66,416 research outputs found

    TMD Evolution: Matching SIDIS to Drell-Yan and W/Z Boson Production

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    We examine the QCD evolution for the transverse momentum dependent observables in hard processes of semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in pppp collisions, including the spin-average cross sections and Sivers single transverse spin asymmetries. We show that the evolution equations derived by a direct integral of the Collins-Soper-Sterman evolution kernel from low to high Q can describe well the transverse momentum distribution of the unpolarized cross sections in the Q^2 range from 2 to 100 GeV^2. In addition, the matching is established between our evolution and the Collins-Soper-Sterman resummation with b*-prescription and Konychev-Nodalsky parameterization of the non-perturbative form factors, which are formulated to describe the Drell-Yan lepton pair and W/Z boson production in hadronic collisions. With these results, we present the predictions for the Sivers single transverse spin asymmetries in Drell-Yan lepton pair production and WΒ±W^\pm boson production in polarized pp and Ο€βˆ’p\pi^- p collisions for several proposed experiments. We emphasize that these experiments will not only provide crucial test of the sign change of the Sivers asymmetry, but also provide important opportunities to study the QCD evolution effects.Comment: 46 pages, 15 figure

    Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity

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    Current-phase relation in a Josephson junction formed by putting two s-wave superconductors on the same edge of a two dimensional topological insulator is investigated. We consider the case that the junction length is finite and magnetic impurity exists. The similarity and difference with conventional Josephson junction is discussed. The current is calculated in the semiconductor picture. Both the 2Ο€2\pi- and 4Ο€4\pi-period current-phase relations (I2Ο€(Ο•),I4Ο€(Ο•)I_{2\pi}(\phi), I_{4\pi}(\phi)) are studied. There is a sharp jump at Ο•=Ο€\phi=\pi and Ο•=2Ο€\phi=2\pi for I2Ο€I_{2\pi} and I4Ο€I_{4\pi} respectively in the clean junction. For I2Ο€I_{2\pi}, the sharp jump is robust against impurity strength and distribution. However for I4Ο€I_{4\pi}, the impurity makes the jump at Ο•=2Ο€\phi=2\pi smooth. The critical (maximum) current of I2Ο€I_{2\pi} is given and we find it will be increased by asymmetrical distribution of impurity.Comment: 7 pages, 5 figure
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