Endpoint Region Research Articles

Improved treatment of the T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} molecular final-states uncertainties for the KATRIN neutrino-mass measurement

The KArlsruhe TRItium Neutrino experiment (KATRIN) aims to determine the effective mass of the electron antineutrino via a high-precision measurement of the tritium β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta $$\\end{document}-decay spectrum in its end-point region. The target neutrino-mass sensitivity of 0.2eV/c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${0.2}~\ ext {eV}/\ ext {c}^2$$\\end{document} at 90% CL can only be achieved in the case of high statistics and good control of the systematic uncertainties. One key systematic effect originates from the calculation of the molecular final states of T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upbeta $$\\end{document} decay. In the first neutrino-mass analyses of KATRIN the contribution of the uncertainty of the molecular final-states distribution (FSD) was estimated via a conservative phenomenological approach to be 2×10-2eV2/c4.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2 \ imes 10^{-2}~\ ext {eV}^{2}/\ ext {c}^{4}.$$\\end{document} In this work a new procedure is presented for estimating the FSD-related uncertainties by considering the details of the final-states calculation, i.e. the uncertainties of constants, parameters, and functions used in the calculation as well as its convergence itself as a function of the basis-set size used in expanding the molecular wave functions. The calculated uncertainties are directly propagated into the experimental observable, the squared neutrino mass mν2,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_\ u ^2,$$\\end{document} and thus have to be determined individually for each experimental configuration. For the experimental conditions of the first KATRIN measurement campaign the new procedure is presented in detail, allowing for the application of this procedure to other experiments. This specific calculation leads to a constraint of the FSD-related uncertainty of 1.3×10-3eV2/c4,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1.3 \ imes 10^{-3}~\ ext {eV}^{2}/\ ext {c}^{4},$$\\end{document} well below the design limit of 7.5×10-3eV2/c4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7.5 \ imes 10^{-3}~\ ext {eV}^{2}/\ ext {c}^{4}$$\\end{document} for any individual systematic contribution.

Robust trajectory optimization of re-entry flight with prescribed endpoint region via sparse grid ensemble pseudospectral optimal control

This paper introduces a sampling-based computational framework with a pseudospectral transcription, designed to investigate performance-robustness tradeoffs for constrained re-entry flights with a non-Gaussian uncertainty propagation. Ensemble of trajectories which are generated with sparse grids with Conjugate Unscented Transformation have been integrated into the nonlinear programming via a vectorized and parallelized formulation. A cross-range maximization problem is formulated to assess the influences of uncertainties in entry interface conditions and model parametric uncertainties. A comprehensive analysis, facilitated by rapid gradient-based optimization convergence and warm-starting, highlights the significant effects of initial speed uncertainties and drag coefficient on problem feasibility, offering insights into optimal control behavior under different degrees and combinations of uncertainties. Proper scaling of controls and the objective function proves pivotal for achieving convergence. Furthermore, a novel phenomenon called “contact arcs” is discovered, composed of contact points that form an arc at the edge of the path constraint in the constrained ensemble optimal control as a counterpart to the boundary arcs in deterministic optimal control problems. Simulation results show excellent agreement with the derived optimality conditions.

Development and characterisation of high-resolution microcalorimeter detectors for the ECHo-100k experiment

The goal of the ECHo experiment is a direct determination of the absolute scale of the neutrino mass by the analysis of the end-point region of the 163Ho electron capture (EC) spectrum. The results of the first phase of the experiment, ECHo-1k, have paved the way for the current phase, ECHo-100k, which aims at a sensitivity below 2eV on the effective electron neutrino mass. In order to reach this goal, a new generation of high-resolution magnetic microcalorimeters with embedded 163Ho have been developed and characterised. The design has been optimised to meet all the challenging requirements of the ECHo-100k experimental phase, such as excellent energy resolution, wafer scale implantation and multi-chip operation with multiplexing read-out. We present the optimisation studies, the final design of the detector array and the first characterisation studies. The obtained results demonstrate that the detectors fully match and even surpass the requirements for the current experimental phase, ECHo-100k.

In Situ Tritium Decontamination of the KATRIN Rear Wall Using an Ultraviolet/Ozone Treatment

The KArlsruhe TRItium Neutrino (KATRIN) collaboration aims to determine the neutrino mass with a sensitivity of 0.2 eV/c2 (90% confidence level). This will be achieved by probing the end-point region of the β-electron spectrum of gaseous tritium with an electrostatic spectrometer. A gold-coated stainless steel disk defines the reference potential for high-precision neutrino mass measurement, and it terminates the β-electron flux as the physical boundary of the tritium source. This so-called rear wall is exposed to tritium, which leads to adsorption and absorption. This in turn leads to systematic uncertainties for the neutrino mass measurements that need to be understood and mitigated. In maintenance phases, during which the gaseous tritium source was emptied (<10−5 of nominal gas density), the activity that accumulated on the rear wall during normal operation was monitored using beta-induced X-ray spectrometry (BIXS) and direct observation of emitted β electrons with a silicon detector. Dependency of the observed activity increase on the integral tritium throughput was investigated and found to converge from limited exponential growth to continuous linear growth. This paper gives an overview of the results that were obtained using several methods of in situ decontamination of the rear wall while continuously monitoring the activity. The decontamination methods included heating during continuous evacuation; flushing the system with nitrogen, deuterium, or air with residual humidity at different pressures; and illumination of the rear wall with ultraviolet (UV) light. These well-known methods led to only a small ( ≈ 15%) decrease in the observed activity. However, a decrease of the surface activity by three orders of magnitude in less than 1 week was achieved by combination of different methods using UV light, a heated surface, and a low (5 to 100 mbar) pressure of air inside the chamber, leading to the production of highly reactive ozone. This proved to be by far the most efficient method, drastically reducing the contribution of the rear wall surface activity to the β spectrum of the gaseous source.

Precision control in lattice calculation of x-dependent pion distribution amplitude

We present a new Bjorken x-dependence analysis of a previous lattice quantum chromodynamics data for the pion distribution amplitude from MILC configurations with three lattice spacing a=0.06,0.09,0.12 fm. A leading renormalon resummation in renormalization as well as the perturbative matching kernel in the framework of large momentum expansion generates the power accuracy of the matching to the light-cone amplitude. Meanwhile, a small momentum log resummation is implemented for both the quark momentum xPz and the antiquark momentum (1−x)Pz inside a meson of boost momentum Pz up to 1.72 GeV along the z direction, allowing us to have more accurate determination of the x-dependence in the middle range. Finally, we use the complementarity between the short-distance factorization and the large momentum expansion to constrain the endpoint regions x∼0,1, thus obtaining the full-range x-dependence of the amplitude.

Factorization at subleading power in deep inelastic scattering in the x→1 limit

We examine the endpoint region of inclusive deep inelastic scattering at next-to-leading power (NLP). Using a soft-collinear effective theory approach with no explicit soft or collinear modes, we discuss the factorization of the cross section at NLP and show that the overlap subtraction procedure introduced to eliminate double counting of degrees of freedom at leading power ensures that spurious endpoint divergences in the rate cancel at NLP at one loop. For this cancellation to occur at all renormalization scales a nontrivial relation between the anomalous dimensions of the leading and subleading operators is required, which is demonstrated to hold at one loop.

KATRIN: status and prospects for the neutrino mass and beyond

The Karlsruhe Tritium Neutrino (KATRIN) experiment is designed to measure a high-precision integral spectrum of the endpoint region of T2 β decay, with the primary goal of probing the absolute mass scale of the neutrino. After a first tritium commissioning campaign in 2018, the experiment has been regularly running since 2019, and in its first two measurement campaigns has already achieved a sub-eV sensitivity. After 1000 days of data-taking, KATRIN’s design sensitivity is 0.2 eV at the 90% confidence level. In this white paper we describe the current status of KATRIN; explore prospects for measuring the neutrino mass and other physics observables, including sterile neutrinos and other beyond-Standard-Model hypotheses; and discuss research-and-development projects that may further improve the KATRIN sensitivity.

Neutrino Mass Measurements Using Cryogenic Detectors

The determination of the absolute mass scale of neutrinos is one of the most important challenges in Particle Physics. The shape of the endpoint region of beta ^--decay and electron capture (EC) spectra depends on the phase space factor, which, in turn, is function of the masses of the neutrino mass eigenstates. High energy resolution and high statistics measurements of beta ^- and EC spectra are therefore considered a model-independent way for the determination of the neutrino mass scale. Since almost four decades, low temperature microcalorimeters are used for the measurement of low energy beta ^- and EC spectra. The first efforts were focused on the development of large arrays for the measurement of the ^{187}Re beta ^--spectrum. In the last ten years, the attention moved to EC of ^{163}Ho. This choice was mainly motivated by the very good performance which could be achieved with low temperature microcalorimeters enclosing ^{163}Ho with respect to microcalorimeters with absorber containing ^{187}Re. The development of low temperature microcalorimeters for the measurement of the finite neutrino mass is discussed and, in particular, the reasons for moving from ^{187}Re to ^{163}Ho. The possibility to reach sub-eV sensitivity on the effective electron neutrino mass with ^{163}Ho, thanks to the multiplexing of large microcalorimeter arrays is demonstrated. In conclusion, an overview on other nuclides which have been proposed as good candidates, motivated by the excellent performance of low temperature microcalorimeters is presented.

Photon PDF within the CT18 global analysis

Building upon the most recent CT18 global fit, we present a new calculation of the photon content of the proton based on an application of the LUX formalism. In this work, we explore two principal variations of the LUX ansatz. In one approach, which we designate "CT18lux," the photon PDF is calculated directly using the LUX formula for all scales, $\mu$. In an alternative realization, "CT18qed," we instead initialize the photon PDF in terms of the LUX formulation at a lower scale, $\mu\! \sim\! \mu_0$, and evolve to higher scales with a combined QED+QCD kernel at $\mathcal{O}(\alpha),~\mathcal{O}(\alpha\alpha_s)$ and $\mathcal{O}(\alpha^2)$. While we find these two approaches generally agree, especially at intermediate $x$ ($10^{-3}\lesssim x\lesssim0.3$), we discuss some moderate discrepancies that can occur toward the end-point regions at very high or low $x$. We also study effects that follow from variations of the inputs to the LUX calculation originating outside the pure deeply-inelastic scattering (DIS) region, including from elastic form factors and other contributions to the photon PDF. Finally, we investigate the phenomenological implications of these photon PDFs for the LHC, including high-mass Drell-Yan, vector-boson pair, top-quark pair, and Higgs associated with vector-boson production.

Forward Beam Monitor for the KATRIN experiment

The KArlsruhe TRItium Neutrino (KATRIN) experiment aims to measure the neutrino mass with a sensitivity of 0.2 eV (90 % CL). This will be achieved by a precision measurement of the endpoint region of the β-electron spectrum of tritium decay. The β-electrons are produced in the Windowless Gaseous Tritium Source (WGTS) and guided magnetically through the beamline. In order to accurately extract the neutrino mass the source activity is required to be stable and known to a high precision. The WGTS therefore undergoes constant extensive monitoring from several measurement systems. The Forward Beam Monitor (FBM) is one such monitoring system. The FBM system comprises a complex mechanical setup capable of inserting a detector board into the KATRIN beamline with a positioning precision of better than 0.3 mm. The electron flux density at that position is on the order of 106 s-1 mm-2. The detector board contains two silicon detector chips of p-i-n diode type which can measure the β-electron flux from the source with a precision of 0.1 % within 60 s with an energy resolution of FWHM = 2 keV. The unique challenge in developing the FBM arises from its designated operating environment inside the Cryogenic Pumping Section which is a potentially tritium contaminated ultra-high vacuum chamber at cryogenic temperatures in the presence of a 1 T strong magnetic field. Each of these parameters do strongly limit the choice of possible materials which e.g. caused difficulties in detector noise reduction, heat dissipation and lubrication. In order to completely remove the FBM from the beam tube a 2 m long traveling distance into the beamline is needed demanding a robust as well as highly precise moving mechanism.

Metallic magnetic calorimeter arrays for the first phase of the ECHo experiment

The ECHo experiment has been designed for the determination of the effective electron neutrino mass by means of the analysis of the end-point region of the 163Ho electron capture spectrum. Metallic magnetic calorimeters enclosing 163Ho are used for the high energy resolution calorimetric measurement of the 163Ho spectrum. For the first phase of the experiment, ECHo-1k, a 72-pixel MMC array has been developed. The single-pixel design has been optimised to reach 100% stopping power for the radiation emitted in the 163Ho electron capture process (besides the electron neutrino) and an energy resolution ΔEFWHM<10eV. We describe the design of the ECHo-1k detector chip, the fabrication steps and the characterisation at room temperature, at 4 K and at the final operation temperatures. In particular, a detailed analysis of the results from these tests allowed to define a quality check protocol based on parameters measurable at room temperature. We discuss the performance achieved with the two ECHo-1k detector chips – the first one with 163Ho implanted in gold and the second one with 163Ho implanted in silver – which have been used for the high statistics measurement of the ECHo-1k experiment. An average activity per pixel of 0.81Bq and 0.71Bq and an average energy resolution of 6.07eV FWHM and 5.55eV FWHM have been achieved with these two detectors, fulfilling the requirements for the first phase of the ECHo experiment.

Study of naturally occurring radionuclides in the ECHo set-up

The determination of the effective electron neutrino mass by analyzing the end point region of the ^{163}Ho electron capture (EC) spectrum relies on the precise description of the expected ^{163}Ho events and background events. In the ECHo experiment, arrays of metallic magnetic calorimeters, implanted with ^{163}Ho, are operated to measure the ^{163}Ho EC spectrum. In an energy range of 10 eV below Q_{mathrm {EC}}, the maximum available energy for the EC decay of about 2.8 keV, a ^{163}Ho event rate of the order of 10^{-4} day^{-1} pixel^{-1} is expected for an activity of 1 Bq of ^{163}Ho per pixel. This means, a control of the background level in the order of 10^{-5} day^{-1} pixel^{-1} is extremely important. We discuss the results of a Monte Carlo study based on simulations, which use the GEANT4 framework to understand the impact of natural radioactive isotopes close to the active detector volume in the case of the ECHo-1k set-up, which is used for the first phase of the ECHo experiment. For this, the ECHo-1k set-up was modeled in GEANT4 using the proper geometry and materials, including the information of screening measurements of some materials used in the ECHo-1k set-up and reasonable assumptions. Based on the simulation and on assumptions, we derive the expected background around Q_{mathrm {EC}} and give upper limits of tolerable concentrations of natural radionuclides in the set-up materials. In addition, we compare our results to background spectra acquired in detector pixels with and without implanted ^{163}Ho. We conclude that typical concentration of radioactive nuclides found in the used materials should not endanger the analysis of the endpoint region of the ^{163}Ho EC spectrum for an exposure time of half a year.

Data reduction for a calorimetrically measured ^{163}mathrm {Ho} spectrum of the ECHo-1k experiment

The electron capture in ^{163}mathrm {Ho} experiment (ECHo) is designed to directly measure the effective electron neutrino mass by analysing the endpoint region of the ^{163}mathrm {Ho} electron capture spectrum. We present a data reduction scheme for the analysis of high statistics data acquired with the first phase of the ECHo experiment, ECHo-1k, to reliably infer the energy of ^{163}mathrm {Ho} events and discard triggered noise or pile-up events. On a first level, the raw data is filtered purely based on the trigger time information of the acquired signals. On a second level, the time profile of each triggered event is analysed to identify the signals corresponding to a single energy deposition in the detector. We demonstrate that events not belonging to this category are discarded with an efficiency above 99.8%, with a minimal loss of ^{163}mathrm {Ho} events of about 0.7%. While the filter using the trigger time information is completely energy independent, a slight energy dependence of the filter based on the time profile is precisely characterised. This data reduction protocol will be important to minimise systematic errors in the analysis of the ^{163}mathrm {Ho} spectrum for the determination of the effective electron neutrino mass.

Heavy quark jet production near threshold

In this paper, we study the fragmentation of a heavy quark into a jet near threshold, meaning that final state jet carries most of the energy of the fragmenting heavy quark. Using the heavy quark fragmentation function, we simultaneously resum large logarithms of the jet radius R and 1 − z, where z is the ratio of the jet energy to the initiating heavy quark energy. There are numerically significant corrections to the leading order rate due to this resummation. We also investigate the heavy quark fragmentation to a groomed jet, using the soft drop grooming algorithm as an example. In order to do so, we introduce a collinear-ultrasoft mode sensitive to the grooming region determined by the algorithm’s zcut parameter. This allows us to resum large logarithms of zcut/(1 − z), again leading to large numerical corrections near the endpoint. A nice feature of the analysis of the heavy quark fragmenting to a groomed jet is the heavy quark mass m renders the algorithm infrared finite, allowing a perturbative calculation. We analyze this for EJR ∼ m and EJR » m, where EJ is the jet energy. To do the latter case, we introduce an ultracollinear-soft mode, allowing us to resum large logarithms of EJR/m. Finally, as an application we calculate the rate for e+e− collisions to produce a heavy quark jet in the endpoint region, where we show that grooming effects have a sizable contribution near the endpoint.

Next-to-leading-logarithm threshold resummation for exclusive B meson decays

We extend the threshold resummation of the large logarithms ln x which appear in factorization formulas for exclusive B meson decays, x being a spectator momentum fraction, to the next-to-leading-logarithm (NLL) accuracy. It is shown that the NLL resummation effect provides suppression in the end-point region with xsim 0 stronger than the leading-logarithm (LL) one, and thus improves perturbative analyses of the above processes. We revisit the Brightarrow Kpi decays under the NLL resummation in the perturbative QCD approach, and find that it induces up to 20% variation of the direct CP asymmetries in various modes relative to the LL results. Our method to avoid the Landau singularity in the inverse Mellin transformation causes at most 10% theoretical uncertainty.

Precision measurement of the electron energy-loss function in tritium and deuterium gas for the KATRIN experiment

The KATRIN experiment is designed for a direct and model-independent determination of the effective electron anti-neutrino mass via a high-precision measurement of the tritium upbeta -decay endpoint region with a sensitivity on m_nu of 0.2 hbox {eV}/hbox {c}^2 (90% CL). For this purpose, the upbeta -electrons from a high-luminosity windowless gaseous tritium source traversing an electrostatic retarding spectrometer are counted to obtain an integral spectrum around the endpoint energy of 18.6 keV. A dominant systematic effect of the response of the experimental setup is the energy loss of upbeta -electrons from elastic and inelastic scattering off tritium molecules within the source. We determined the energy-loss function in-situ with a pulsed angular-selective and monoenergetic photoelectron source at various tritium-source densities. The data was recorded in integral and differential modes; the latter was achieved by using a novel time-of-flight technique. We developed a semi-empirical parametrization for the energy-loss function for the scattering of 18.6-keV electrons from hydrogen isotopologs. This model was fit to measurement data with a 95% hbox {T}_2 gas mixture at 30 K, as used in the first KATRIN neutrino-mass analyses, as well as a hbox {D}_2 gas mixture of 96% purity used in KATRIN commissioning runs. The achieved precision on the energy-loss function has abated the corresponding uncertainty of sigma (m_nu ^2)< {{10}^{-2}}{hbox {eV}^{2}} [1] in the KATRIN neutrino-mass measurement to a subdominant level.

Study of muon-induced background in MMC detector arrays for the ECHo experiment

For above ground particle physics experiments, cosmic muons are common source of background, not only for direct detector hits, but also for secondary radiation created in neighboring materials. The ECHo experiment has been designed for the determination of the effective electron neutrino mass by the analysis of the endpoint region of the ^{163}text {Ho} electron capture spectrum. The fraction of events occurring in the region of interest of 10 eV below the Q_{mathrm {EC}} value of about 2.8 keV is only of the order of 10^{-9}. This means that the background in that region need to be studied, characterized and methods to suppress it need to be developed. We expect a major background contribution to be due to cosmic muons and radiation produced by muons traveling through material around the detectors. To determine the muon-related background in metallic magnetic calorimeters (MMCs) used in the ECHo experiment, we have performed an experiment in which a muon veto was installed around the cryostat used for the operation of the detectors. We analysed the acquired events to investigate the pulse shape of MMC events in coincidence with the muon veto and the rate of multiple coincidences among detector array pixels. With different methods used for identification of muon related events, we studied events generated by muons and secondary radiation depositing energy in the substrate close to the ECHo pixels. In addition, energy depositions of muons and secondary radiation in the detectors was studied via Monte Carlo simulation. At the present status of investigation, we conclude that muon related events will be a negligible background in the region of interest of the ^{163}text {Ho} spectrum.

Baseline Correction Based on a Search Algorithm from Artificial Intelligence.

Many spectra have a polynomial-like baseline. Iterative polynomial fitting is one of the most popular methods for baseline correction of these spectra. However, the baseline estimated by iterative polynomial fitting may have a substantial error when the spectrum contains significantly strong peaks or have strong peaks located at the endpoints. First, iterative polynomial fitting uses temporary baseline estimated from the current spectrum to identify peak data points. If the current spectrum contains strong peaks, then the temporary baseline substantially deviates from the true baseline. Some good baseline data points of the spectrum might be mistakenly identified as peak data points and are artificially re-assigned with a low value. Second, if a strong peak is located at the endpoint of the spectrum, then the endpoint region of the estimated baseline might have a significant error due to overfitting. This study proposes a search algorithm-based baseline correction method (SA) that aims to compress sample the raw spectrum to a dataset with small number of data points and then convert the peak removal process into solving a search problem in artificial intelligence to minimize an objective function by deleting peak data points. First, the raw spectrum is smoothened out by the moving average method to reduce noise and then divided into dozens of unequally spaced sections on the basis of Chebyshev nodes. Finally, the minimal points of each section are collected to form a dataset for peak removal through search algorithm. SA selects the mean absolute error as the objective function because of its sensitivity to overfitting and rapid calculation. The baseline correction performance of SA is compared with those of three baseline correction methods, the Lieber and Mahadevan-Jansen method, adaptive iteratively reweighted penalized least squares method, and improved asymmetric least squares method. Simulated and real Fourier transform infrared and Raman spectra with polynomial-like baselines are employed in the experiments. Results show that for these spectra the baseline estimated by SA has fewer error than those by the three other methods.

Factorization at subleading power and endpoint divergences in h \u2192 \u03b3\u03b3 decay. Part II. Renormalization and scale evolution

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = mb/Mh « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order {alpha alpha}_s^2{L}^k in the three-loop decay amplitude, where L=ln left(-{M}_h^2/{m}_b^2right) and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms sim {alpha alpha}_s^n{L}^{2n+1} .

Time-focusing time-of-flight, a new method to turn a MAC-E-filter into a quasi-differential spectrometer

Spectrometers based on the magnetic adiabatic collimation followed by an electrostatic filter (MAC-E-filter) principle combine high angular acceptance with an excellent energy resolution. These features make MAC-E-filters very valuable for experiments where the kinetic energy of ions or electrons from rare processes has to be measured with utmost sensitivity and precision. Examples are direct neutrino mass experiments like KATRIN which investigate the energy of electrons in the endpoint region of the tritium beta -spectrum. However, the MAC-E-filter is a very sharp energy high-pass filter but not a differential spectrometer. To determine a spectral shape of a charged particle source, different electric retarding potentials have to be used sequentially, reducing the statistics. In a previous work we have shown that the advantages of the standard MAC-E-filter can be combined with a measurement of the time-of-flight (TOF), allowing to determine spectral information over a certain energy range with one retarding potential only, with the corresponding gain in statistics. This TOF method requires one to know the start time of the charged particles, which is not always possible. Therefore, we propose a new method which does not require the determination of the start time and which we call “time-focusing time-of-flight” (tfTOF): by applying a time dependent acceleration and deceleration potential at a subsequent MAC-E-filter, an energy dependent post-bunching of the charged particles is achieved.