Top quark produced through the electroweak force: Discovery using the matrix element analysis and search for heavy gauge bosons using boosted decision trees

The top quark produced through the electroweak channel provides a direct measurement of the Vtb element in the CKM matrix which can be viewed as a transition rate of a top quark to a bottom quark. This production channel of top quark is also sensitive to different theories beyond the Standard Model such as heavy charged gauged bosons termed W'..;This thesis measures the cross section of the electroweak produced top quark using a technique based on using the matrix elements of the processes under consideration. The technique is applied to 2.3 fb--1 of data from the DO detector. From a comparison of the matrix element discriminants between data and the signal and background model using Bayesian statistics, we measure the cross section of the top quark produced through the electroweak mechanism spp&d1;→ tb+X,tqb+X=4.30+0.98-1.2 0pb .;The measured result corresponds to a 4.9sigma Gaussian-equivalent significance. By combining this analysis with other analyses based on the Bayesian Neural Network (BNN) and Boosted Decision Tree (BDT) method, the measured cross section is 3.94 +/- 0.88 pb with a significance of 5.0sigma, resulting in the discovery of electroweak produced top quarks. Using this measured cross section and constraining |Vtb| 0.78.;Additionally, a search is made for the production of W' using the same samples from the electroweak produced top quark. An analysis based on the BDT method is used to separate the signal from expected backgrounds. No significant excess is found and 95% C.L. upper limits on the production cross section are set for W' with masses within 600--950 GeV. For four general models of W' boson production using decay channel W' → tb¯, the lower mass limits are the following: M( W'L with SM couplings) > 840 GeV; M( W'R ) > 880 GeV or 890 GeV if the right-handed neutrino is lighter or heavier than W'R ; and M( W'L+R ) > 915 GeV.