[Statistics] b' quarks decaying to b quark and Higgs boson in LHC data

[**:house: Home**](https://hackmd.io/s/rkkDP_l4M) | [:boy: **About**](https://hackmd.io/s/B149Z8v7b) | [**:microscope: Researches**](https://hackmd.io/s/rJPFNKlVz) | [**:rocket: Side projects**](https://hackmd.io/s/H1aS2qe4G) | [**:airplane: Life gallery**](https://hackmd.io/s/HJN4JslNM) [Journal Publication](https://hackmd.io/s/rJPFNKlVz#journal-publication) **>** [Particle search] b' quarks decaying to b quark and Higgs boson in LHC data --- # [Statistics] b' quarks decaying to b quark and Higgs boson in LHC data <div style="text-align: center;" markdown="1"><a href="http://dx.doi.org/10.1103/PhysRevD.93.112009">Phys. Rev. D 93 (2016) 112009</a></div> *"Search for pair-produced vector-like quarks of charge -1/3 decaying to bH using boosted Higgs jet-tagging in pp collisions at sqrt(s) = 8 TeV"* *<div style="text-align: center;" markdown="1">`upper limit` `background model` `Monte Carol` `big data` `statistics`</div>* ## Introduction The data analysis is for searching new pair-produced particles from proton-proton collision data collected by the CMS detector at CERN-LHC. The new particle is called vector-like quark (right- and left-chirality symmetry) with bottom flavor ($\text{b}'$), which is expected to be a possible mechanism to explain the difference mass of the fundamental particles. Since the several data analysis results show the possible mass is out of the $800\,\text{GeV}$, this research focus on the boosted energy scale. In this research we focus on $\text{b}'$s decays: a bottom quark ($\text{b}$), which is clustered a ***jet*** in data, and a Higgs boson ($\text{H}$). Since the $\text{b}'$ is predicted to be a massive particle, the event (data) containing it is extremely rare, e.g. one of millions events. The background noise becomes the major challenge in this data analysis. Thus, the **background estimation** play the important roles. Since the mass of $\text{b}'$ is unknown, the mass can be pushed to any high scale, e.g. TeV. The $\text{H}$ is expected to become boosted and decaying to $\text{b}\bar{\text{b}}$-quark pair. The $\text{b}\bar{\text{b}}$ pair will merge a *fat jet* with a big cone shape, i.e. it also presents a single $\text{H}$ jet. Thus, the another important feature of this analysis is the feature extraction (identification) of the boosted $\text{H}$ jet. The overall topologies of physics is as $$ \text{pp}\to\text{b'}\bar{\text{b'}}\to \text{bH}\bar{\text{b}}\text{X} \to \text{bb}\bar{\text{b}}\bar{\text{b}}\text{X}\ , $$ where $X$ can be any vector boson, i.e. $\text{W}^-$, $\text{W}^+$, $\text{Z}$ or $\text{H}$. One of possible final state of the new physics can be illustrated as <div style="text-align: center;" markdown="1"><img src="http://hep1.phys.ntu.edu.tw/~alpha78718/cv/bprimetobH.png" height="300" ></div> ## Techniques #### 1. Data selection & feature selection The data are recorded by several layer of detector and stored with electronic digits. The quality of data depends on the data taking processes and the reconstruction algorithm. The data must be filtered according to the condition of each processes, e.g. data taking trigger, particle track algorithm, vertex algorithm etc.... The features of the reconstructed particles are also selected according to the interesting region, e.g. at least 4 **jets** in data including at least 2 **b jet** and 1 high energy $\text{H}$ jet. Of course, the structure of detectors are also included, e.g. the particle is not possible to be detector from the gap of detectors. The following Figures show the predicted signal data and background noise, by ***Monte Carol (MC) method***, and data after selections. The background noise are expected to dominated in data by comparing the ratio between predicted signal data and background noise. <div style="text-align: center;" markdown="1"><img src="http://hep1.phys.ntu.edu.tw/~alpha78718/cv/bpbkg.png" height="200"></div> #### 2. Background estimation & validation The background is expected to dominate in data from ***MC*** study. However, the background is actually hard to simulate, we have to estimate it from data. The used technique here for **predicting the background distribution (model)** of background noise in signal data is called ***Data-driven ABCD method***, which inverses the feature selections and obtains the model from the outlier data. Here I illustrated the method in this analysis: <div style="text-align: center;" markdown="1"><img src="http://hep1.phys.ntu.edu.tw/~alpha78718/cv/bpabcd.png" height="200"></div> The signal region is at $B$, the background noise can be extrapolated from $A$ by applying scale of $D/C$ as $$ B(x)=A(x)\frac{N_D}{N_C}\ , $$ where $B(x)$ and $A(x)$ is a certain kinematic distribution as function of a feature $x$; $N_C$ and $N_D$ is the yields in region $C$ and $D$, respectively. The assumption of this method is expected the probability of background noise is random and smoothly distributed in overall data, and it has been validated by **MC method** and **Data-driven control sample** in this analysis. The control sample is also defined from the extremely outlier data, i.e. the data is not in *ABCD* regions. The selection of control sample requires the jets in data are not from $\text{b}$ quark. The total background in following Figure shows the predicted background model, which is matched with data, i.e. there is no any new significant new physics event (data) in current data-driven research. <div style="text-align: center;" markdown="1"><img src="http://hep1.phys.ntu.edu.tw/~alpha78718/cv/bpht1.png" height="250"> <img src="http://hep1.phys.ntu.edu.tw/~alpha78718/cv/bpht2.png" height="250"></div> ## Results Although there is no any signal found in data, it doesn't mean the physics mechanism is failed. We can still estimated the possible energy region which the new physics may exist there, i.e. the energy of LHC is not large enough to produce the new particle. Thus, we provide the **up-limit** of the probabilities of $\text{b}'\bar{\text{b}'}$ pair production as function of mass of $\text{b}'$ to shows the possible region to have $\text{b}'$. The **up-limit** is estimated by [*Hypothesis Testing*](https://onlinecourses.science.psu.edu/statprogram/node/138) which give the conference interval with 95% by using data, predicted background (from the ***Data-driven ABCD method***) and $\text{b}'$-MC samples. The following Figure shows the up-limit of the $\text{b}'$ mass. <div style="text-align: center;" markdown="1"><img src="http://hep1.phys.ntu.edu.tw/~alpha78718/cv/bplimit.png" height="250"></div> - The blue dashed line shows the theoretical probabilities of $\text{b}\bar{\text{b}}$ pair production which are applying to generate signal MC data. - The blue dot line within yellow and green bands present the predicted probabilities by data-driven predicted background and $\text{b}'$-MC sample. It compares the gaussian distribution of the yields of predicted background and predicted background + $\text{b}'$-MC, i.e. comparing the predicted yields with and without signal exists. The probabilities of $\text{b}'$ thus can be obtained by some calculation according to the coverage between two distributions. The yellow and green band are also estimated in same way but by variating the coverage. They are called *expected limit*. - The black solid line is made by same way as expected limit, but the predicted background is replaced by data. This is called *observed limit*. Since there is no significant evidence excessing signal, the observe limit agrees with the expected limit within the uncertainty. - The widths of the gaussian distributions of the yields are obtained by uncertainty study. Except the statistical uncertainty, the systematic uncertainties are included due to the MC sample is used, and it is applied some corrections for matching with data. The detail study can be found in the **[References]**. By comparing the probability of theory and limits, the observed (expected) region of the $\text{b}'$ mass can excludes the region below 846 (811) GeV at 95% confidence level. ## References 1. Github : <https://github.com/juifa-tsai/BprimeTobHAnalysis> 2. [Phys. Rev. D 93 (2016) 112009](http://dx.doi.org/10.1103/PhysRevD.93.112009). 3. [CERN-CMS-B2G-14-001](http://cms-results.web.cern.ch/cms-results/public-results/preliminary-results/B2G-14-001/index.html). 4. [CERN-CMS-B2G-13-006](http://cms-results.web.cern.ch/cms-results/public-results/publications/B2G-13-006/index.html) 5. [121th LHCC-CERN](https://indico.cern.ch/event/369822/#21-search-for-pair-produced-ve) <br> --- [:ghost: Github](https://github.com/juifa-tsai) | [:busts_in_silhouette: Linkedin ](https://www.linkedin.com/in/jui-fa-tsai-08ba0a93)