Measurement of the Total Neutrino-nucleon Cross-section with Atmospheric Muon Neutrinos in IceCube

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Book Synopsis Measurement of the Total Neutrino-nucleon Cross-section with Atmospheric Muon Neutrinos in IceCube by : Sarah Caitlin Nowicki

Download or read book Measurement of the Total Neutrino-nucleon Cross-section with Atmospheric Muon Neutrinos in IceCube written by Sarah Caitlin Nowicki and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The discovery of neutrino oscillations, and therefore that they have non-zero mass, provided the first conclusive proof of physics beyond the Standard Model [1]. Recently, neutrinos have become a valuable addition to the field of multi-messenger astrophysics to improve the study of distant astrophysical phenomena [2]. Fundamental to the operation of the numerous current neutrino experiments across a broad energy-scale is knowledge of the neutrino interaction rate or cross-section. In neutrino experiment, there exists a gap in the measurement of the neutrino-nucleon cross-section between approximately 300 GeV and a TeV. In this region, the Standard Model cross- section transitions away from its linear relationship with neutrino energy. This thesis describes a measurement of the total muon-neutrino-nucleon cross-section from 100 GeV to 5 TeV via a flux- dependent analysis performed on a dataset of through-going neutrino-induced muons detected by the IceCube Neutrino Observatory. An updated energy reconstruction utilizing DirectReco, a new method that generates event hypotheses using direct photon propagation, and tailored to the physics of the region of interest is applied. This provides several benefits, including improved accuracy of the event hypotheses and incorporation of the latest models of the glacial detector medium. The cross-section is measured as a normalization of the predicted flux where the parameters are scaling factors on the Standard Model cross-section, the Cooper-Sarkar-Mertsch-Sarkar (CSMS) model [3]. Two bins are defined, 100 - 350 GeV, overlapping with existing data, and 350 GeV - 5 TeV, the unmeasured region of phase space. A prior is calculated from existing accelerator neutrino beam cross-section measurements for the overlapping energy range of 100 - 350 GeV, additional input in constraining the fit for the low-energy region of the sample. The resultant Standard Model cross- section scaling factors are calculated both with the accelerator prior applied (case A) and without (case B). The results are, for 100 - 350 GeV and 350 GeV - 5 TeV regions, respectively, 0.82+0.088́20.07 and 1.23+0.07-0.07 for case A and 0.27+0.07-0.05 and 0.78+0.08-0.07 for case B. This is the world's first measurement for the 350 GeV to 5 TeV energy region of the neutrino-nucleon cross-section, although forthcoming accelerator neutrino experiment FASER? will provide a comparable measurement of the cross-section of this energy range in the near future [4]. Both indicate tension with Standard Model, although interpretation of the result is subtly different for the two cases. Case A is a "best possible" measurement that utilizes the current maximal public knowledge of the cross-section. Case B is an IceCube-data-driven result, relatively free of influences inherent in existing cross-section models. The results presented here set a benchmark for future prospects of improvements and expansion of the IceCube-based cross-section studies -- to higher energies, and to multiple flavours -- and for the broad field.

Earth Versus Neutrinos

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ISBN 13 :
Total Pages : 164 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Earth Versus Neutrinos by : Sandra C. Miarecki

Download or read book Earth Versus Neutrinos written by Sandra C. Miarecki and published by . This book was released on 2016 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The IceCube Neutrino Detector at the South Pole was constructed to measure the flux of high-energy neutrinos and to try to identify their cosmic sources. In addition to these astrophysical neutrinos, IceCube also detects the neutrinos that result from cosmic ray interactions with the atmosphere. These atmospheric neutrinos can be used to measure the total muon neutrino-to-nucleon cross section by measuring neutrino absorption in the Earth. The measurement involves isolating a sample of 10,784 Earth-transiting muons detected by IceCube in its 79-string configuration. The cross-section is determined using a two-dimensional fit in measured muon energy and zenith angle and is presented as a multiple of the Standard Model expectation as calculated by Cooper-Sarkar, Mertsch, and Sarkar in 2011. A multiple of 1.0 would indicate agreement with the Standard Model. The results of this analysis find the multiple to be 1.30 (+0.21 -0.19 statistical) (+0.40 -0.44 systematic) for the neutrino energy range of 6.3 to 980 TeV, which is in agreement with the Standard Model expectation.

Measurement of Atmospheric Muon Neutrino Disappearance with IceCube Using Convolutional Neural Network Reconstructions

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ISBN 13 :
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Book Rating : 4.8/5 (417 download)

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Book Synopsis Measurement of Atmospheric Muon Neutrino Disappearance with IceCube Using Convolutional Neural Network Reconstructions by : Jessie Micallef

Download or read book Measurement of Atmospheric Muon Neutrino Disappearance with IceCube Using Convolutional Neural Network Reconstructions written by Jessie Micallef and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrinos are neutral, fundamental particles that oscillate, or change flavor, while they travel. This phenomenon means that neutrinos deviate from the Standard Model prediction that they are massless, creating an exciting window into physics exploration beyond the Standard Model. Understanding neutrino oscillation and constraining their behavior is crucial to furthering the understanding of these particles and how they fit, or do not fit, into the Standard Model. The IceCube Neutrino Observatory has been detecting neutrinos for more than 10 years, leading to a large sample of atmospheric neutrino data available for studying neutrino oscillations. Reconstructing the neutrino interactions, such as the neutrino's energy and direction, are key to constraining neutrino oscillation. A fast and robust reconstruction method was developed using convolutional neural networks (CNNs) and optimized to reconstruct parameters necessary to both reconstruct and isolate a pure atmospheric neutrino sample using the IceCube detector. This work compares the performance of this reconstruction to the current likelihood-based reconstruction currently used in IceCube. An analysis of the muon neutrino disappearance is then pursued using 9.28 years of neutrino data. The analysis shows competitive projected sensitivity, the ability to account for numerous systematics, and robust recovery of the physics parameters under statistical and systematic variations. While the 9.28 year sample is still under collaboration review, one year of the total data is used to perform a confirmatory study on the CNN reconstruction and sample. The oscillation parameter constraints from this one year analysis are in alignment with past IceCube analyses and other neutrino experiments within one sigma. This opens the pathway to use the CNN reconstruction for future analyses studying low energy neutrinos on IceCube.

First Evidence for Atmospheric Neutrino-induced Cascades with the IceCube Detector

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ISBN 13 :
Total Pages : 388 pages
Book Rating : 4.:/5 (35 download)

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Book Synopsis First Evidence for Atmospheric Neutrino-induced Cascades with the IceCube Detector by : Michelangelo Vincent D'Agostino

Download or read book First Evidence for Atmospheric Neutrino-induced Cascades with the IceCube Detector written by Michelangelo Vincent D'Agostino and published by . This book was released on 2009 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Measuring the Atmospheric Neutrino Oscillation Parameters with Icecube Deepcore

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (138 download)

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Book Synopsis Measuring the Atmospheric Neutrino Oscillation Parameters with Icecube Deepcore by : Kayla Leonard DeHolton

Download or read book Measuring the Atmospheric Neutrino Oscillation Parameters with Icecube Deepcore written by Kayla Leonard DeHolton and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For decades, the Standard Model of Particle Physics has stood the test of time, being one of the most comprehensive and reliable models ever proposed. One of the few exceptions to its robustness was the discovery of neutrino oscillations (and consequently the implication that neutrinos have mass). It is one of the only confirmed pieces of evidence of physics beyond the Standard Model. Since this discovery, there has been a worldwide effort on both the theoretical and experimental fronts to answer many questions that this discovery raised. Many neutrino experiments around the world seek to measure the model parameters that describe these oscillations within the current theoretical 3 neutrino framework. The IceCube Neutrino Observatory is a kilometer-scale detector embedded in the Antarctic ice at the South Pole and detects Cherenkov light produced by neutrinos interacting in the ice. DeepCore is a densely instrumented sub-array within the full detector that observes interactions of atmospheric neutrinos down to 5 GeV. At these energies, Earth-crossing muon neutrinos have a high chance of oscillating to tau neutrinos. DeepCore is able to measure these oscillations with precision comparable to accelerator-based experiments, but it is also complementary to accelerator measurements because it probes longer distance scales and higher energies, peaking above the tau lepton production threshold. This dissertation presents the effort involved in curating one of the largest neutrino oscillation datasets in the world, with over 200,000 events spanning almost 10 years (from April 2012 to January 2022) and a neutrino purity of over 99%. This sample is optimized for performing a measurement of the atmospheric neutrino oscillation parameters. The nearly unprecedented level of statistics also requires unprecedented precision in the treatment of systematic uncertainties. Compared to previous DeepCore analyses, this analysis benefits from improved background rejection, new simulation, a new reconstruction, a new machine learning particle classification algorithm, improved modeling of systematic uncertainties, and more years of data. Given the large number of changes compared to previous analyses, an extensive suite of quality and robustness checks were performed. Even with the extensive testing program, our fit to data informed us that our modeling is not yet on par with the level of statistical precision achieved with the new sample; the goodness-of-fit between our data and simulation yielded a p-value of 0[percent]. At the time of writing, there remains an ongoing effort to improve our models to describe the full dataset. This dissertation includes the unblinded results of an analysis performed with a sub-sample containing 20[percent] of the full dataset.

Measurement of Atmospheric Muon Neutrino Disappearance with IceCube-DeepCore

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Book Synopsis Measurement of Atmospheric Muon Neutrino Disappearance with IceCube-DeepCore by : Matthew Dunkman

Download or read book Measurement of Atmospheric Muon Neutrino Disappearance with IceCube-DeepCore written by Matthew Dunkman and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The measurement of muon neutrino disappearance presentedhere was designed to make use of neutrinos of all flavors,exploiting $\nu_e$ events and more poorly reconstructedcascade-like neutrino events to better constrain systematicuncertainties associated with neutrino fluxes and interactions. Inaccordance with IceCube Collaboration policy, the analysis was developed "blind,'' with reference to Monte Carlo simulations and down-going events where no oscillation signal could be visible. Discrepancies observed in the data when they were examined after theanalysis was finalized led to the conclusion that the cascade-like and intermediate data samples were affected by unexpected systematiceffects, so that their inclusion in the analysis produced substantialbias. This analysis thus relied exclusively on the track-like data sample, while investigations into the nature of these systematic effects continue in preparation for an IceCubejournal article.The best fit and 68% confidence interval from this analysison the two oscillation parameters which drive muon neutrino disappearance are\begin{align*} \sin^2 \theta_{23} &= 0.53_{-0.11}^{+0.07}, \\ \Delta m_{32}^2 / 10^{-3}\mathrm{eV}^2 &= 2.35_{-0.17}^{+0.14},\end{align*}which are compatible and competitive with measurements madeby dedicated beam-line neutrino experiments.

Measurement of the Total Cross Section for Neutrino-nucleon Interactions

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ISBN 13 :
Total Pages : 383 pages
Book Rating : 4.:/5 (828 download)

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Book Synopsis Measurement of the Total Cross Section for Neutrino-nucleon Interactions by : Priscilla Stanton Auchincloss

Download or read book Measurement of the Total Cross Section for Neutrino-nucleon Interactions written by Priscilla Stanton Auchincloss and published by . This book was released on 1987 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Study of Atmospheric Neutrino Oscillation Using the IceCube DeepCore Detector

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ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (99 download)

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Book Synopsis A Study of Atmospheric Neutrino Oscillation Using the IceCube DeepCore Detector by :

Download or read book A Study of Atmospheric Neutrino Oscillation Using the IceCube DeepCore Detector written by and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The IceCube detector at the South Pole is a cubic-kilometer-scale neutrino detector designed to observe TeV-range charged particle secondaries from neutrino interactions, and thus do neutrino astronomy. As a main background to the search for astrophysical point sources of neutrinos, IceCube also observes muons and neutrinos from the atmospheric interactions of cosmic rays. By observing a spectrum of atmospheric neutrinos and comparing it to independent predictions of atmospheric fluxes with and without oscillations, IceCube can test various values of oscillation parameters. Neutrino oscillations have been observed experimentally for several decades; IceCube is the first experiment to extend this measurement to the 10-20 GeV energy range. An initial analysis has established that IceCube can see oscillations using the 79-string detector configuration ("IC79"), which was the first year of data that included the DeepCore detector. As a follow-up, this analysis uses a less restrictive event selection and thus a higher total event count, around 3,000 for one year of data. The fit is a Poisson likelihood fit of a two-dimensional rate histogram, using both oscillated length and observed energy. The arrival zenith angle of the muon is used as a proxy for oscillation length. The error contours are dominated by systematic effects more than by statistical limitations of the data. Major systematics include uncertainties in the atmospheric neutrino flux at high energies and uncertainties in the distribution of the cosmic ray muon background. This analysis was designed to produce limits on the mixing angle &theta23 that are competitive with other current experiments, although this is still uncertain as error analysis work is ongoing. Future work will further refine the event selection and systematic error analysis; the statistical methods and software used here are expected to become the IceCube oscillations standard. This thesis also includes background information about the history of neutrino physics, basics of oscillation formalism, and the IceCube DeepCore detector. A brief chapter is included on the search for a deficit in cosmic ray muons from the direction of the Moon, and the implications of that deficit for the pointing resolution of IceCube.

Neutrino Mass

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Publisher : Springer
ISBN 13 : 3540449019
Total Pages : 0 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Neutrino Mass by : Guido Altarelli

Download or read book Neutrino Mass written by Guido Altarelli and published by Springer. This book was released on 2004-02-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reviews the current state of knowledge of neutrino masses and the related question of neutrino oscillations. After an overview of the theory of neutrino masses and mixings, detailed accounts are given of the laboratory limits on neutrino masses, astrophysical and cosmological constraints on those masses, experimental results on neutrino oscillations, the theoretical interpretation of those results, and theoretical models of neutrino masses and mixings. The book concludes with an examination of the potential of long-baseline experiments. This is an essential reference text for workers in elementary-particle physics, nuclear physics, and astrophysics.

Measurements of the Flavor Composition and Inelasticity Distribution of High-Energy Neutrino Interactions in IceCube

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Total Pages : 184 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Measurements of the Flavor Composition and Inelasticity Distribution of High-Energy Neutrino Interactions in IceCube by : Gary Allen Binder

Download or read book Measurements of the Flavor Composition and Inelasticity Distribution of High-Energy Neutrino Interactions in IceCube written by Gary Allen Binder and published by . This book was released on 2017 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the IceCube Neutrino Observatory, neutrino interactions are observed across a broad energy range extending from ~ 5 GeV to ~ 1 PeV. Above ~ 100 TeV, neutrinos primarily originate from distant astrophysical objects whose identity is yet unknown. At lower energies, most neutrinos result from cosmic-ray interactions in Earth's atmosphere. In this work, two studies of contained neutrino interactions in IceCube are presented. In the first study, three years of IceCube data recorded from May 2010 to May 2013 are analyzed to measure the flavor composition of astrophysical neutrinos in the energy range from 35 TeV to 1.9 PeV. The flavor composition is found to be consistent with the ratio of ~ (1/3 : 1/3 : 1/3) expected from the oscillation of neutrinos produced by complete pion decay in distant astrophysical sources. Limits are placed on non-standard flavor compositions that could arise in exotic physics scenarios. The energy spectrum of astrophysical neutrinos is also measured and is well-described by a falling power law with index 2.6+-0.15. In the second study, five years of IceCube data from May 2011 to May 2016 are analyzed with improved background rejection and event classification techniques, and the inelasticity in charged-current muon neutrino interactions is reconstructed. Improved limits on the flavor composition of astrophysical neutrinos are obtained, and there is consistency with the expected flavor ratio of ~ (1/3 : 1/3 : 1/3). Additionally, the energy spectrum of astrophysical neutrinos is found to be consistent with a power-law with index 2.62+-0.07 in the energy range from 6.6 TeV to 2.2 PeV. Limits are placed on a power-law flux from a second population of astrophysical sources that may explain the harder power-law index of 2.13+-0.13 found in an IceCube analysis of up-going muons at higher energies. The inelasticity distribution of charged-current muon neutrino interactions is also obtained and is found to be consistent with the calculation of Cooper-Sarkar et al. across an energy range from 1 TeV to 100 TeV. The inelasticity distribution can also be used measure the neutrino to antineutrino ratio of the atmospheric neutrino flux. A scaling factor on the muon neutrino to antineutrino flux ratio calculated by Honda et al. is found to be 0.77+0.44-0.25 in the energy range from 770 GeV to 21 TeV. Lastly, the inelasticity distribution can also be used to perform an indirect search for charged-current charm production by neutrinos. Assuming a leading-order calculation of the inelasticity distribution for charm production events, zero charm production can be excluded at 91% confidence level in the energy range from 1.5 TeV to 340 TeV. In the future, it is expected that the techniques developed for this analysis can be applied to search for neutrino interactions beyond the Standard Model in IceCube and next-generation neutrino telescopes.

Total Cross Section Measurements for Muon Neutrino and Antineutrino Charged Current Deep Inelastic Scattering

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ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.:/5 (135 download)

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Book Synopsis Total Cross Section Measurements for Muon Neutrino and Antineutrino Charged Current Deep Inelastic Scattering by : Terrance Foy Eldridge

Download or read book Total Cross Section Measurements for Muon Neutrino and Antineutrino Charged Current Deep Inelastic Scattering written by Terrance Foy Eldridge and published by . This book was released on 1985 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Detection of Atmospheric Muon Neutrinoswith the IceCube 9-String Detector

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ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (727 download)

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Book Synopsis Detection of Atmospheric Muon Neutrinoswith the IceCube 9-String Detector by :

Download or read book Detection of Atmospheric Muon Neutrinoswith the IceCube 9-String Detector written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The IceCube neutrino detector is a cubic kilometer TeV to PeV neutrino detector under construction at the geographic South Pole. The dominant population of neutrinos detected in IceCube is due to meson decay in cosmic-ray air showers. These atmospheric neutrinos are relatively well understood and serve as a calibration and verification tool for the new detector. In 2006, the detector was approximately 10% completed, and we report on data acquired from the detector in this configuration. We observe an atmospheric neutrino signal consistent with expectations, demonstrating that the IceCube detector is capable of identifying neutrino events. In the first 137.4 days of livetime, 234 neutrino candidates were selected with an expectation of 211 ± 76.1(syst.) ± 14.5(stat.) events from atmospheric neutrinos.

Measurement of Neutrino Oscillations in Atmospheric Neutrinos with the IceCube DeepCore Detector

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ISBN 13 :
Total Pages : 130 pages
Book Rating : 4.:/5 (915 download)

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Book Synopsis Measurement of Neutrino Oscillations in Atmospheric Neutrinos with the IceCube DeepCore Detector by :

Download or read book Measurement of Neutrino Oscillations in Atmospheric Neutrinos with the IceCube DeepCore Detector written by and published by . This book was released on 2014 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Atmospheric Muon Neutrino Disappearance Measurement with the MINOS Far Detector

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ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis An Atmospheric Muon Neutrino Disappearance Measurement with the MINOS Far Detector by : Jeremy Peter Gogos

Download or read book An Atmospheric Muon Neutrino Disappearance Measurement with the MINOS Far Detector written by Jeremy Peter Gogos and published by . This book was released on 2007 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Particle Physics Reference Library

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Publisher : Springer Nature
ISBN 13 : 3030353184
Total Pages : 1083 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Particle Physics Reference Library by : Christian W. Fabjan

Download or read book Particle Physics Reference Library written by Christian W. Fabjan and published by Springer Nature. This book was released on 2020 with total page 1083 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second open access volume of the handbook series deals with detectors, large experimental facilities and data handling, both for accelerator and non-accelerator based experiments. It also covers applications in medicine and life sciences. A joint CERN-Springer initiative, the "Particle Physics Reference Library" provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A, B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open access

Neutrino-nucleon Cross Section Measurements in NOMAD.

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ISBN 13 : 9781109840711
Total Pages : 128 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Neutrino-nucleon Cross Section Measurements in NOMAD. by : Qun Wu

Download or read book Neutrino-nucleon Cross Section Measurements in NOMAD. written by Qun Wu and published by . This book was released on 2006 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NOMAD (Neutrino Oscillation MAgnetic Detector) experiment, using the SPS (Super Proton Syncrotron) neutrino beam (1 GeV

MEASUREMENT OF ATMOSPHERIC TAU NEUTRINO APPEARANCE WITH ICECUBE/DEEPCORE.

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Book Synopsis MEASUREMENT OF ATMOSPHERIC TAU NEUTRINO APPEARANCE WITH ICECUBE/DEEPCORE. by : Feifei Huang

Download or read book MEASUREMENT OF ATMOSPHERIC TAU NEUTRINO APPEARANCE WITH ICECUBE/DEEPCORE. written by Feifei Huang and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: IceCube is a neutrino detector located inside a cubic kilometer of ice at the South Pole. Its geometry design makes it able to measure neutrinos in a large energy range from as low as 5~GeV up to a few PeV. The low energy subarray DeepCore can measure neutrinos as low as 5 GeV to roughly 100~GeV.This dissertation presented a measurement of atmospheric tau neutrino appearance with three years of IceCube/DeepCore data.The key physics parameter is $\nu_\tau~\rm{(CC+NC)\ normalization}$, a scale factor assigned to the signal $\nu_\tau$ (CC+NC) events, varying between 0 and 1, where the value of one corresponds to the expected rate assuming the standard three-flavor neutrino oscillations.The best fit $\nu_\tau~\rm{(CC+NC)\ normalization}$ was 0.59 with the $68\%$ C.I. in [0.34, 0.90], $\it{i.e.}$, $0.59_{-0.25}^{+0.31}$. The 90\% C.I. was [0.18, 1.12]. This corresponds to 1379 $\nu_\tau$ events out of a total of 40,959 events (which includes 39,070 all-neutrino-flavor events and 1,889 atmospheric muons).To compare with two previous experiments, the measurement of $\rm{\nu_{\tau}~CC}$ normalization was also conducted, where a scale factor $\nu_\tau \ \rm{CC\ normalization}$ is assigned to the signal $\nu_\tau$ CC-only events. The best fit $\nu_\tau \ \rm{CC\ normalization}$ was 0.43, with the 68\% C.I. being [0.12, 0.80], $\it{i.e.}$, $0.43_{-0.43}^{+0.36}$, and the $90\%$ C.I. was [0, 1.07]. Both the measured $\nu_\tau~\rm{(CC+NC)\ normalization}$ and $\nu_\tau \ \rm{CC\ normalization}$ are consistent with existing measurements and the standard three-flavor oscillation paradigm at 90\% C.L.