853 research outputs found
Convergence Acceleration via Combined Nonlinear-Condensation Transformations
A method of numerically evaluating slowly convergent monotone series is
described. First, we apply a condensation transformation due to Van Wijngaarden
to the original series. This transforms the original monotone series into an
alternating series. In the second step, the convergence of the transformed
series is accelerated with the help of suitable nonlinear sequence
transformations that are known to be particularly powerful for alternating
series. Some theoretical aspects of our approach are discussed. The efficiency,
numerical stability, and wide applicability of the combined
nonlinear-condensation transformation is illustrated by a number of examples.
We discuss the evaluation of special functions close to or on the boundary of
the circle of convergence, even in the vicinity of singularities. We also
consider a series of products of spherical Bessel functions, which serves as a
model for partial wave expansions occurring in quantum electrodynamic bound
state calculations.Comment: 24 pages, LaTeX, 12 tables (accepted for publication in Comput. Phys.
Comm.
Primordial Black Holes as Silver Bullets for New Physics at the Weak Scale
Observational constraints on gamma rays produced by the annihilation of
weakly interacting massive particles around primordial black holes (PBHs) imply
that these two classes of Dark Matter candidates cannot coexist. We show here
that the successful detection of one or more PBHs by radio searches (with the
Square Kilometer Array) and gravitational waves searches (with LIGO/Virgo and
the upcoming Einstein Telescope) would set extraordinarily stringent
constraints on virtually all weak-scale extensions of the Standard Model with
stable relics, including those predicting a WIMP abundance much smaller than
that of Dark Matter. Upcoming PBHs searches have in particular the potential to
rule out almost the entire parameter space of popular theories such as the
minimal supersymmetric standard model and scalar singlet Dark Matter.Comment: 10 pages, 3 figures. Code available at
https://github.com/adam-coogan/pbhs_vs_wimps , archived at
https://zenodo.org/badge/latestdoi/169754838 . v2: Matches version published
in PR
Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962
- 968 (2003)] introduced in connection with the summation of the divergent
perturbation expansion of the hydrogen atom in an external magnetic field a new
sequence transformation which uses as input data not only the elements of a
sequence of partial sums, but also explicit estimates
for the truncation errors. The explicit
incorporation of the information contained in the truncation error estimates
makes this and related transformations potentially much more powerful than for
instance Pad\'{e} approximants. Special cases of the new transformation are
sequence transformations introduced by Levin [Int. J. Comput. Math. B
\textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189
- 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and
also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A
\textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations
- explicit expressions, recurrence formulas, explicit expressions in the case
of special remainder estimates, and asymptotic order estimates satisfied by
rational approximants to power series - is formulated in terms of hitherto
unknown mathematical properties of the new transformation introduced by
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable
formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of
Mathematical Physic
A Unique Multi-Messenger Signal of QCD Axion Dark Matter
We propose a multi-messenger probe of QCD axion Dark Matter based on
observations of black hole-neutron star binary inspirals. It is suggested that
a dense Dark Matter spike may grow around intermediate mass black holes
(). The presence of such a spike produces
two unique effects: a distinct phase shift in the gravitational wave strain
during the inspiral and an enhancement of the radio emission due to the
resonant axion-photon conversion occurring in the neutron star magnetosphere
throughout the inspiral and merger. Remarkably, the observation of the
gravitational wave signal can be used to infer the Dark Matter density and,
consequently, to predict the radio emission. We study the projected reach of
the LISA interferometer and next-generation radio telescopes such as the Square
Kilometre Array. Given a sufficiently nearby system, such observations will
potentially allow for the detection of QCD axion Dark Matter in the mass range
to .Comment: 5 pages, 3 figures. Appendix added with additional figures. Updated
to published versio
Albatross:a scalable simulation-based inference pipeline for analysing stellar streams in the Milky Way
Stellar streams are potentially a very sensitive observational probe of galactic astrophysics, as well as the dark matter population in the Milky Way. On the other hand, performing a detailed, high-fidelity statistical analysis of these objects is challenging for a number of key reasons. First, the modelling of streams across their (potentially billions of years old) dynamical age is complex and computationally costly. Secondly, their detection and classification in large surveys such as Gaia renders a robust statistical description regarding e.g. the stellar membership probabilities, challenging. As a result, the majority of current analyses must resort to simplified models that use only subsets or summaries of the high quality data. In this work, we develop a new analysis framework that takes advantage of advances in simulation-based inference techniques to perform complete analysis on complex stream models. To facilitate this, we develop a new, modular dynamical modelling code sstrax for stellar streams that is highly accelerated using jax. We test our analysis pipeline on a mock observation that resembles the GD1 stream, and demonstrate that we can perform robust inference on all relevant parts of the stream model simultaneously. Finally, we present some outlook as to how this approach can be developed further to perform more complete and accurate statistical analyses of current and future data
Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients
We propose a method for the resummation of divergent perturbative expansions in quantum electrodynamics and related field theories. The method is based on a nonlinear sequence transformation and uses as input data only the numerical values of a finite number of perturbative coefficients. The results obtained in this way are for alternating series superior to those obtained using Padé approximants. The nonlinear sequence transformation fulfills an accuracy-through-order relation and can be used to predict perturbative coefficients. In many cases, these predictions are closer to available analytic results than predictions obtained using the Padé method
Digging for Dark Matter: Spectral Analysis and Discovery Potential of Paleo-Detectors
Paleo-detectors are a recently proposed method for the direct detection of
Dark Matter (DM). In such detectors, one would search for the persistent damage
features left by DM--nucleus interactions in ancient minerals. Initial
sensitivity projections have shown that paleo-detectors could probe much of the
remaining Weakly Interacting Massive Particle (WIMP) parameter space. In this
paper, we improve upon the cut-and-count approach previously used to estimate
the sensitivity by performing a full spectral analysis of the background- and
DM-induced signal spectra. We consider two scenarios for the systematic errors
on the background spectra: i) systematic errors on the normalization only, and
ii) systematic errors on the shape of the backgrounds. We find that the
projected sensitivity is rather robust to imperfect knowledge of the
backgrounds. Finally, we study how well the parameters of the true WIMP model
could be reconstructed in the hypothetical case of a WIMP discovery.Comment: 14 pages, 5 figures, code available at
https://github.com/tedwards2412/paleo_detectors/ . v2: Added additional
analysis theory details, matches version published in PR
Acceleration of generalized hypergeometric functions through precise remainder asymptotics
We express the asymptotics of the remainders of the partial sums {s_n} of the
generalized hypergeometric function q+1_F_q through an inverse power series z^n
n^l \sum_k c_k/n^k, where the exponent l and the asymptotic coefficients {c_k}
may be recursively computed to any desired order from the hypergeometric
parameters and argument. From this we derive a new series acceleration
technique that can be applied to any such function, even with complex
parameters and at the branch point z=1. For moderate parameters (up to
approximately ten) a C implementation at fixed precision is very effective at
computing these functions; for larger parameters an implementation in higher
than machine precision would be needed. Even for larger parameters, however,
our C implementation is able to correctly determine whether or not it has
converged; and when it converges, its estimate of its error is accurate.Comment: 36 pages, 6 figures, LaTeX2e. Fixed sign error in Eq. (2.28), added
several references, added comparison to other methods, and added discussion
of recursion stabilit
Dark Matter Model or Mass, but Not Both: Assessing Near-Future Direct Searches with Benchmark-free Forecasting
Forecasting the signal discrimination power of dark matter (DM) searches is
commonly limited to a set of arbitrary benchmark points. We introduce new
methods for benchmark-free forecasting that instead allow an exhaustive
exploration and visualization of the phenomenological distinctiveness of DM
models, based on standard hypothesis testing. Using this method, we reassess
the signal discrimination power of future liquid Xenon and Argon direct DM
searches. We quantify the parameter regions where various non-relativistic
effective operators, millicharged DM, and magnetic dipole DM can be
discriminated, and where upper limits on the DM mass can be found. We find that
including an Argon target substantially improves the prospects for
reconstructing the DM properties. We also show that only in a small region with
DM masses in the range 20-100 GeV and DM-nucleon cross sections a factor of a
few below current bounds can near-future Xenon and Argon detectors discriminate
both the DM-nucleon interaction and the DM mass simultaneously. In all other
regions only one or the other can be obtained.Comment: 5 pages, 4 figures + appendices. Code for the calculations throughout
the paper can be found at
https://github.com/tedwards2412/benchmark_free_forecasting/ . v2: Minor
corrections, matches version published in PRL as "Assessing Near-Future
Direct Dark Matter Searches with Benchmark-Free Forecasting
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