Calculate the partial widths of the three decay modes Z →e^+ e^-, ?u, d d. Hence, predict the to

step 1 In this exercise, we have y equals z times sine of x, y, squared, plus 2z, and we want to find t

Calculate the partial widths of the three decay modes Z →e^+...

Calculate the partial widths of the three decay modes $Z \rightarrow \mathrm{e}^{+} \mathrm{e}^{-}$, ?u, $\overline{\mathrm{d}} d$. Hence, predict the total width of the $Z$ in the standard model, assuming $\sin ^{2} \theta_{W}=\frac{1}{4}$ and $M_{Z}=90 \mathrm{GeV}$. Do not forget color.

Key Concepts

Z Boson

The Z boson is a neutral carrier of the weak force in the Standard Model of particle physics. It mediates interactions such as the decay into fermion-antifermion pairs and has properties (such as mass and width) that are predicted and measured to high precision, providing crucial tests of the Standard Model and its electroweak sector.

Partial Decay Width

A partial decay width is the probability per unit time that a particle will decay via a specific channel. In the context of the Z boson, each decay mode (such as into an electron-positron pair or a quark-antiquark pair) has its own partial width, which, when summed over all channels, gives the total decay rate of the particle.

Total Decay Width

The total decay width is the sum of all partial decay widths for the various decay modes of a particle. It is inversely related to the particle’s lifetime and provides an overall measure of the particle's instability. For the Z boson, the predicted total width is a crucial observable that combines its decays into leptons and quarks.

Electroweak Couplings

Electroweak couplings describe how the Z boson interacts with fermions through vector and axial-vector components. These couplings depend on the intrinsic properties of the fermions, such as their electric charge and weak isospin, dictating the strength and structure of the interaction and influencing the calculated decay widths.

Weak Mixing Angle

The weak mixing angle (often denoted as ?_W) is a fundamental parameter in the electroweak theory, defining the relationship between the electromagnetic and weak interactions. Its sine squared value appears in the formulas for fermion couplings to the Z boson and thus impacts the partial widths of its decay channels.

Color Factor

The color factor arises from Quantum Chromodynamics (QCD) when considering quark decays. Since quarks come in three colors, each quark decay channel gains a multiplicative factor compared to leptonic decays. This factor is essential in correctly calculating the decay widths for processes where the Z boson decays into quark-antiquark pairs.

Transcript

Please give Ace some feedback