Z0 Data Analysis Workbook

Santiago.R, Birge Ken Tok

Reading Function [RD Parsons]

Hadronic event selection

The selected hadronic events are chosen based on two criteria;

  1. The total calorimetric energy of the selected hadrons needs to be around the value of the invariant mass $\sqrt{s}$. With an energy of
    $E_{Vis}= \sum_{i=1}^n E_i = \sum_{i=1}^n \sqrt{\vec{p_i}^2+m_i^2} \approx \sum_{i=1}^n \sqrt{p_{xi}^2+p_{yi}^2+p_{zi}^2}$
    for a total of n particles, the following relation for the ratio must hold true
    $0.5 < \frac{E_{Vis}}{\sqrt{s}} < 1.5$
  2. According to Chapter 5 PPE 93, the energy imbalances along the beam direction $\Delta E_{\parallel}$ and perpendicular to it $\Delta E_{\perp}$ as given by the formulas
    $\Delta E_{\perp} = \sqrt{(\sum_{i=1}^np_{xi})^2+(\sum_{i=1}^np_{yi})^2}$
    $\Delta E_{\parallel} = \sum_{i=1}^np_{zi}$
    need to also stay within a range of
    $|\Delta E_{\parallel}|/E_{vis} < 0.6$
    $\Delta E_{\perp}/E_{vis} < 0.5$

Muon Event Selection

For the selected muon events, the criteria are somewhat different than for hadronic events. First, as according to Chapter 5 PPE 93, the muon event must be within the angular range
$0<|cos(\Theta)|<0.8$ with $cos(\Theta) = \frac{p_z}{\sqrt{p_x^2+p_y^2+p_z^2}}$
Then, their energy in the form of their momentum $E_{mu} \approx \sqrt{p_{xi}^2+p_{yi}^2+p_{zi}^2}$ should be roughly $1/2\sqrt{s}$ since most of the beam energy is conserved and thus
$40GeV \leq E_{mu} \approx \sqrt{p_{xi}^2+p_{yi}^2+p_{zi}^2} \leq 50GeV$
with the total impulse of both muons lying below 5GeV since their opposite directions would make their total impulse add up to 0.
$p_{tot} = \sqrt{\vec{p_{\mu}}+\vec{p_{\overline{\mu}}}} \leq 5GeV$

Select Data [RD Parsons]

Calculate the Hadron and Muon Cross Sections

Fitting the Breit Wigner PDF [RD Parsons]

Computing the Partial Width of Electron $\Gamma _e$

Computing the Decay Width of Hadrons and Neutrinos $\Gamma _{hadron}$, $\Gamma _\nu$

Calculate Weinberg Angle $\Theta _W$

Calculate Decay Widths of Quarks $\Gamma _{u}$, $\Gamma _d$ and NC factor