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    Geometrical exponents of contour loops on synthetic multifractal rough surfaces: multiplicative hierarchical cascade p-model

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    In this paper, we study many geometrical properties of contour loops to characterize the morphology of synthetic multifractal rough surfaces, which are generated by multiplicative hierarchical cascading processes. To this end, two different classes of multifractal rough surfaces are numerically simulated. As the first group, singular measure multifractal rough surfaces are generated by using the pp model. The smoothened multifractal rough surface then is simulated by convolving the first group with a so-called Hurst exponent, HH^* . The generalized multifractal dimension of isoheight lines (contours), D(q)D(q), correlation exponent of contours, xlx_l, cumulative distributions of areas, ξ\xi, and perimeters, η\eta, are calculated for both synthetic multifractal rough surfaces. Our results show that for both mentioned classes, hyperscaling relations for contour loops are the same as that of monofractal systems. In contrast to singular measure multifractal rough surfaces, HH^* plays a leading role in smoothened multifractal rough surfaces. All computed geometrical exponents for the first class depend not only on its Hurst exponent but also on the set of pp values. But in spite of multifractal nature of smoothened surfaces (second class), the corresponding geometrical exponents are controlled by HH^*, the same as what happens for monofractal rough surfaces.Comment: 14 pages, 14 figures and 6 tables; V2: Added comments, references, table and major correction

    Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

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    The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum
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