Measurement of the $W$ boson polarization in top quark decays using the di-lepton final state of the top quark pair in $pp$ collisions with $\sqrt{s}$ = 7 TeV

The Standard Model (SM) is a framework that has succeeded to describe the behavior of the elementary particle to a great extent. After the discovery of a Higgs-boson-like particle in 2012, its reliability has increased more. At the same time, however, the importance of problems related to the Higgs mechanism such as the fine tuning of the mass of the Higgs particle has grown. In order to find a clue to the problems, the top quark is an interesting subject by focusing on the Higgs mechanism from the following two points. One thing is that the top quark mass of $ 173.2 \pm 0.9 $ GeV is much larger than that of other fermions such as electron and up-quark although their masses are originated from the same Higgs mechanism. The other is that the top quark mass is at the energy scale of the Higgs mechanism, and it is suspected that the top quark has some relation with it. \begin{align*} \end{align*} In the LHC-ATLAS experiment, where protons are collided with 7 TeV center of mass energy, the precise measurement of the top quark properties with enormous top quark samples is possible through mainly the top quark pair ($t\bar{t}$) production. In the ATLAS experiment, the cross section is measured in the various final states, and the result of $177 \pm 3(\mathrm{stat.}) ^{+8}_{-7}(\mathrm{syst.}) \pm 7(\mathrm{luminosity}) $ is consistent with the SM expectation of $ 164.6 ^{+11.4 } _{- 15.7} $ pb. These analyses however, have counted the number of events inclusively after some event selections. In order to investigate prodution and decay of the top quark more closely, it is quite important to look into the kinematical distributions that strongly relate to the top quark properties. \begin{align*} \end{align*} On that point, the $W$ boson polarization measurement in the top quark decay is important from the point that it directly related to the interaction in the top quark decay. In the SM, the top quark decays into a $W$ boson and a $b$-quark almost exclusively, with $V$-$A$ weak interaction. Due to the large decay width, the top quark decays before hadronization and behaviors of bare quark can be observed. Here, the $W$ boson polarization fraction in the SM expectation is \begin{align*} F_0 &= 0.687 \pm 0.005 \\ F_L &= 0.311 \pm 0.005 \\ F_R &= 0.0017 \pm 0.0001 \end{align*} where $F_0, F_L $ and $F_R$ are the fraction of $W$ boson polarization in longitudinal, left- and right-handed defined with respect to the momentum direction of the $W$ boson ($F_0+F_L+F_R=1$). As the result of $V$-$A$ interaction, the $F_R$ is strongly suppressed and its deviation from zero stands for the existence of new physics. \begin{align*} \end{align*} The $W$ boson polarization can be measured by the charged lepton emission angle distribution in the leptonic decay of the top quark : $t\to Wb \to l\nu b$. The differential cross section as a function of the charged lepton emission angle is \begin{align*} \frac{1}{N}\frac{\mathrm{d}N}{\mathrm{d}\cos \theta^*} = F_0 \frac{3}{4} \sin ^ 2 \theta ^* + F_L \frac{3}{8} (1-\cos \theta ^* )^2 + F_R \frac{3}{8} (1+\cos \theta ^* )^2 , \end{align*} where $\theta^*$ is defined as the angle between the momentum of the charged lepton on the $W$ boson rest frame and that of the $W$ boson on the top quark rest frame. The angle $\theta^*$ in one top quark decay can be reconstructed by measuring the momentum of the $b$-quark, charged lepton and neutrino from the top quark. \begin{align*} \end{align*} In this study, proton-proton collision data of 1.04 fb$^{-1}$ accumulated with the ATLAS detector is used. The analysis focuses on the di-lepton final state in which high purity top quark samples can be prepared from $10^{9}$ larger background thanks to the signature of the two charged leptons. \begin{align*} \end{align*} The signature of the charged leptons with high energy is important not only for the $\cos \theta ^*$ measurement but also for event trigger of the data acquisition. The existence of such object can be used to reject enormous QCD background events in hadron collisions and the performance of charged lepton trigger is essential. The muon trigger system is established systematially during the commissioning period, and the evaluation of the muon reconstruction performance is done. \begin{align*} \end{align*} Concerning the $t\bar{t} $ event reconstruction, the two neutrinos in the event are also important. This analysis establishes method that can reconstruct all the decay products of the two top quark with keeping the kinematical information. By applying the method on the selected events, the $W$ boson polarization fraction is measured from $\theta^*$(in practical, $\cos \theta^*$) distribution and the result is \begin{align*} F_0 &= 0.920 \pm 0.095(\mathrm{stat.}) \pm 0.104(\mathrm{syst.}) \\ F_L &= 0.172 \pm 0.063(\mathrm{stat.}) \pm 0.074(\mathrm{syst.}) \\ F_R &= - 0.092 \pm 0.046(\mathrm{stat.}) \pm 0.057(\mathrm{syst.}). \end{align*} The background is lowered to almost negligible level as expected, and the uncertainty from the background contribution is less than 0.01. The result is consistent with the SM expectation, for example, $F_R$ is consistent with zero. Also it is consistent with other $W$ boson polarization measurement in the ATLAS experiment. \begin{align*} \end{align*} This analysis is the first measurement of the $W$ boson polarization in the top quark decay in proton-proton collisions at a center of mass energy of 7 TeV. Following the inclusive cross section measurement, this is a more precise measurement by focusing on kinematical variables and the results is consistent with the SM with its uncertainty. In addition to the method to reconstruct $t\bar{t}$ with the di-lepton final state, this study provides the validity of the $t\bar{t}$ production and decay modeling for the future analyses related to the $t\bar{t}$ di-lepton or di-lepton-like signatures such as a fourth-generation quark $t'$ and the charged Higgs boson decays.