88,043 research outputs found

    Splitting and non-splitting in the difference hierarchy

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    Copyright © Cambridge University Press 2016In this paper, we investigate splitting and non-splitting properties in the Ershov difference hierarchy, in which area major contributions have been made by Barry Cooper with his students and colleagues. In the first part of the paper, we give a brief survey of his research in this area and discuss a number of related open questions. In the second part of the paper, we consider a splitting of 0′ with some additional properties

    Splitting and non-splitting in the difference hierarchy

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    Исследованы свойства разложения степени проблемы остановк

    Light-Quark SU(3)SU(3) Flavour Splitting of Heavy-Light Constituent Diquark Masses and Doubly-Strange Diquarks from QCD Sum-Rules

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    QCD Laplace sum-rules are used to examine the constituent mass spectrum of JP{0+,1+}J^P\in\{0^+,1^+\} heavy-light [Qq] diquarks with Q{c,b}Q\in\{c,b\} and q{u,d,s}q\in\{u,d,s\}. As in previous sum-rule studies, the negative parity JP{0,1}J^P\in\{0^-, 1^-\} [Qq] diquark mass predictions do not stabilize, so the sum-rule analysis focuses on positive parity [Qq] diquarks. Doubly-strange JP=1+J^P=1^{+} [ss] diquarks are also examined, but the resulting sum rules do not stabilize. Hence there is no sum-rule evidence for JP=1+J^P=1^{+} [ss] diquark states, aiding the interpretation of sum-rule analyses of fully-strange tetraquark states. The SU(3) flavour splitting effects for [Qq] diquarks are obtained by calculating QCD correlation functions of JP{0+,1+}J^P\in\{0^+,1^+\} diquark composite operators up to next-to-leading order in perturbation theory, leading-order in the strange quark mass, and in the chiral limit for non-strange (u,d) quarks with an isospin-symmetric vacuum =<uˉu>==<\bar uu>=. Apart from the strange quark mass parameter msm_s, the strange quark condensate parameter κ=/\kappa=/ has an important impact on SU(3) flavour splittings. A Laplace sum-rule analysis methodology is developed for the mass difference M[Qs]M[Qn]M_{[Qs]}-M_{[Qn]} between the strange and non-strange heavy-light diquarks to reduce the theoretical uncertainties from all other QCD input parameters. The mass splitting is found to decrease with increasing κ\kappa, providing an upper bound on κ\kappa where the M[Qs]M[Qn]M_{[Qs]}-M_{[Qn]} mass hierarchy reverses. In the typical QCD sum-rule range 0.56<κ<0.740.56<\kappa< 0.74, 55 MeV<M[cs]M[cn]<100 MeV55~MeV < M_{[cs]}-M_{[cn]} < 100~MeV and 75 MeV<M[bs]M[bn]<150 MeV75~MeV < M_{[bs]}-M_{[bn]}< 150~MeV, with a slight tendency for larger splittings for the JP=1+J^P=1^+ channels. These constituent mass splitting results are discussed in comparison with values used in constituent diquark models for tetraquark and pentaquark hadronic states.Comment: 30 pages, 19 figures, 7 tables. v2 contains extended discussio

    Effects of the neutrino mass splitting on the non-linear matter power spectrum

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    We have performed cosmological N-body simulations which include the effect of the masses of the individual neutrino species. The simulations were aimed at studying the effect of different neutrino hierarchies on the matter power spectrum. Compared to the linear theory predictions, we find that non-linearities enhance the effect of hierarchy on the matter power spectrum at mildly non-linear scales. The difference between the different hierarchies is about 0.5% for a sum of neutrino masses of 0.1eV. Albeit this is a small effect, it is potentially measurable from upcoming surveys. In combination with neutrinoless double-beta decay experiments, this opens up the possibility of using the sky to determine if neutrinos are Majorana or Dirac fermions.Comment: 5 pages, 5 figures, submitted to ApJ

    Can we measure the neutrino mass hierarchy in the sky?

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    Cosmological probes are steadily reducing the total neutrino mass window, resulting in constraints on the neutrino-mass degeneracy as the most significant outcome. In this work we explore the discovery potential of cosmological probes to constrain the neutrino hierarchy, and point out some subtleties that could yield spurious claims of detection. This has an important implication for next generation of double beta decay experiments, that will be able to achieve a positive signal in the case of degenerate or inverted hierarchy of Majorana neutrinos. We find that cosmological experiments that nearly cover the whole sky could in principle distinguish the neutrino hierarchy by yielding 'substantial' evidence for one scenario over the another, via precise measurements of the shape of the matter power spectrum from large scale structure and weak gravitational lensing.Comment: Submitted to JCA

    Muon antineutrino disappearance and non-standard interactions at the T2K experiment

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    T2K is a long-baseline neutrino oscillation experiment, which studies the changing avour composition of a beam over a 295 km baseline from an accelerator at J-PARC to Super-Kamiokande, a 50 kt water Cerenkov detector. The T2K neutrino beam has an energy peak at 0.6 GeV which gives strong sensitivity to oscillations at the atmospheric mass squared splitting. The beam can be run in two modes, producing a beam either dominated by neutrinos or by antineutrinos. Collecting data in antineutrino-mode allows the measurement of the neutrino mixing parameters on antineutrinos only. In the first analysis of T2K antineutrino-mode data, we use beam data collected up to June 2015 to measure sin2⊖23 and j m2 32j. The 90% CL allowed values for mixing angle are 0.327 < sin2⊖23 < 0.692 (normal hierarchy) and 0.332 < sin2⊖23 < 0.697 (inverted hierarchy). The 90% CL allowed values for mass splitting are 2.03x10-3 eV2 < j m2 32j < 2.92x10-3 eV2 (normal hierarchy) and 2.03x10-3 eV2 < j m2 31j < 2.92x10-3 eV2(inverted hierarchy). This is the world's best measurement in sin2⊖23. A difference between neutrino and antineutrino survival probabilities could result from physics beyond the Standard Model, known as non-standard interactions. A simultaneous fit to the T2K neutrino-mode and antineutrino-mode datasets allows for a direct search for such interactions. We see no evidence for this hypothesis

    Optimization of mesh hierarchies in Multilevel Monte Carlo samplers

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    We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and non-geometric sequences of mesh sizes and show that geometric hierarchies, when optimized, are nearly optimal and have the same asymptotic computational complexity as non-geometric optimal hierarchies. We discuss how enforcing constraints on parameters of MLMC hierarchies affects the optimality of these hierarchies. These constraints include an upper and a lower bound on the mesh size or enforcing that the number of samples and the number of discretization elements are integers. We also discuss the optimal tolerance splitting between the bias and the statistical error contributions and its asymptotic behavior. To provide numerical grounds for our theoretical results, we apply these optimized hierarchies together with the Continuation MLMC Algorithm. The first example considers a three-dimensional elliptic partial differential equation with random inputs. Its space discretization is based on continuous piecewise trilinear finite elements and the corresponding linear system is solved by either a direct or an iterative solver. The second example considers a one-dimensional It\^o stochastic differential equation discretized by a Milstein scheme

    On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD

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    We study some structural aspects of the evolution equations with Pomeron loops recently derived in QCD at high energy and for a large number of colors, with the purpose of clarifying their probabilistic interpretation. We show that, in spite of their appealing dipolar structure and of the self-duality of the underlying Hamiltonian, these equations cannot be given a meaningful interpretation in terms of a system of dipoles which evolves through dissociation (one dipole splitting into two) and recombination (two dipoles merging into one). The problem comes from the saturation effects, which cannot be described as dipole recombination, not even effectively. We establish this by showing that a (probabilistically meaningful) dipolar evolution in either the target or the projectile wavefunction cannot reproduce the actual evolution equations in QCD.Comment: 31 pages, 2 figure

    Neutrino footprint in Large Scale Structure

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    Recent constrains on the sum of neutrino masses inferred by analyzing cosmological data, show that detecting a non-zero neutrino mass is within reach of forthcoming cosmological surveys, implying a direct determination of the absolute neutrino mass scale. The measurement relies on constraining the shape of the matter power spectrum below the neutrino free streaming scale: massive neutrinos erase power at these scales. Detection of a lack of small-scale power, however, could also be due to a host of other effects. It is therefore of paramount importance to validate neutrinos as the source of power suppression at small scales. We show that, independent on hierarchy, neutrinos always show a footprint on large, linear scales; the exact location and properties can be related to the measured power suppression (an astrophysical measurement) and atmospheric neutrinos mass splitting (a neutrino oscillation experiment measurement). This feature can not be easily mimicked by systematic uncertainties or modifications in the cosmological model. The measurement of such a feature, up to 1% relative change in the power spectrum, is a smoking gun for confirming the determination of the absolute neutrino mass scale from cosmological observations. It also demonstrates the synergy of astrophysics and particle physics experiments.Comment: arXiv admin note: text overlap with arXiv:1003.591
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