The Gaussian CL _{s} method for searches of new physics
Here we describe a method based on the CL _{s} 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 nonnested 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 CL _{s} method. Our work provides a selfcontained mathematical proof for the Gaussian CL _{s} 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 CL _{s} method in an example of searching for a sterile neutrino, where the CL _{s} approach was rarely used before. We also compare data analysis results produced by the Gaussian CL _{s} method and various CI methods to showcase their differences.
 Authors:

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 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Univ. of Iowa, Iowa City, IA (United States). Dept. of Statistics and Actuarial Science
 Univ. of Illinois, UrbanaChampaign, IL (United States). Dept. of Physics
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Report Number(s):
 BNL1121182016JA
Journal ID: ISSN 01689002; R&D Project: PO022; KA2201020
 Grant/Contract Number:
 SC00112704
 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 01689002
 Publisher:
 Elsevier
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; gaussian; method
 OSTI Identifier:
 1335444
 Alternate Identifier(s):
 OSTI ID: 1359662
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.,
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.. 2016.
"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 nonnested 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 selfcontained 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}
}