819 research outputs found

    One-Loop Matching for Parton Distributions: Non-Singlet Case

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    We derive one-loop matching condition for non-singlet quark distributions in transverse-momentum cut-off scheme, including unpolarized, helicity and transversity distributions. The matching is between the quasi-distribution defined by static correlation at finite nucleon momentum and the light-cone distribution measurable in experiments. The result is useful for extracting the latter from the former in a lattice QCD calculation.Comment: 10 pages, 1 figur

    Spin Decomposition of Electron in QED

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    We perform a systematic study on the spin decomposition of an electron in QED at one-loop order. It is found that the electron orbital angular momentum defined in Jaffe-Manohar and Ji spin sum rules agrees with each other, and the so-called potential angular momentum vanishes at this order. The calculations are performed in both dimensional regularization and Pauli-Villars regularization for the ultraviolet divergences, and they lead to consistent results. We further investigate the calculations in terms of light-front wave functions, and find a missing contribution from the instantaneous interaction in light-front quantization. This clarifies the confusing issues raised recently in the literature on the spin decomposition of an electron, and will help to consolidate the spin physics program for nucleons in QCD.Comment: 8 page

    Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions

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    In a large-momentum nucleon state, the matrix element of a gauge-invariant Euclidean Wilson line operator accessible from lattice QCD can be related to the standard light-cone parton distribution function through the large-momentum effective theory (LaMET) expansion. This relation is given by a factorization theorem with a non-trivial matching coefficient. Using the operator product expansion we prove the large-momentum factorization of the quasi-parton distribution function in LaMET, and show that the more recently discussed Ioffe-time distribution approach also obeys an equivalent factorization theorem. Explicit results for the coefficients are obtained and compared at one-loop. Our proof clearly demonstrates that the matching coefficients in the MS\overline{\rm MS} scheme depend on the large partonic momentum rather than the nucleon momentum.Comment: 19 pages, 4 figure

    Proton spin after 30 years: what we know and what we don't?

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    More than three decades has passed since the European Muon Collaboration published the first surprising result on the spin structure of the proton. Much theoretical and experimental progress has been made in understanding the origins of the proton spin. In this review, we will discuss what we have learned so far, what are still missing, and what we shall expect to learn from the upcoming experiments including JLab 12 GeV and Electron-Ion Collider. In particular, we focus on first principles calculations and experimental measurements of the total gluon helicity ΔG\Delta G, and quark and gluon orbital angular momenta.Comment: 17 pages, 4 figures, to appear in Nature Revie

    Gluon Helicity Delta G from a Universality Class of Operators on a Lattice

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    We show that the total gluon helicity ΔG\Delta G in a polarized nucleon can be calculated on a Euclidean lattice through a universality class of QCD operators that describe the helicity or polarization of the onshell gluon radiation. We in particular find some operators whose matrix elements in a nucleon of momentum PzP^z are directly related to ΔG\Delta G with only power-law (1/Pz)n(n2)(1/P^z)^n (n\ge 2) corrections.Comment: 11 page

    Comparison and Design Optimization of a Five-Phase Flux-Switching PM Machine for In-Wheel Traction Applications

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    A comparative study of five-phase outer-rotor flux-switching permanent magnet (FSPM) machines with different topologies for in-wheel traction applications is presented in this paper. Those topologies include double-layer winding, single-layer winding, C-core, and E-core configurations. The electromagnetic performance in the low-speed region, the flux-weakening capability in the high-speed region, and the fault-tolerance capability are all investigated in detail. The results indicate that the E-core FSPM machine has performance advantages. Furthermore, two kinds of E-core FSPM machines with different stator and rotor pole combinations are optimized, respectively. In order to reduce the computational burden during the large-scale optimization process, a mathematical technique is developed based on the concept of computationally efficient finite-element analysis. While a differential evolution algorithm serves as a global search engine to target optimized designs. Subsequently, multiobjective tradeoffs are presented based on a Pareto-set for 20 000 candidate designs. Finally, an optimal design is prototyped, and some experimental results are given to confirm the validity of the simulation results in this paper

    NATURE OF THE LATE CARBONIFEROUS TO TRIASSIC MAGMATISM ALONG THE NORTHERN MARGIN OF THE NORTH CHINA BLOCK: LINK WITH THE EVOLUTION OF THE CENTRAL ASIAN OROGEN

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    There are two episodes of magmatism along the northern margin of the North China block during the Late Carboniferous to Late Triassic, one at 310–250 Ma (Late Carboniferous to Permian) and the other at 235–210 Ma (Late Triassic). The former group comprises plutonic rocks (gabbro-diorite-monzodioritemonzogranite-granite), mafic to intermediate dykes (diorite to dolerite) and a few felsic volcanics (andesite to dacite).There are two episodes of magmatism along the northern margin of the North China block during the Late Carboniferous to Late Triassic, one at 310–250 Ma (Late Carboniferous to Permian) and the other at 235–210 Ma (Late Triassic). The former group comprises plutonic rocks (gabbro-diorite-monzodioritemonzogranite-granite), mafic to intermediate dykes (diorite to dolerite) and a few felsic volcanics (andesite to dacite)
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