Skip to main content

Advertisement

Log in

On a χ2-function with Previously Estimated Background

  • Particles and Fields
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

There are intensive efforts searching for new phenomena in many present and future scientific experiments such as LHC at CERN, CLIC, ILC and many others. These new signals are usually rare and frequently contaminated by many different background events. Starting from the concept of profile likelihood, we obtain what can be called a profile χ2-function for counting experiments which has no background parameters to be fitted. Signal and background statistical fluctuations are automatically taking into account even when the content of some bins is zero. This paper analyzes the profile χ2-function for fitting binned data in counting experiment when signal and background events obey Poisson statistics. The background events are estimated previously, by either Monte Carlo events, “idle” run events, or any other reasonable way. The here studied method applies only when the background and signal are completely independent events, i.e., they are non-coherent events. The profile χ2-function has shown to have a fast convergence, with fewer events, to the “true” values for counting experiments as shown in MC toy tests. It works properly even when the bin contents are low and also when the signal to background ratio is small. Other interesting points are also presented and discussed. One of them is that the background parameter does not need to be estimated with very high precision even when there are few signal events during a fitting procedure. An application to Higgs boson discovery is discussed using previously published ATLAS/LHC experiment data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. G.W. Phillips, . Nucl. Instrum.Meth. Phys. Res. A153, 449 (1978)

    Article  ADS  Google Scholar 

  2. T. Awaya, . Nucl. Instrum.Meth. Phys. Res. A165, 317 (1979)

    Article  ADS  Google Scholar 

  3. S. Baker, R.D. Cousins, . Nucl. Instrum.Meth. Phys. Res. A221, 437 (1984)

    Article  ADS  Google Scholar 

  4. F.M.L. Almeida, M. Barbi, M.A.B. do Vale, . Nucl. Instrum.Meth. Phys. Res. A449, 383 (2000)

    Article  ADS  Google Scholar 

  5. W.A. Rolke, A.M. Lopez, . Nucl. Instrum. Meth. Phys. Res. A458, 745 (2001)

    Article  ADS  Google Scholar 

  6. W.A. Rolke, A.M. Lopez, J. Conrad, . Nucl. Instrum. Meth. Phys. Res. A551, 493 (2005)

    Article  ADS  Google Scholar 

  7. W.T. Eadie, D. Drijard, F.E. James, M. Ross, B. Sadoulet. Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971)

    Google Scholar 

  8. D.G. Papegeorgiou, I.N. Demetropoulos, I.E. Lagaris, . Comput. Phys. Commun. 109, 227 (1998)

    Article  ADS  Google Scholar 

  9. S.A. Murphy, W. Van Der Vaart, . J. Am. Stat. Assoc. 95, 459 (2000)

    Google Scholar 

  10. C. Amster, et al., (Particle Data Group) Phys. Lett. B667, 1 (2008)

    ADS  Google Scholar 

  11. G. Aad, et al., Phys. Lett. B716, 1 (2012)

    Article  ADS  Google Scholar 

Download references

Funding

This work was partially supported by National Council for Scientific and Technological Development (CNPq) under grant 402846/2016-8

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. A. Nepomuceno.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Almeida, F.M.L., Nepomuceno, A.A. On a χ2-function with Previously Estimated Background. Braz J Phys 50, 471–479 (2020). https://doi.org/10.1007/s13538-020-00760-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-020-00760-z

Keywords

Navigation