Boundedness and unboundedness results for some maximal operators on functions of bounded variation

We characterize the space $BV(I)$ of functions of bounded variation on an arbitrary interval $I\subset \mathbb{R}$, in terms of a uniform boundedness condition satisfied by the local uncentered maximal operator $M_R$ from $BV(I)$ into the Sobolev space $W^{1,1}(I)$. By restriction, the corresponding characterization holds for $W^{1,1}(I)$. We also show that if $U$ is open in $\mathbb{R}^d, d >1$, then boundedness from $BV(U)$ into $W^{1,1}(U)$ fails for the local directional maximal operator $M_T^{v}$, the local strong maximal operator $M_T^S$, and the iterated local directional maximal operator $M_T^{d}\circ ...\circ M_T^{1}$. Nevertheless, if $U$ satisfies a cone condition, then $M_T^S:BV(U)\to L^1(U)$ boundedly, and the same happens with $M_T^{v}$, $M_T^{d} \circ ...\circ M_T^{1}$, and $M_R$.Comment: 15 page

Holography, Pade Approximants and Deconstruction

We investigate the relation between holographic calculations in 5D and the Migdal approach to correlation functions in large N theories. The latter employs Pade approximation to extrapolate short distance correlation functions to large distances. We make the Migdal/5D relation more precise by quantifying the correspondence between Pade approximation and the background and boundary conditions in 5D. We also establish a connection between the Migdal approach and the models of deconstructed dimensions.Comment: 28 page

A Triple Protostar System Formed via Fragmentation of a Gravitationally Unstable Disk

Binary and multiple star systems are a frequent outcome of the star formation process, and as a result, almost half of all sun-like stars have at least one companion star. Theoretical studies indicate that there are two main pathways that can operate concurrently to form binary/multiple star systems: large scale fragmentation of turbulent gas cores and filaments or smaller scale fragmentation of a massive protostellar disk due to gravitational instability. Observational evidence for turbulent fragmentation on scales of $>$1000~AU has recently emerged. Previous evidence for disk fragmentation was limited to inferences based on the separations of more-evolved pre-main sequence and protostellar multiple systems. The triple protostar system L1448 IRS3B is an ideal candidate to search for evidence of disk fragmentation. L1448 IRS3B is in an early phase of the star formation process, likely less than 150,000 years in age, and all protostars in the system are separated by $<$200~AU. Here we report observations of dust and molecular gas emission that reveal a disk with spiral structure surrounding the three protostars. Two protostars near the center of the disk are separated by 61 AU, and a tertiary protostar is coincident with a spiral arm in the outer disk at a 183 AU separation. The inferred mass of the central pair of protostellar objects is $\sim$1 M$_{sun}$, while the disk surrounding the three protostars has a total mass of $\sim$0.30 M_{\sun}. The tertiary protostar itself has a minimum mass of $\sim$0.085 M$_{sun}$. We demonstrate that the disk around L1448 IRS3B appears susceptible to disk fragmentation at radii between 150~AU and 320~AU, overlapping with the location of the tertiary protostar. This is consistent with models for a protostellar disk that has recently undergone gravitational instability, spawning one or two companion stars.Comment: Published in Nature on Oct. 27th. 24 pages, 8 figure

Measurement of radon-induced backgrounds in the NEXT double beta decay experiment

The measurement of the internal $^{222}$Rn activity in the NEXT-White detector during the so-called Run-II period with $^{136}$Xe-depleted xenon is discussed in detail, together with its implications for double beta decay searches in NEXT. The activity is measured through the alpha production rate induced in the fiducial volume by $^{222}$Rn and its alpha-emitting progeny. The specific activity is measured to be $(38.1\pm 2.2~\mathrm{(stat.)}\pm 5.9~\mathrm{(syst.)})$~mBq/m$^3$. Radon-induced electrons have also been characterized from the decay of the $^{214}$Bi daughter ions plating out on the cathode of the time projection chamber. From our studies, we conclude that radon-induced backgrounds are sufficiently low to enable a successful NEXT-100 physics program, as the projected rate contribution should not exceed 0.1~counts/yr in the neutrinoless double beta decay sample.Comment: 28 pages, 10 figures, 6 tables. Version accepted for publication in JHE

First Light And Reionisation Epoch Simulations (FLARES) XI: [OIII] emitting galaxies at 5<z<105<z<10

JWST has now made it possible to probe the rest-frame optical line emission of high-redshift galaxies extending to z~9, and potentially beyond. To aid in the interpretation of these emerging constraints, in this work we explore predictions for [OIII] emission in high-redshift galaxies using the First Light and Reionisation Epoch Simulations (FLARES). We produce predictions for the [OIII] luminosity function, its correlation with the UV luminosity, and the distribution of equivalent widths (EWs). We also explore how the [OIII] EW correlates with physical properties including specific star formation rate, metallicity, and dust attenuation. Our predictions are largely consistent with recent observational constraints on the luminosity function, average equivalent widths, and line ratios. However, they fail to reproduce the observed tail of high-EW sources and the number density of extreme line emitters. Possibilities to explain these discrepancies include an additional source of ionising photons and/or greater stochasticity in star formation in the model or photometric scatter and/or bias in the observations. With JWST now rapidly building larger samples and a wider range of emission lines the answer to this remaining discrepancy should be available imminently.Comment: 15 pages, accepted for publication in MNRAS, minor changes from original versio

Demonstration of the event identification capabilities of the NEXT-White detector

In experiments searching for neutrinoless double-beta decay, the possibility of identifying the two emitted electrons is a powerful tool in rejecting background events and therefore improving the overall sensitivity of the experiment. In this paper we present the first measurement of the efficiency of a cut based on the different event signatures of double and single electron tracks, using the data of the NEXT-White detector, the first detector of the NEXT experiment operating underground. Using a 228Th calibration source to produce signal-like and background-like events with energies near 1.6 MeV, a signal efficiency of 71.6 ± 1.5 stat± 0.3 sys% for a background acceptance of 20.6 ± 0.4 stat± 0.3 sys% is found, in good agreement with Monte Carlo simulations. An extrapolation to the energy region of the neutrinoless double beta decay by means of Monte Carlo simulations is also carried out, and the results obtained show an improvement in background rejection over those obtained at lower energies. [Figure not available: see fulltext.

Radiogenic backgrounds in the NEXT double beta decay experiment

Natural radioactivity represents one of the main backgrounds in the search for neutrinoless double beta decay. Within the NEXT physics program, the radioactivity- induced backgrounds are measured with the NEXT-White detector. Data from 37.9 days of low-background operations at the Laboratorio Subterráneo de Canfranc with xenon depleted in 136Xe are analyzed to derive a total background rate of (0.84±0.02) mHz above 1000 keV. The comparison of data samples with and without the use of the radon abatement system demonstrates that the contribution of airborne-Rn is negligible. A radiogenic background model is built upon the extensive radiopurity screening campaign conducted by the NEXT collaboration. A spectral fit to this model yields the specific contributions of 60Co, 40K, 214Bi and 208Tl to the total background rate, as well as their location in the detector volumes. The results are used to evaluate the impact of the radiogenic backgrounds in the double beta decay analyses, after the application of topological cuts that reduce the total rate to (0.25±0.01) mHz. Based on the best-fit background model, the NEXT-White median sensitivity to the two-neutrino double beta decay is found to be 3.5σ after 1 year of data taking. The background measurement in a Qββ±100 keV energy window validates the best-fit background model also for the neutrinoless double beta decay search with NEXT-100. Only one event is found, while the model expectation is (0.75±0.12) events. [Figure not available: see fulltext.]

Sensitivity of a tonne-scale NEXT detector for neutrinoless double beta decay searches

The Neutrino Experiment with a Xenon TPC (NEXT) searches for the neutrinoless double-beta decay of Xe-136 using high-pressure xenon gas TPCs with electroluminescent amplification. A scaled-up version of this technology with about 1 tonne of enriched xenon could reach in less than 5 years of operation a sensitivity to the half-life of neutrinoless double-beta decay decay better than 1E27 years, improving the current limits by at least one order of magnitude. This prediction is based on a well-understood background model dominated by radiogenic sources. The detector concept presented here represents a first step on a compelling path towards sensitivity to the parameter space defined by the inverted ordering of neutrino masses, and beyond.Comment: 22 pages, 11 figure