The Energy Scale of the Pierre Auger Observatory

A method is suggested to decompose the statistical and systematic uncertainties from the residues between the calculation of a theoretical model and the observed data. The residues and the parameters of the model can be obtained through the standard statistical fitting procedures. The present work concentrates on the decomposition of the total uncertainty, of which the distribution corresponds to that of the residues. The distribution of the total uncertainty is considered as two normal distributions, statistical and systematic uncertainties. The standard deviation of the statistical part, ${\ensuremath{\sigma}}_{\mathrm{stat}}$, is estimated through random parameters distributed around their best fitted values. The two normal distributions are obtained by minimizing the moments of the distribution of the residues with the fixed ${\ensuremath{\sigma}}_{\mathrm{stat}}$. The method is applied to the liquid drop model (LD). The statistical and systematic uncertainties are decomposed from the residues of the nuclear binding energies with and without the consideration of the shell effect in LD. The estimated distributions of the statistical and systematic uncertainties can well describe that of the residues. The normal assumption of the distribution of the statistical and systematic uncertainties is examined through various approaches. The comparison between the distributions of the specific nuclei and those of the statistical and systematic uncertainties are consistent with the physical considerations, although the latter two can be obtained without the knowledge of these considerations. Such as, the LD are more suitable to describe the heavy nuclei. The light and heavy nuclei are indeed distributed mostly inside the distributions of the systematic and statistical uncertainties, respectively. A similar situation is also found for the nuclei close to and far from shell. The present method is also performed for nuclei around the stability line. The results are used to investigate all measured nuclei, which show the usefulness of the uncertainty decomposition method in the exploration of the unmeasured nuclei.

The Telescope Array experiment is the largest hybrid detector to observe ultra‐high energy cosmic rays in the northern hemisphere. The observation started in November 2007 for Fluorescence Detector (FD) and in March 2008 for Surface Detectors (SD). The hybrid events which are detected both by SD and FD have good performance not only to compare the reconstructed energy scales between SD and FD but also to measure the energy spectrum. Here, we present the preliminary results of the energy spectrum with energies above 1018.7 eV measured by hybrid events from TA 1.5‐year observation. To carry out this study, the method of the hybrid analysis, in which the timing of SD data is applied to FD monocular reconstruction, is developed. The angular resolution is less than 1.1 degrees and the energy resolution is less than 8% above 1018.7 eV. The systematic uncertainty to determine the energy is estimated to be 19%. The main contributions are the detector calibration (10%), atmospheric correction (11%) and fluorescence yield (12%). The obtained energy spectrum is consistent with the result of HiRes within the systematic uncertainty.

The Telescope Array experiment (TA) is the largest cosmic-ray detector in the northern hemi- sphere and consists of a surface detector (SD) array, plus three fluorescence detector (FD) stations overlooking the SD. The large field-of-view of an FD allows for reconstruction of the air-shower development in the atmosphere by imaging ultra-violet fluorescence light from atmospheric nitrogen excited by UHECRs. In estimation of the primary energy it is necessary to add to the calorimetric energy observed by the FD a “missing energy”, meaning the fraction of the primary energy that is not deposited by charged particles in the air. We report on the measurement of the missing energy from observed data collected by the TA FD and TA SD, independently of Monte Carlo simulations, using a technique pioneered by the Pierre Auger Observatory. We also address the effect on the energy scale attributed to fluorescence yield parameters.

At the annual general meeting of the International Committee for Radionuclide Metrology (ICRM) held last June at the Physikalisch-Technische Bundesanstalt, it was suggested that letters should be sent to the editors of journals that publish nucleardecay data, drawing attention to the need for specific statements of the uncertainties that are associated with such data. Authors frequently fail to state clearly the nature of their estimates of uncertainty, and not all editors insist on such clarity, so that evaluators of nuclear-decay data often f'md that it is necessary to consult with the individual authors to arrive at the weighting factors appropriate to their data. If uncertainties could be dearly characterized in the abstracts or in the text of papers reporthag values of nuclear parameters, there would be a corresponding shortening of the time required for the data to be evaluated and tabulated. There are many methods of stating estimates of conventional random and systematic uncertainties that are acceptable, provided that the methods used are described. Thus random error may be stated as: (i) the estimate of the standard deviation (or the square root of the variance), which is in the same units as the observed data and indicates the order of magnitude of the spread of the data: (ii) the standard error (or the estimated standard deviation of the mean of the distribution); and (ri) the estimated limits for the mean at stated levels of confidence (C1) (e.g. limits at the 99-percent CI define the range within which there is a 99:percent probability of ineluding the mean of a population). Provided that the author states the number of independent measurements made of the given parameter, or the number of degrees of freedom, these statements of random uncertainty are related uniquely to each other. The other component of the overall uncertainty is the estimate of possible systematic error. The significance, or meaning, of the estimate of systematic uncertainties should be dearly stated and also related to the method chosen to state the random uncertainties. Thus an estimate of maximum conceivable systematic uncertainties would logically be combined with a random uncertainty at a 99-percent confidence level. An appropriate fraction of the estimate of maximum conceivable systematic uncertainty would be chose to match smaller random confidence levels. The methods used to combine random and systematic uncertainties should also be stated by authors, and an explicit listing of all components of these uncertainties will allow an evaluator of nuclear data to "unravel" the statements of uncertainty and to choose

Nuclear-decay data: The statement of uncertainties

Nuclear-decay data: The statement of uncertainties

Nuclear-decay data: The statement of uncertainties

The Pierre Auger Observatory’s Fluorescence Detector (FD) consists of 27 telescopes arranged in four sites around the perimeter of the 3000 square kilometre Surface Detector (SD). Cosmic ray extensive air showers are viewed via the nitrogen fluorescence light they induce in the atmosphere. Careful treatment of light attenuation processes must be made, especially given that some showers are viewed at distances in excess of 30 km. Of particular importance is the attenuation due to scattering by aerosol particles, a challenging topic given that aerosol concentrations can vary on time-scales of hours. At the Auger Observatory, the vertical distribution of aerosols is measured hourly with a series of bi-static lidar systems (consisting of central laser facilities and each of the FD sites), and three times per night with a Raman lidar system. In this contribution we describe the use of aerosol profiles in the analysis of air shower data, in particular in the estimation of the cosmic ray primary energy, and the depth of shower maximum, Xmax. We also demonstrate how statistical and systematic uncertainties in the aerosol concentrations propagate through to a contribution to energy and Xmax uncertainties.

This paper discusses the effect of statistical uncertainties present in Monte Carlo (MC) calculated dose distributions on the evaluation of a ‘cost function’ that expresses the suitability of a treatment plan for the intended treatment. The mathematical derivations given are valid for any ‘well-behaved’ cost function. The validity of the general expressions is demonstrated using numerical examples. It is shown that random dose uncertainties lead to statistical and systematic uncertainties on the cost function. The balance between the two types of uncertainty and the desired accuracy on the cost function presents a clear criterion for the maximum acceptable MC dose uncertainties. It is demonstrated that it is possible to remove the systematic cost function uncertainty. Finally, it is shown that when the dose distribution is close to a true optimum, MC calculations of the cost function converge to the true result as one over the number of particles simulated, i. e. much faster than the individual dose uncertainties.

At the annual general meeting of the International Committee for Radionuclide Metrology (ICRM) held last June at the Physikalisch-Technische Bundesanstalt, it was suggested that letters should be sent to the editors of journals that publish nucleardecay data, drawing attention to the need for specific statements of the uncertainties that are associated with such data. Authors frequently fail to state clearly the nature of their estimates of uncertainty, and not all editors insist on such clarity, so that evaluators of nuclear-decay data often f'md that it is necessary to consult with the individual authors to arrive at the weighting factors appropriate to their data. If uncertainties could be dearly characterized in the abstracts or in the text of papers reporthag values of nuclear parameters, there would be a corresponding shortening of the time required for the data to be evaluated and tabulated. There are many methods of stating estimates of conventional random and systematic uncertainties that are acceptable, provided that the methods used are described. Thus random error may be stated as: (i) the estimate of the standard deviation (or the square root of the variance), which is in the same units as the observed data and indicates the order of magnitude of the spread of the data: (ii) the standard error (or the estimated standard deviation of the mean of the distribution); and (ri) the estimated limits for the mean at stated levels of confidence (C1) (e.g. limits at the 99-percent CI define the range within which there is a 99:percent probability of ineluding the mean of a population). Provided that the author states the number of independent measurements made of the given parameter, or the number of degrees of freedom, these statements of random uncertainty are related uniquely to each other. The other component of the overall uncertainty is the estimate of possible systematic error. The significance, or meaning, of the estimate of systematic uncertainties should be dearly stated and also related to the method chosen to state the random uncertainties. Thus an estimate of maximum conceivable systematic uncertainties would logically be combined with a random uncertainty at a 99-percent confidence level. An appropriate fraction of the estimate of maximum conceivable systematic uncertainty would be chose to match smaller random confidence levels. The methods used to combine random and systematic uncertainties should also be stated by authors, and an explicit listing of all components of these uncertainties will allow an evaluator of nuclear data to unravel the statements of uncertainty and to choose

Theoretical uncertainties in the predictions of inner fission barrier heights in superheavy elements have been investigated in a systematic way for a set of state-of-the-art covariant energy density functionals which represent major classes of the functionals used in covariant density functional theory. They differ in basic model assumptions and fitting protocols. Both systematic and statistical uncertainties have been quantified where the former turn out to be larger. Systematic uncertainties are substantial in superheavy elements and their behavior as a function of proton and neutron numbers contains a large random component. The benchmarking of the functionals to the experimental data on fission barriers in the actinides allows to reduce the systematic theoretical uncertainties for the inner fission barriers of unknown superheavy elements. However, even then they on average increase on moving away from the region where benchmarking has been performed. In addition, a comparison with the results of non-relativistic approaches is performed in order to define full systematic theoretical uncertainties over the state-of-the-art models. Even for the models benchmarked in the actinides, the difference in the inner fission barrier height of some superheavy elements reaches $5-6$ MeV. This uncertainty in the fission barrier heights will translate into huge (many tens of the orders of magnitude) uncertainties in the spontaneous fission half-lives.

In the present work, the authors propose a standard analytical method to estimate systematic uncertainties in the Monte Carlo particle transport simulation based on analysis of variance (ANOVA). As sample problems, two sets of neutron-shielding calculations for evaluating effective dose were performed using the Particle and Heavy Ion Transport code System coupled with ANOVA. In the simulation, we selected the total cross section and the water density in material as unclear physical quantities to induce systematic uncertainties. Systematic and statistical uncertainties were evaluated by changing the number of simulation conditions and trials per condition, where each condition is associated with one set of unclear quantities. Then, we analyzed the dependence of convergence of the systematic uncertainties on the number of conditions and trials. The analysis results show that simulations with only three conditions are adequate in the case where variations in the conditions have a monotonic effect on the calculation results, while more than 100 conditions are required in the other cases. In addition, we propose a useful criterion to determine the appropriate number of trials for converging systematic uncertainties.

The Telescope Array (TA) experiment is world's first and only air shower detector to be directly calibrated by an on-site accelerator beam. For wider and deeper understanding of cosmic rays via high precision measurements, we have several future plans for TA experiment. The first extension plan is an on-going project, called as TA low energy extension (TALE), to extend sensitive energy range to 10 16.5 eV in order to study second knee, predicted galactic-extragalactic transition of dominant sources and air shower phenomena comparing with LHC measurements. The second proposition is exchanges of FDs and SDs between TA and Pierre Auger Observatory, toward understanding systematic uncertainties of these experiments and to solve discrepancies in energy scales and Xmax. The third plan is a huge air shower array, the world observatory, consisting of a huge number of SDs and/or FDs for world's largest exposure and finest accuracy to open a new window on astronomy with ultra high energy particles. surface detectors (SDs) arrayed with a spacing of 1.2km between each SD in an area of approximately 680km 2 , and air fluorescence detectors (FDs) in three stations located around SDs facing inward and looking over array. The full operation of detectors have been started in March 2008. In TA experiment we have most valuable calibration facility which is a electron linear accelerator, called Electron Light Source (ELS) (2). ELS installed 100m away from south-east FD station (called BRM station) shoots calibrated electron beams for FDs. The typical energy per electron and number of electrons are 40MeV and 10 9 , respectively. With this equipment we will achieve an end to end calibration for FDs. After four years of very stable operations, we have successfully released our results in this conference, although some of these are still preliminary. The results are briefly summarized as follows: The energy spectrum has a clear ankle at 10 18.7 eV and a sharp cutoff above 10 19.7 eV. The flux is consistent with HiRes result. The shape of spectrum curve, it means spectral indexes and break points on curve, are fitted to spectrum curves by HiRes and that by Auger, However, to fit our curve with that by Auger we need to shift primary energies about 20%. Our preliminary results of mass composition analyses, which are averaged Xmax and their distributions, show that protons dominate primary composition of observed showers. This preliminary conclusion contradicts Auger's results (3), which show a transition of dominant composition from light to heavy, derived from averaged Xmax values and their distributions. From arrival direction distribution analyses, we do not observe

The measurement of the top-antitop pair production cross section in p{bar p} collisions at {radical}s = 1.96 TeV in the dielectron decay channel using 384 pb{sup -1} of D0 data yields a t{bar t} production cross-section of {sigma}{sub t{bar t}} = 7.9{sub -3.8}{sup +5.2}(stat){sub -1.0}{sup +1.3}(syst) {+-} 0.5 (lumi) pb. This measurement [98] is based on 5 observed events with a prediction of 1.04 background events. The cross-section corresponds to the top mass of 175 GeV, and is in good agreement with the Standard Model expectation of 6.77 {+-} 0.42 pb based on next-to-next-leading-order (NNLO) perturbative QCD calculations [78]. This analysis shows significant improvement from our previous cross-section measurement in this channel [93] with 230 pb{sup -1} dataset in terms of significantly better signal to background ratio and uncertainties on the measured cross-section. Combination of all the dilepton final states [98] yields a yields a t{bar t} cross-section of {sigma}{sub t{bar t}} = 8.6{sub -2.0}{sup +2.3}(stat){sub -1.0}{sup +1.2}(syst) {+-} 0.6(lumi) pb, which again is in good agreement with theoretical predictions and with measurements in other final states. Hence, these results show no discernible deviation from the Standard Model. Fig. 6.1 shows the summary of cross-section measurements in different final states by the D0 in Run II. This measurement of cross-section in the dilepton channels is the best dilepton result from D0 till date. Previous D0 result based on analysis of 230 pb{sup -1} of data (currently under publication in Physics Letters B) is {sigma}{sub t{bar t}} = 8.6{sub -2.7}{sup +3.2}(stat){sub -1.1}{sup +1.1}(syst) {+-} 0.6(lumi) pb. It can be seen that the present cross-section suffers from less statistical uncertainty. This result is also quite consistent with CDF collaboration's result of {sigma}{sub t{bar t}} = 8.6{sub -2.4}{sup +2.5}(stat){sub -1.1}{sup +1.1}(syst) pb. These results have been presented as D0's preliminary results in the high energy physics conferences in the Summer of 2005 (Hadron Collider Physics Symposium, European Physical Society Conference, etc.). The uncertainty on the cross-section is still dominated by statistics due to the small number of observed events. It can be seen that we are at a level where statistical uncertainties are becoming closer to the systematic ones. Future measurements of the cross section will benefit from considerably more integrated luminosity, leading to a smaller statistical error. Thus the next generation of measurements will be limited by systematic uncertainties. Monte Carlo samples with higher statistics are also being generated in order to decrease the uncertainty on the background estimation. In addition, as the jet energy scale, the electron energy scale, the detector resolutions, and the luminosity measurement are fine-tuned, the systematic uncertainties will continue to decrease.

We analyze the low-energy nucleon–nucleon (NN) interaction by confronting statistical versus systematic uncertainties. This is carried out with the help of model potentials fitted to the Granada-2013 database where a statistically meaningful partial wave analysis comprising a total of 6713 np and pp published scattering data below 350 MeV from 1950 till 2013 has been made. We extract threshold parameter uncertainties from the coupled-channel effective range expansion up to . We find that for threshold parameters systematic uncertainties are generally at least an order of magnitude larger than statistical uncertainties. Similar results are found for np phase shifts and amplitude parameters.