1. JET CHARGE AT LHC Scott Lieberman New Jersey Institute of Technology TUNL REU 2013 Duke High Energy Physics Group Working with: Professor Ayana Arce Dave Bjergaard

2. Outline The detector Jets and Jet Charge Unfolding and Inverse Problems Unfolding of Jet Charge 2

3. The ATLAS Detector 3

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5. What is a Jet? Jets are only meaningful once you have a “jet definition” Jets are as close as we can get to a physical single hard quark or gluon (Salam, “Jets in QCD, an Introduction”) 5

6. Jet Definition/Algorithm A jet definition is a systematic procedure that projects away the multiparticle dynamics, so as to leave a simple picture of what happened in an event (Salam) 6

7. Sequential Recombination 7 (Salam)

8. Sequential Recombination 8 (Salam)

9. Sequential Recombination 9 (Salam)

10. Sequential Recombination 10 (Salam)

11. Sequential Recombination 11 (Salam)

12. Sequential Recombination 12 (Salam)

13. Feynman Diagram for W Jet p+p → W + + q + x μ + + υ 13

14. Jet Charge Put in words, it’s the sum of the charge of the constituent particles weighted by the particle's transverse momentum. (Bjergaard) Krohn et al., “Jet Charge at the LHC”, June 2013, 14

15. Unfolding and Inverse Problems Easy to take pdf or “ideal” data and add smearing and probabilistic effects Ex. A delta function becomes a Gaussian Preferred Method – Unfolding should be avoided if possible Compare models by smearing truth data and comparing to measured data 15

16. A Simple Unfolding Method y=Ax where x is the truth data and y is measured A is the “response matrix” which shows the probability for data to shift from each and to each bin Obtained by Monte Carlo simulations of data and assumptions about the smearing So A -1 y=A -1 Ax=x, the original distribution 16

17. The Problem with Inversion But Unfolding (deconvolution) with the inverse transition is a complex mathematical operation (ill-posed problem, instability of solution) and requires a good understanding of the detector. Straightforward methods can result in solutions which look chaotic. Alternative home-made methods usually produce biased results. (Blobel) Small eigenvalues don’t converge and cause oscillations in the solutions. Matrix inversion only works with very symmetrical, simple problems. 17

18. Detector Response 18

19. Blobel (DESY) 19

20. Other Methods Least Squares Regression Gauss-Markov theorem: least square estimate is unbiased and efficient But result will often show large fluctuations inherent to the problem Diagonalization with eigenvalue truncation Only sum over the larger, significant eigenvalues Issue: truncation causes covariance matrix of result x to be singular Regularization Methods Incorporate certain a-priori assumptions about the size and/or smoothness of the solution!); control the norm of the residuals and, simultaneously, the norm of the solution x 20

21. D’Agostini: Iterative Bayesian Unfolding Twenty iterations with smoothing (D’Agostini, “Improved iterative Bayesian unfolding”) 21

22. Why Unfold Jet Charge Bias in the jet charge equation that shifts results negative Individual peaks of charge 1/3, 2/3 are obscured by detector effects and fragmentation effects By Unfolding, we can: Experimentally determine the charge of quarks and bosons (which produce quarks in certain interactions) Use charge to help identify different particles (W bosons) Utilize conservation of charge more effectively in particle collisions, including the search for new particles 22

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