88,043 research outputs found
Splitting and non-splitting in the difference hierarchy
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
Исследованы свойства разложения степени проблемы остановк
Light-Quark Flavour Splitting of Heavy-Light Constituent Diquark Masses and Doubly-Strange Diquarks from QCD Sum-Rules
QCD Laplace sum-rules are used to examine the constituent mass spectrum of
heavy-light [Qq] diquarks with and
. As in previous sum-rule studies, the negative parity
[Qq] diquark mass predictions do not stabilize, so the
sum-rule analysis focuses on positive parity [Qq] diquarks. Doubly-strange
[ss] diquarks are also examined, but the resulting sum rules do not
stabilize. Hence there is no sum-rule evidence for [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
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 . Apart from the strange quark mass parameter , the strange
quark condensate parameter has an important impact
on SU(3) flavour splittings. A Laplace sum-rule analysis methodology is
developed for the mass difference 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 , providing an upper bound on where the
mass hierarchy reverses. In the typical QCD sum-rule range
, and , with a slight tendency for larger splittings for
the 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
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?
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
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
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
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
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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