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Title: The Gaussian CLs method for searches of new physics

Abstract

Here we describe a method based on the CLs approach to present results in searches of new physics, under the condition that the relevant parameter space is continuous. Our method relies on a class of test statistics developed for non-nested hypotheses testing problems, denoted by ΔT, which has a Gaussian approximation to its parent distribution when the sample size is large. This leads to a simple procedure of forming exclusion sets for the parameters of interest, which we call the Gaussian CLs method. Our work provides a self-contained mathematical proof for the Gaussian CLs method, that explicitly outlines the required conditions. These conditions are milder than that required by the Wilks' theorem to set confidence intervals (CIs). We illustrate the Gaussian CLs method in an example of searching for a sterile neutrino, where the CLs approach was rarely used before. We also compare data analysis results produced by the Gaussian CLs method and various CI methods to showcase their differences.

Authors:
 [1];  [2];  [3];  [4];  [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. Univ. of Iowa, Iowa City, IA (United States). Dept. of Statistics and Actuarial Science
  3. Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Physics
  4. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1335444
Alternate Identifier(s):
OSTI ID: 1359662
Report Number(s):
BNL-112118-2016-JA
Journal ID: ISSN 0168-9002; R&D Project: PO-022; KA2201020
Grant/Contract Number:  
SC00112704
Resource Type:
Accepted Manuscript
Journal Name:
Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment
Additional Journal Information:
Journal Volume: 827; Journal Issue: C; Journal ID: ISSN 0168-9002
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; gaussian; method

Citation Formats

Qian, X., Tan, A., Ling, J. J., Nakajima, Y., and Zhang, C. The Gaussian CLs method for searches of new physics. United States: N. p., 2016. Web. doi:10.1016/j.nima.2016.04.089.
Qian, X., Tan, A., Ling, J. J., Nakajima, Y., & Zhang, C. The Gaussian CLs method for searches of new physics. United States. doi:10.1016/j.nima.2016.04.089.
Qian, X., Tan, A., Ling, J. J., Nakajima, Y., and Zhang, C. Sat . "The Gaussian CLs method for searches of new physics". United States. doi:10.1016/j.nima.2016.04.089. https://www.osti.gov/servlets/purl/1335444.
@article{osti_1335444,
title = {The Gaussian CLs method for searches of new physics},
author = {Qian, X. and Tan, A. and Ling, J. J. and Nakajima, Y. and Zhang, C.},
abstractNote = {Here we describe a method based on the CLs approach to present results in searches of new physics, under the condition that the relevant parameter space is continuous. Our method relies on a class of test statistics developed for non-nested hypotheses testing problems, denoted by ΔT, which has a Gaussian approximation to its parent distribution when the sample size is large. This leads to a simple procedure of forming exclusion sets for the parameters of interest, which we call the Gaussian CLs method. Our work provides a self-contained mathematical proof for the Gaussian CLs method, that explicitly outlines the required conditions. These conditions are milder than that required by the Wilks' theorem to set confidence intervals (CIs). We illustrate the Gaussian CLs method in an example of searching for a sterile neutrino, where the CLs approach was rarely used before. We also compare data analysis results produced by the Gaussian CLs method and various CI methods to showcase their differences.},
doi = {10.1016/j.nima.2016.04.089},
journal = {Nuclear Instruments and Methods in Physics Research. Section A, Accelerators, Spectrometers, Detectors and Associated Equipment},
number = C,
volume = 827,
place = {United States},
year = {2016},
month = {4}
}

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