No Arabic abstract
I re-examine a recent work by G. Landi and G. E. Landi. [arXiv:1808.06708 [physics.ins-det]], in which the authors claim that the resolution of a tracker ca vary linearly with the number of detection layers, $N$, that is, faster than the commonly known $sqrt{N}$ variation, for a tracker of fixed length, in case the precision of the position measurement is allowed to vary from layer to layer, i.e. heteroscedasticity, and an appropriate analysis method, a weighted least squares fit, is used.
We discuss the fundamental noise limitations of a ferromagnetic torque sensor based on a levitated magnet in the tipping regime. We evaluate the optimal magnetic field resolution taking into account the thermomechanical noise and the mechanical detection noise at the standard quantum limit (SQL). We find that the Energy Resolution Limit (ERL), pointed out in recent literature as a relevant benchmark for most classes of magnetometers, can be surpassed by many orders of magnitude. Moreover, similarly to the case of a ferromagnetic gyroscope, it is also possible to surpass the standard quantum limit for magnetometry with independent spins, arising from spin-projection noise. Our finding indicates that magnetomechanical systems optimized for magnetometry can achieve a magnetic field resolution per unit volume several orders of magnitude better than any conventional magnetometer. We discuss possible implications, focusing on fundamental physics problems such as the search for exotic interactions beyond the standard model.
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the well known fact that commonly used variants of the least-squares fit applied to Poisson-distributed data produce biased estimates. The bias can be overcome with an iterated weighted least-squares method, which produces results identical to the maximum-likelihood method. For linear models, the iterated weighted least-squares method converges faster than the equivalent maximum-likelihood method, and does not require problem-specific starting values, which may be a practical advantage. The equivalence of both methods also holds for binomially distributed data. We further show that the unbinned maximum-likelihood method can be derived as a limiting case of the iterated least-squares fit when the bin width goes to zero, which demonstrates a deep connection between the two methods.
It is well known that $G=langle x,y:x^2=y^3=1rangle$ represents the modular group $PSL(2,Z)$, where $x:zrightarrowfrac{-1}{z}, y:zrightarrowfrac{z-1}{z}$ are linear fractional transformations. Let $n=k^2m$, where $k$ is any non zero integer and $m$ is square free positive integer. Then the set $$Q^*(sqrt{n}):={frac{a+sqrt{n}}{c}:a,c,b=frac{a^2-n}{c}in Z~textmd{and}~(a,b,c)=1}$$ is a $G$-subset of the real quadratic field $Q(sqrt{m})$ cite{R9}. We denote $alpha=frac{a+sqrt{n}}{c}$ in $ Q^*(sqrt{n})$ by $alpha(a,b,c)$. For a fixed integer $s>1$, we say that two elements $alpha(a,b,c)$, $alpha(a,b,c)$ of $Q^*(sqrt{n})$ are $s$-equivalent if and only if $aequiv a(mod~s)$, $bequiv b(mod~s)$ and $cequiv c(mod~s)$. The class $[a,b,c](mod~s)$ contains all $s$-equivalent elements of $Q^*(sqrt{n})$ and $E^n_s$ denotes the set consisting of all such classes of the form $[a,b,c](mod~s)$. In this paper we investigate proper $G$-subsets and $G$-orbits of the set $Q^*(sqrt{n})$ under the action of Modular Group $G$
The Muon g-2 experiment at Fermilab will measure the anomalous magnetic moment of the muon to a precision of 140 parts per billion, which is a factor of four improvement over the previous E821 measurement at Brookhaven. The experiment will also extend the search for the muon electric dipole moment (EDM) by approximately two orders of magnitude. Both of these measurements are made by combining a precise measurement of the 1.45T storage ring magnetic field with an analysis of the modulation of the decay rate of the higher-energy positrons from the (anti-)muon decays recorded by 24 calorimeters and 3 straw tracking detectors. The current status of the experiment as well as results from the initial beam delivery and commissioning run in the summer of 2017 will be discussed.
The couplings between the soft pion and the doublet of heavy-light mesons are basic parameters of the ChPT approach to the heavy-light systems. We compute the unquenched (Nf=2) values of two such couplings in the static heavy quark limit: (1) g^, coupling to the lowest doublet of heavy-light mesons, and (2) g~, coupling to the first orbital excitations. A brief description of the calculation together with a short discussion of the results is presented.