Abstract
We study the covariant version of the quark-parton model, in which the general rules of the angular momentum composition are accurately taken into account. We demonstrate how these rules affect the relativistic interplay between the quark spins and orbital angular momenta, which collectively contribute to the proton spin. The spin structure functions $g_{1}$ and $g_{2}$ corresponding to the many-quark state $J=1/2$ are studied and it is shown they satisfy constraints and relations well compatible with the available experimental data including proton spin content $\Delta\Sigma\lesssim1/3$. The suggested Lorentz invariant 3D approach for calculation of the structure functions is compared with the approach based on the conventional collinear parton model.
Highlights
The question of correct interpretation and quantitative explanation of the low value ΔΣ denoting the contribution of spins of quarks to the proton spin remains still open
We have studied the interplay between the spins and orbital angular momentum (OAM) of the quarks, which are in conditions of DIS effectively free and collectively generate the proton spin
The covariant kinematics is an important condition for a consistent handling of the OAM
Summary
The question of correct interpretation and quantitative explanation of the low value ΔΣ denoting the contribution of spins of quarks to the proton spin remains still open. The space-time domain of the photon momentum transfer to the quark in different Lorentz frames. The limited extent of the domain prevents the quark from any interaction with the rest of nucleon, absence of interaction is synonym for freedom This argument is valid in any reference frame as it is illustrated, where the light cone domain Δτ = 0.25 fm in the nucleon of radius Rn = 0.8 fm is displayed for different Lorentz boosts: λ(β) = λ0 + βτ0 , τ(β) = τ0 + βλ0. We assume that the approximation of quarks by the free waves in this limited space-time domain is acceptable for description of DIS regardless of the reference frame.
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