Boosted W Jets in Electroweak W+W- Decays Joseph Flanigan Department of Physics at University of Wisconsin- Milwaukee; REU at Wayne State University (Dated: August 15, 2012) Abstract Particle accelerators such as the late Tevatron in Batavia, IL. or the LHC in Geneva, Switzerland have been making major contributions to the standard model of particle physics and beyond for decades. With the recent discovery of the Higgs Boson the standard model of particle physics is nearly complete. Scientists everywhere may find themselves wondering what is next for research centers in which many countries are so heavily invested. The answer: intensive research in physics beyond the standard model. Part of this topic includes electroweak decays in which hadronic jets from W-boson decays are merged as a resulted of the boson being boosted.
Introduction: With the standard model of particle physics essentially complete, physics beyond the standard model will become an increasingly popular topic in the near future. Merged jets as a result of boosted boson decays can play a vital role in many topics of particle physics beyond the standard model. Before any intensive research on the subject begins, it is important for researchers to know whether or not boosted jets can be identified and selected in data collected in the Compact Muon Solenoid detector at the Large Hadron Collider. The following experiment analyzed data generated by Monte-Carlo methods as a feasibility study on the matter, then used identical techniques on data from CERN. Merged jets occur in a number of channels and although a fairly good sample can be seen in pure tt-bar samples it is best to analyze whole sets of data from CERN to pick out a greater number of events, and study boosted W-boson decay in more than one channel. The typical case for a boosted Wboson outside of tt-bar events involves an intermediate boson, usually a γ or a Z-boson (see Feynmann diagrams below). Figure 1: In the Feynman diagram to the left, a qq-bar pair eliminate producing a W boson which decays into a lepton and a neutrino, this decay is not boosted and will not produce any jets. In the image to the right, a qq-bar pair eliminate producing an intermediate photon or Z-boson before decaying into a W+/W- pair which produces a lepton, neutrino and qqbar pair. The qq-bar pair hadronizes to produce jets which are merged. Given that merged jets have unique properties, it can be proposed that if cuts are made based on those properties, and a mass distribution is plotted for events in the detector before and after cuts, a peak should be visible at the mass of the W-boson (80 GeV) in the post-cut plot. The trouble is developing a set of cuts that will eliminate backgrounds, but not the signal events. This is why beginning with data generated via Monte-Carlo methods is so important. Signal and background data can be separated, and
distributions of numerous variables that cuts can be made on can be plotted to help determine the properties of merged jets. Process of Analysis: The analysis started with Monte-Carlo data, in the form of several ROOT trees, using only background and signal events, ignoring tt-bar events completely for now. CERN's ROOT program was used with basic C++ programming techniques to sort through the data and plot several variables. For this analysis, only Cambridge-Achen 8 pruned jets were studied (ca8pr), and we selected only class 2 events, or lυj events. These events occur when a jet from a W-boson is formed along with the second boson decaying into a lepton and a neutrino. The variables best suited for cuts were determined to be as follows, note that the variables will be referred to by the abbreviation in parenthesis following the name from here on: 1. Jet Mass (M) 2. Jet transverse momentum (jet PT) 3. W-boson transverse momentum (W PT) 4. Transverse Mass (MT) 5. Missing transverse energy (MET) 6. Lepton Transverse Momentum (Lepton PT) 7. Phi (see illustration on following page for clarification on angles, φ) 8. R (η2 + φ2) 9. Phi Missing Transverse Energy ( φmet) 10. Transverse Momentum Subjet 1 (PT1) 11. Mass Subjet 1 (M1) 12. Mass Subjet 2 (M2) 13. Transverse Momentum Subjet 2 (PT2) 14. Mu (note this is M1/M, μ)
Once these variables were plotted using ROOT, they could be studied and appropriate cuts could be made. Of course it was also quite easy to make cuts based on the current understanding of the properties of W-bosons, and their behavior in certain decays. This allowed an initial set of cuts to made to eliminate some of the background noise right away. Although merged jets share some characteristics with the background, so not all variables yield significant gains in signal. φ η Figure 2: A simple representation of the detector and the angles used to describe the positions of any events within. Based on the current understanding of W-boson decay, the following set of initial cuts was used to created a set of graphs on which further cuts could be made: 1. Jet PT > 200 GeV 2. W PT > 150 GeV 3. MT > 50 GeV 4. MET > 50 GeV 5. Lepton PT > 80 GeV 6. φ > 2.0 radians 7. R > 1.0 radians 8. φmet > 0.4 radians Graphs of these variables can be found at the end of the article. After this initial set of cuts was made, it was important to observe the mass distribution, and distributions of the variables PT1, PT2, and μ (see figures below) so the vital set of cuts that would eliminate a good portion of background could be
made, allowing the peak at 80 GeV to be visible in an updated mass distribution. Once these cuts were determined by simple observation of the distributions, the numbers could be plugged into an if statement inside of a for loop in the program that created the graphs from the ROOT trees. Once the mass distribution was replotted the results could finally be seen. The program would loop through all events in the ROOT trees and select events to be displayed on the histograms based on whether or not they passed the cuts. Figure 3: The mass distribution after the initial set of cuts. The blue is signal events stacked on the background events, in green. Notice how insignificant the amount of signal is in comparison to the background. Figure 4: The distribution of μ normalized to unity. From this distribution it is (hopefully) clear that if a cut were to be made at μ <.25 a good portion of background (green) events could be eliminated while keeping the majority of signal (blue) events.
Figure 5: The distribution of the transverse momentum of sub-jet 2, signal is once again in blue and background is in green. From this image it was determined that the optimal cut for eliminating background and maintaining signal was to be made at Pt2 > 50 GeV. Figure 6: The distribution of the transverse momentum of sub-jet 1, signal in green and background in blue. There is no terribly obvious cut that would effectively eliminate background while maintaining a large portion of signal. The cut was made at Pt1 > 50 GeV, more as a formality than an effective method of background elimination.
The final set of cuts to be made was determined after examination of these graphs. The cuts were to be performed in addition to the initial 8 cuts for a total of 11 cuts. The three additional cuts were: 1. PT1 > 50 GeV 2. PT2 > 50 GeV 3. 0.00 < μ <.25 After these cuts were added into a second if statement in the program's for loop, the following jet mass distribution was the output: Figure 7: The mass distribution after the final set of cuts had been determined and made. Notice the peak at 80 GeV, the mass of the W-boson, and also an improved ratio of signal-to-background. This result was exactly as expected, and provides optimism for the idea that boosted W decays can be observed and selected with ease. The next step in the process was to include tt-bar data, and reduce the number of tt-bar events present in our distributions. Although there is a strong sample of boosted jets in tt-bar data, it is not the type of decay desired in this analysis. TT-Bar events were originally excluded because they are easily suppressed by cuts on two additional variables, and inclusion of tt-bar events in the initial analysis could have proved to be problematic visually. Using a third set of Monte-Carlo generated data
including only tt-bar events the program for event selection was modified, now with 3 separate for loops (one for a tree containing boosted jets, one for a tree containing background, and one for a tree containing only tt-bar.). The same 8 initial cuts and 11 final cuts were used on all three types of events for the sake of consistency, as each variable could only hold one value in either the initial or final sets during analysis of actual data from CERN where one tree contains all three event types. Thus is it important to be sure that one initial and one final set of cuts would provide good results across all three data sets. The additional two cuts, for elimination of tt-bar events, were therefore applied to all three trees as well. The mass distributions obtained from this part of the analysis should very closely resemble the distributions of the actual data from CERN after analysis, showing that the selection technique is valid. The extra variables to be cut on that would eliminate a good portion of tt-bar events, while maintaining signal events were the number of b-tagged AK5 jets outside of the CA8PR jets (BAK5O), and the number of AK5 jets outside of the CA8PR jets (AK5O). BAK5O was held at less than one, while two separate distributions were printed for AK5O one of them being less than one and one of them being less than two. The mass including tt-bar distribution under only our initial set of cuts, followed by the two distributions for the different AK5O cuts are below. Figure 8: The mass distribution after the initial set of cuts. TT-Bar events are in red, notice a more defined bump at 80 GeV
Figure 9: On the left we have the set of cuts B-tagged AK5 outside CA8pr < 1 and AK5 outside CA8pr < 2, on the right AK5 outside CA8pr < 1. Notice that on the right there are significantly less ttbar events (in red), and that the number of important signal events (in blue) is fairly strong. This gives us our final set of cuts that we will then apply to actual data. Note: These results have not yet been weighted to more closely resemble data from CERN. From the images above it was determined that cuts on the variable AK5O should be under 1 jet, as that eliminated more tt-bar events and kept a greater number of signal events. From here the next step was weighting of the above graphs to more closely resemble CERN's data, and finally applying the analysis to actual data from CERN. Weighting the graphs was a simple matter of filling both the pre-cut and post-cut graphs with an extra variable, and was implemented in the analysis program during the same revision that added the data from CERN. Addition of the actual data was simple, just apply the same programming techniques used on the three Monte-Carlo data sets to a ROOT tree containing the data and print the mass distributions of the data over the mass distributions of the Monte-Carlo. Below are the mass distributions provided by this final revision, and the final product of this analysis.
Figure 10: The final pre-cut mass distribution featuring actual data collected by CERN in the CMS detector, and weighted Monte-Carlo data. The data is printed as black crosses. Notice that although the data displays a lower number of events than the Monte-Carlo its shape is virtually the same with a peak at the low end, and a small bump at 80 GeV where the signals of interest lie. Figure 11: The post-cut mass distributions after weighting of Monte-Carlo data and inclusion of actual data collected in the CMS detector at the Large Hadron Collider. The actual data is again featured as black crosses. Although the actual data doesn't follow the same pattern as the Monte-Carlo data there is an obvious peak at 80 GeV. This is a great result, and it shows that boosted W+/W- decays can be isolated and studied.
Conclusions: Results of this analysis were remarkably good, and displayed almost exactly what was expected. Although further adjustments can and should be made, there are conclusions that can be drawn from the results in-hand. The distributions in figures 10 and 11 show that the set of cuts determined in the feasibility study are effective in analyzing actual data. This provides a way of selecting for boosted W decays in data sets where it is otherwise barely visible. The study also provides some insight into the characteristics of such decays. Characteristics of actual boosted W decays in CERN's data sets can be studied with ease, using similar programming techniques, if this set of cuts (or perhaps a to be determined better set of cuts) is used to ensure that a good portion of the events whose characteristics are being studied are actual boosted W decays. Overall the results are very positive, and this leaves future researchers a solid background to perform more in-depth analyses of the subject. In the future it would be simple to perform similar analyses on different jet-trimming algorithms than CA8PR, perhaps something a bit fancier. Of course this analysis should give researchers a basic understanding of how one might search for heavy resonances, for example Higgs greater than 500 GeV. Overall, the study was a success, but there is always room for improvements. The study of physics beyond the standard model will continue for a long time, and analyses such as this are just the beginning.
Resources: [1] K. Krylova, Anomalous Gauge Couplings, http://rhig.physics.wayne.edu/reu/allreports.htm [2] F. Tanedo, When you're a jet you're a jet all the way, http://www.quantumdiaries.org/2011/04/22/when-youre-a-jet-youre-a-jet-all-the-way/ [3] N. Glover, Jets at Hadron Colliders, www.phys.psu.edu/~cteq/schools/summer06/glover/gloverpp.pdf [4] A. Altheimer, G. Brooijmans, Matrix Elements, Parton Showers and Jet Merging: Jet Substructure and New Physics at the LHC, Arxiv: 1109.0030 [5] R.V. Sierra, Searches for Boosted Particles in CMS, https://indico.cern.ch/getfile.py/access? contribid=1&resid=0&materialid=slides&confid=138809