Summary of Columbia REU Research. ATLAS: Summer 2014

Transcription

1 Summary of Columbia REU Research ATLAS: Summer 2014 ì 1

2 2 Outline ì Brief Analysis Summary ì Overview of Sta<s<cal Analysis ì Comparisons between the Asympto<cs and the Toys ì Applica<ons for Mass Dependent Cuts

3 3 Quest for the Randall- Sundrum Graviton ì Search for a new RSG par<cle around 1 TeV ì Decay products will become Lorentz boosted causing the standard ΔR = 0.4 jets to overlap ì Move into the boosted regime with the b- quarks from each H contained in a large- R jet with ΔR = 1.0 ΔR = 1.0 b b H RSG H b b ΔR = 1.0

4 4 The Standard Cuts Following are the standard cuts for the analysis now: ì MV1 > 0.70 ì Leading jet p T > 350 GeV ì Subleading jet p T > 250 GeV ì Track jet p T > 20 GeV ì Coupling: c = 2.0

5 5 Hypothesis Testing ì ì Two hypotheses: null hypothesis: H 0, and alterna<ve hypothesis: H 1 Assuming H 0 true, calculate the probability, p, that H 0 is true given the data ì Compare p to the cri<cal value, α (i.e., α = 0.05) ì Two Conclusions: 1. If p < α => reject the H 0 in favor of H 1 2. If p > α => fail to reject H 0

6 6 Choices of the Null Hypothesis ì For Discovery, let H 0 = there is no RSG ì For Limit Se]ng, let H 0 = there is a RSG with signal strength µ and we just missed it. For example: consider a histogram with N bins ν i = b i + µ s i ν i : probability of an event landing in i th bin b i : probability of background event being in i th bin s i : probability of signal event being in i th bin

7 7 Likelihood function ì The number of events in each of the bins follows a Poisson distribu<on ì Independent probabili<es => mul<ply them together ì Nuisance parameters (θ ) : values that have to be derived from the data and are not known a priori

8 8 Motivation for Test Statistic ì Quan<fy the agreement of the null and alterna<ve hypothesis through their ra<o θ : θ that maximizes L for a given µ µ and θ : µ and θ values that together maximize L ì Since mul<plica<on is computa<onally expensive, take the logarithm

9 9 Refining the test statistic ì If μ < 0, this does not support the null hypothesis that there is a signal. ì If μ > μ, this should support our null that we have a signal strength of at least μ.

10 10 Toys Method ì Scan over a range of µ s for each mass point and find the pdfs for H 0 and H 1 and the value ì Find the CL s value for each of these mu scans as CL s = p s /(1- p b ) p s : probability that p b : probability that is greater than is less than ì Determine which corresponds to a CL s of 0.05

11 11 Refining the µ scans ì Increasing the µ makes it harder to observe a value this extreme and decreases the CL s value

12 12 Finding the 95% CL s value ì From these CL s values for all of the µ scans, found the µ corresponding to a CL s = 0.05 ì Con<nued adding µ scans where higher accuracy was desired un<l the error was less than 1%. err = 100% x (µ up - µ low )/(2µ current )

13 13 Brazil Plot from the Toys ì Repeat this procedure for every RSG poten<al mass point that we are considering to find the Brazil plot for the toys Cuts: MV1 > 0.75 c = 1.0

14 14 Brazil Plot from the Asymptotics ì Generate Brazil plots more quickly by using an asympto<c approxima<on allowing us to find the cross sec<on using a formula Cuts: MV1 > 0.75 c = 1.0

15 15 Comparing Asymptotics vs. Toys ì Test how well the asympto<cs approximates the toys by overlaying the plots on previous two slides 25 background events

16 16 Asymptotics vs. Toys ì Compare the toys and asympto<cs for two different MV1 cuts of 0.50 and 0.90 to test if the discrepancy is due to the limited background sta<s<cs in the signal region. 88 background events 18 background events

17 17 Ratio Comparisons ì Appear to follow basically the same trend ì So the discrepancy apparently is not due to the background

18 18 Scaling the signal ì Test if discrepancy is due to small number of expected signal events by scaling the signal by 30.

19 19 Investigating Mass Dependent Cuts ì Test what p T cut we can make on the leading large R jet to maintain 90% efficiency

20 Sensitivity Plots ì Sensi<vity for cuts MV1 = 0.70, track jet p T > 20 GeV 20

21 21 Conclusions: ì The toys appear to do a beler job than the asympto<cs for the signal sample size that we are dealing with, although it may not be possible to use them with all the systema<cs for the analysis. ì Using different cuts for the different RSG masses that we are considering can improve our efficiency substan<ally. ì Many thanks to the Columbia REU program and my supervisor, Dr. Emily Thompson, for providing this summer research opportunity at CERN!

22 22 References ì ì ì G. Cowan, K. Crammer, E. Gross, and O. Vitells, Asympto9c formulae for likelihood- based tests of new physics, European Physical Journal C 71 (2011) 1554, arxiv: [physics.data- an] ATLAS Collabora<on, CMS Collabora<on, and LHC Higgs Combina<on Group, Procedure for the LHC Higgs boson search combina9on in Summer 2011, ATL- PHYS- PUB and CMS NOTE- 2011/005, August 18, ATLAS Collabora<on, \emph{performance of jet substructure techniques for large- R jets in proton- proton collisions at sqrt(s) = 7 TeV using the ATLAS detector}, JHEP 09 (2013) 076, arxiv: [hep- ex].