Using airborne vector magnetic data to calculate the projection of magnetic anomaly vector onto normal geomagnetic field

The total-field magnetic anomaly [Formula: see text] is an approximation of the projection [Formula: see text] of the magnetic anomaly vector [Formula: see text] onto the normal geomagnetic field [Formula: see text]. However, for highly magnetic sources, the approximation error of [Formula: see text] cannot be ignored. To reduce the error, we have developed a method for calculating [Formula: see text] by using airborne vector magnetic data based on the vector relationship of geomagnetic field [Formula: see text]. The calculation uses the magnitude of the vectors [Formula: see text], [Formula: see text], and [Formula: see text] through a simple approach. To ensure that each magnitude has the same level, we normalize the magnitude of [Formula: see text] using the total-field magnetic data measured by the scalar magnetic sensor. The method is applied to the measured airborne vector magnetic data at the Qixin area of the East Tianshan Mountains in China. The results indicate that the calculated [Formula: see text] has high precision and can distinguish the approximation error less than 3.5 nT. We also analyze the characteristics of the approximation error that are caused by the effects of different total magnetization inclinations. These error characteristics are used to predict the total magnetization inclination of a 2D magnetic source based on the measured airborne vector magnetic data.

A remark about the anomalies of cyclic holomorphic permutation orbifolds

Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net [Formula: see text] with central charge [Formula: see text] depends on the “gravitational anomaly” [Formula: see text]. In particular, the conjecture that holomorphic permutation orbifolds are non-anomalous and therefore a stronger conjecture of Müger about braided crossed [Formula: see text]-categories arising from permutation orbifolds of completely rational conformal nets are wrong. More generally, we show that cyclic permutations of order [Formula: see text] are non-anomalous if and only if [Formula: see text] or [Formula: see text]. We also show that all cyclic permutation gaugings of [Formula: see text] arise from conformal nets.

Relative anomalies in (2+1)D symmetry enriched topological states

Certain patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. An important question is to determine how to compute this anomaly, which means determining which SPT hosts a given symmetry-enriched topological order at its surface. While special cases are known, a general method to compute the anomaly has so far been lacking. In this paper we propose a general method to compute relative anomalies between different symmetry fractionalization classes of a given (2+1)D topological order. This method applies to all types of symmetry actions, including anyon-permuting symmetries and general space-time reflection symmetries. We demonstrate compatibility of the relative anomaly formula with previous results for diagnosing anomalies for \mathbb{Z}_2^{T}ℤ2T space-time reflection symmetry (e.g. where time-reversal squares to the identity) and mixed anomalies for U(1) \times \mathbb{Z}_2^{T}U(1)×ℤ2T and U(1) \rtimes \mathbb{Z}_2^{T}U(1)⋊ℤ2T symmetries. We also study a number of additional examples, including cases where space-time reflection symmetries are intertwined in non-trivial ways with unitary symmetries, such as \mathbb{Z}_4^{T}ℤ4T and mixed anomalies for \mathbb{Z}_2 \times \mathbb{Z}_2^{T}ℤ2×ℤ2T symmetry, and unitary \mathbb{Z}_2 \times \mathbb{Z}_2ℤ2×ℤ2 symmetry with non-trivial anyon permutations.

Muon loss rates from betatron resonances at the Muon g − 2 Storage Ring at Fermilab

The Muon [Formula: see text] Experiment at Fermilab (E989) is directed toward measuring the muon magnetic anomaly, [Formula: see text], with total statistical and systematic errors of 0.14 ppm. This new measurement will serve as strong probe of effects of as yet undiscovered particles beyond the Standard Model (SM), and perhaps validate or disprove other theoretical models beyond the SM. Of special interest is the reduction of muon losses from the storage ring to achieve the precision needed at the Muon [Formula: see text] Experiment. For this purpose, we have developed a detailed and precise symplectic model of the Muon [Formula: see text] Storage Ring using COSY INFINITY that considers measured inhomogeneities of the magnetic field; high-order representation of the Electrostatic Quadrupole System (EQS) electrostatic field at different stages of the experiment including fringe fields; injection to the ring based on measurements; and beam collimation. Specifically, we have performed numerical analyses of the rate of muons that are lost before they have a chance to decay for several possible configurations of the EQS in order to find the best possible scenarios that minimize muon losses and understand the resonance mechanisms that contribute to betatron and possibly spin resonances. Additionally, comparisons with measurements have permitted the determination of whether observed resonances come from anticipated features of the [Formula: see text] storage ring or from unexpected sources of error whose effect could be detrimental to the precision of E989.

Accommodating three low-scale anomalies (g − 2, Lamb shift, and Atomki) in the framed Standard Model

The framed Standard Model (FSM) predicts a [Formula: see text] boson with mass around 20 MeV in the “hidden sector,” which mixes at tree level with the standard Higgs [Formula: see text] and hence acquires small couplings to quarks and leptons which can be calculated in the FSM apart from the mixing parameter [Formula: see text]. The exchange of this mixed state [Formula: see text] will contribute to [Formula: see text] and to the Lamb shift. By adjusting [Formula: see text] alone, it is found that the FSM can satisfy all present experimental bounds on the [Formula: see text] and Lamb shift anomalies for [Formula: see text] and [Formula: see text], and for the latter for both hydrogen and deuterium. The FSM predicts also a [Formula: see text] boson in the “hidden sector” with a mass of 17 MeV, that is, right on top of the Atomki anomaly [Formula: see text]. This mixes with the photon at 1-loop level and couples thereby like a dark photon to quarks and leptons. It is however a compound state and is thought likely to possess additional compound couplings to hadrons. By adjusting the mixing parameter and the [Formula: see text]’s compound coupling to nucleons, the FSM can reproduce the production rate of the [Formula: see text] in beryllium decay as well as satisfy all the bounds on [Formula: see text] listed so far in the literature. The above two results are consistent in that the [Formula: see text], being [Formula: see text], does not contribute to the Atomki anomaly if parity and angular momentum are conserved, while [Formula: see text], though contributing to [Formula: see text] and Lamb shift, has smaller couplings than [Formula: see text] and can, at first instance, be neglected there. Thus, despite the tentative nature of the three anomalies in experiment on the one hand and of the FSM as theory on the other, the accommodation of the former in the latter has strengthened the credibility of both. Indeed, if this FSM interpretation were correct, it would change the whole aspect of the anomalies from just curiosities to windows into a vast hitherto hidden sector comprising at least in part the dark matter which makes up the bulk of our universe.

Thermodynamic and transport properties in Au + Au collisions at RHIC energies from the clustering of color strings

In this work, we have extracted the initial temperature from the transverse momentum spectra of charged particles in Au + Au collisions using STAR data at RHIC energies from [Formula: see text] = 7.7–200 GeV. The initial energy density [Formula: see text], shear viscosity to entropy density ratio [Formula: see text], trace anomaly [Formula: see text], the squared speed of sound [Formula: see text], entropy density, and bulk viscosity to entropy density ratio [Formula: see text] are obtained and compared with the lattice QCD calculations for (2 + 1) flavor. The initial temperatures obtained are compared with various hadronization and chemical freeze-out temperatures. The analysis of the data shows that the deconfinement-to-confinement transition possibly takes place between [Formula: see text] = 11.5 and 19.6 GeV.

Dynamical role of Polyakov loops in the QCD thermodynamics

Polyakov loops [Formula: see text], [Formula: see text] are shown to give the most important non-perturbative (np) contribution to the thermodynamic potentials. Derived from the gluonic field correlators (FCs), they enter as factors into free energy. It is shown in the SU(3) case that [Formula: see text] define to a large extent the behavior of the free energy and the trace anomaly [Formula: see text], most sensitive to np effects.