Two-variable longitudinal distribution of the $Λ_b$ in a three-quark light-front model

Abstract

We determine a normalized two-variable longitudinal distribution of the $Λ_b=(ud)b$ baryon from a covariant three-quark light-front wave function. The scalar $ud$ channel is selected with the good-component structure $Cγ_5γ^+$, and the two independent transverse momenta are integrated without introducing an elementary diquark. The resulting model-scale valence distribution, $Ψ_2^{\rm LF}(x_u,x_d)$, retains both the heavy--light and internal-light momentum scales of the parent wave function. It is symmetric under $x_u\leftrightarrow x_d$, is concentrated where both light-quark fractions are small, and separates the total light-pair momentum from its internal sharing. For the central parameter set we find $\langle x_u\rangle=\langle x_d\rangle=0.130$, $\langle x_b\rangle=0.739$, $\langleζ^2\rangle=0.153$, and $\langleζ^4\rangle=0.055$, where $ζ=(x_u-x_d)/(x_u+x_d)$. Parameter variations give $\langle x_u\rangle=0.130^{+0.007}_{-0.007}$, $\langle x_b\rangle=0.739^{+0.014}_{-0.014}$, $\langleζ^2\rangle=0.153^{+0.014}_{-0.016}$, and $\langleζ^4\rangle=0.055^{+0.009}_{-0.009}$. The heavy--light momentum partition is controlled mainly by $β_{b,ud}$ and $m_b$, whereas the internal $u$--$d$ sharing is most sensitive to $β_{ud}$. The result provides a compact finite-mass benchmark for three-quark longitudinal structure, with distinct observables for heavy--light momentum sharing and correlations inside the light pair.