278 research outputs found

    On Factorization of Generalized Macdonald Polynomials

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    A remarkable feature of Schur functions -- the common eigenfunctions of cut-and-join operators from W∞W_\infty -- is that they factorize at the peculiar two-parametric topological locus in the space of time-variables, what is known as the hook formula for quantum dimensions of representations of Uq(SLN)U_q(SL_N) and plays a big role in various applications. This factorization survives at the level of Macdonald polynomials. We look for its further generalization to {\it generalized} Macdonald polynomials (GMP), associated in the same way with the toroidal Ding-Iohara-Miki algebras, which play the central role in modern studies in Seiberg-Witten-Nekrasov theory. In the simplest case of the first-coproduct eigenfunctions, where GMP depend on just two sets of time-variables, we discover a weak factorization -- on a codimension-one slice of the topological locus, what is already a very non-trivial property, calling for proof and better understanding.Comment: 8 page

    The 2-leg vertex in K-theoretic DT theory

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    K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vertex. In this paper we derive a formula for the vertex in the case when two out of three entries are nontrivial. We also discuss some applications of this result.Comment: 27 page

    On factorization of generalized Macdonald polynomials

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    Measurement of J/ψ→γηcJ/\psi\to\gamma\eta_{\rm c} decay rate and ηc\eta_{\rm c} parameters at KEDR

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    Using the inclusive photon spectrum based on a data sample collected at the J/ψJ/\psi peak with the KEDR detector at the VEPP-4M e+e−e^+e^- collider, we measured the rate of the radiative decay J/ψ→γηcJ/\psi\to\gamma\eta_{\rm c} as well as ηc\eta_{\rm c} mass and width. Taking into account an asymmetric photon lineshape we obtained Γγηc0=2.98±0.18∣−0.33+0.15\Gamma^0_{\gamma\eta_{\rm c}}=2.98\pm0.18 \phantom{|}^{+0.15}_{-0.33} keV, Mηc=2983.5±1.4∣−3.6+1.6M_{\eta_{\rm c}} = 2983.5 \pm 1.4 \phantom{|}^{+1.6}_{-3.6} MeV/c2c^2, Γηc=27.2±3.1∣−2.6+5.4\Gamma_{\eta_{\rm c}} = 27.2 \pm 3.1 \phantom{|}^{+5.4}_{-2.6} MeV.Comment: 6 pages, 3 figure

    Measurement of B(J/psi->eta_c gamma) at KEDR

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    We present a study of the inclusive photon spectrum from 6.3 million J/psi decays collected with the KEDR detector at the VEPP-4M e+e- collider. We measure the branching fraction of the radiative decay J/psi -> eta_c gamma, eta_c width and mass. Taking into account an asymmetric photon line shape we obtain: M(eta_c) = (2978.1 +- 1.4 +- 2.0) MeV/c^2, Gamma(eta_c) = (43.5 +- 5.4 +- 15.8) MeV, B(J/psi->eta_c gamma) = (2.59 +- 0.16 +- 0.31)%$.Comment: 6 pages, 1 figure. To be published in the proceedings of the 4th International Workshop on Charm Physics (Charm2010), October 21-24, 2010, IHEP, Beijin

    Precise measurement of RudsR_{\text{uds}} and RR between 1.84 and 3.72 GeV at the KEDR detector

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    The present work continues a series of the KEDR measurements of the RR value that started in 2010 at the VEPP-4M e+e−e^+e^- collider. By combining new data with our previous results in this energy range we measured the values of RudsR_{\text{uds}} and RR at nine center-of-mass energies between 3.08 and 3.72 GeV. The total accuracy is about or better than 2.6%2.6\% at most of energy points with a systematic uncertainty of about 1.9%1.9\%. Together with the previous precise RR measurement at KEDR in the energy range 1.84-3.05 GeV, it constitutes the most detailed high-precision RR measurement near the charmonium production threshold.Comment: arXiv admin note: text overlap with arXiv:1610.02827 and substantial text overlap with arXiv:1510.0266

    Measurement of J/psi to eta_c gamma at KEDR

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    We present a study of the inclusive photon spectra from 5.9 million J/psi decays collected with the KEDR detector at the VEPP-4M e+e- collider. We measure the branching fraction of radiative decay J/psi to eta_c gamma, eta_c width and mass. Our preliminary results are: M(eta_c) = 2979.4+-1.5+-1.9 MeV, G(eta_c) = 27.8+-5.1+-3.3 MeV, B(J/psi to eta_c gamma) = (2.34+-0.15+-0.40)%.Comment: To be published in Proceedings of the PhiPsi09, Oct. 13-16, 2009, Beijing, Chin
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