parameters and evaluate their statistical sensitivities. For the HL-LHC at $\sqrt{s}=14\mathrm{T}\mathrm{e}\mathrm{V}$ with an integrated luminosity of $3000{\mathrm{f}\mathrm{b}}^{-1}$, the proposed method yields improved constraints on most anomalous $Wtb$ couplings, with the sensitivity to $V_R$ enhanced by a factor of 8 and that to $g_L$ by a factor of about 6.