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Register a new userAspects of Quark Orbital Angular Momentum
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Authors
Matthias Burkardt
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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.
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The orbital angular momentum of quarks and gluons contributes significantly to the proton spin budget and attracted a lot of attention in the recent years, both theoretically and experimentally. We summarize the various definitions of parton orbital angular momentum together with their relations with parton distributions functions. In particular, we highlight current theoretical puzzles and give some prospects.
We show that quark orbital angular momentum is directly related to off-forward correlation functions which include intrinsic transverse momentum corresponding to a derivative with respect to the transverse coordinates. Its possible contribution to scattering processes is therefore of higher twist and vanishes in the forward limit. The relation of OAM to other twist 2 and 3 distributions known in the literature is derived and formalized by an unintegrated sum rule.
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}
We calculate the leading-twist helicity-dependent generalized parton distributions (GPDs) of the proton at finite skewness in the Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics (QCD). From these (and previously calculated helicity-independent GPDs) we obtain the spin decomposition of the proton, including predictions for quark intrinsic spin and orbital angular momentum. The inclusion of multiple species of diquarks is found to have a significant effect on the flavor decomposition, and resolving the internal structure of these dynamical diquark correlations proves essential for the mechanical stability of the proton. At a scale of $Q^2=4,$GeV$^2$ we find that the up and down quarks carry an intrinsic spin and orbital angular momentum of $S_u=0.534$, $S_d=-0.214$, $L_u=-0.189$, and $L_d=0.210$, whereas the gluons have a total angular momentum of $J_g=0.151$. The down quark is therefore found to carry almost no total angular momentum due to cancellations between spin and orbital contributions. Comparisons are made between these spin decomposition results and lattice QCD calculations.
We present a general analysis of the orbital angular momentum (OAM) distribution of gluons $L_g(x)$ inside the nucleon with particular emphasis on the small-$x$ region. We derive a novel operator representation of $L_g(x)$ in terms of Wilson lines and argue that it is approximately proportional to the gluon helicity distribution $L_g(x) approx -2Delta G(x)$ at small-$x$. We also compute longitudinal single spin asymmetry in exclusive diffractive dijet production in lepton-nucleon scattering in the next-to-eikonal approximation and show that the asymmetry is a direct probe of the gluon helicity/OAM distribution as well as the QCD odderon exchange.
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