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Register a new userSpin and Orbital Angular Momentum Distribution Functions of the Nucleon
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A theoretical prediction is given for the spin and orbital angular momentum distribution functions of the nucleon within the framework of an effective quark model of QCD, i.e. the chiral quark soliton model. An outstanding feature of the model is that it predicts fairly small quark spin fraction of the nucleon $Delta Sigma simeq 0.35$, which in turn dictates that the remaining 65% of the nucleon spin is carried by the orbital angular momentum of quarks and antiquarks at the model energy scale of $Q^2 simeq 0.3 {GeV}^2$. This large orbital angular momentum necessarily affects the scenario of scale dependence of the nucleon spin contents in a drastic way.
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Parallel to the construction of gauge invariant spin and orbital angular momentum for QED in paper (I) of this series, we present here an analogous but non-trivial solution for QCD. Explicitly gauge invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an impossible task, and opens a more promising avenue towards the understanding of the nucleon spin structure.
This two-paper series addresses and fixes the long-standing gauge invariance problem of angular momentum in gauge theories. This QED part reveals: 1) The spin and orbital angular momenta of electrons and photons can all be consistently defined gauge invariantly. 2) These gauge-invariant quantities can be conveniently computed via the canonical, gauge-dependent operators (e.g, $psi ^dagger vec x timesfrac 1i vec abla psi$) in the Coulomb gauge, which is in fact what people (unconsciously) do in atomic physics. 3) The renowned formula $vec xtimes(vec Etimesvec B)$ is a wrong density for the electromagnetic angular momentum. The angular distribution of angular-momentum flow in polarized atomic radiation is properly described not by this formula, but by the gauge invariant quantities defined here. The QCD paper [arXiv:0907.1284] will give a non-trivial generalization to non-Abelian gauge theories, and discuss the connection to nucleon spin structure.
The difference between the quark orbital angular momentum (OAM) defined in light-cone gauge (Jaffe-Manohar) compared to defined using a local manifestly gauge invariant operator (Ji) is interpreted in terms of the change in quark OAM as the quark leaves the target in a DIS experiment.
We determine the small Bjorken $x$ asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton in the double-logarithmic approximation (DLA), which resums powers of $alpha_s ln^2 (1/x)$ with $alpha_s$ the strong coupling constant. Starting with the operator definitions for the quark and gluon OAM, we simplify them at small $x$, relating them, respectively, to the polarized dipole amplitudes for the quark and gluon helicities defined in our earlier works. Using the small-$x$ evolution equations derived for these polarized dipole amplitudes earlier we arrive at the following small-$x$ asymptotics of the quark and gluon OAM distributions in the large-$N_c$ limit: begin{align} L_{q + bar{q}} (x, Q^2) = - Delta Sigma (x, Q^2) sim left(frac{1}{x}right)^{frac{4}{sqrt{3}} , sqrt{frac{alpha_s , N_c}{2 pi}} }, L_G (x, Q^2) sim Delta G (x, Q^2) sim left(frac{1}{x}right)^{frac{13}{4 sqrt{3}} , sqrt{frac{alpha_s , N_c}{2 pi}}} . end{align}
In this work, we explore the feasibility of performing satellite-to-Earth quantum key distribution (QKD) using the orbital angular momentum (OAM) of light. Due to the fragility of OAM states the conventional wisdom is that turbulence would render OAM-QKD non-viable in a satellite-to-Earth channel. However, based on detailed phase screen simulations of the anticipated atmospheric turbulence we find that OAM-QKD is viable in some system configurations, especially if quantum channel information is utilized in the processing of post-selected states. More specifically, using classically entangled light as a probe of the quantum channel, and reasonably-sized transmitter-receiver apertures, we find that non-zero QKD rates are achievable on sea-level ground stations. Without using classical light probes, OAM-QKD is relegated to high-altitude ground stations with large receiver apertures. Our work represents the first quantitative assessment of the performance of OAM-QKD from satellites, showing under what circumstances the much-touted higher dimensionality of OAM can be utilized in the context of secure communications.
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