Assuming the standard model coupling, show that Γ(Z →νe ν̅e)=(g^2)/(96 πcos^2 θW) MZ see Exercis

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Assuming the standard model coupling, show that Γ(Z →νe...

Assuming the standard model coupling, show that $$ \Gamma\left(Z \rightarrow \nu_{e} \bar{\nu}_{e}\right)=\frac{g^{2}}{96 \pi \cos ^{2} \theta_{W}} M_{Z} $$ see Exercise 13.2. Given that $\sin ^{2} \theta_{W}=0.25$ and $M_{Z}=90 \mathrm{GeV}$, predict the numerical value of the partial width.

Assuming the standard model coupling, show that
$$
\Gamma\left(Z \rightarrow \nu_{e} \bar{\nu}_{e}\right)=\frac{g^{2}}{96 \pi \cos ^{2} \theta_{W}} M_{Z}
$$ see Exercise 13.2. Given that $\sin ^{2} \theta_{W}=0.25$ and $M_{Z}=90 \mathrm{GeV}$, predict the numerical value of the partial width.

Key Concepts

Partial Decay Width

The partial decay width is a measure of the probability per unit time that an unstable particle decays into a particular final state. It is derived from elements of the matrix element and phase space considerations (as in Fermi's Golden Rule). This concept is crucial in comparing theoretical predictions, like those made using the Standard Model coupling, with experimental observations.

Weak Mixing Angle

The weak mixing angle, often denoted as ?W, quantifies the mixing between the electromagnetic and weak interactions in the electroweak theory. It determines how the gauge bosons couple to the fermions and appears in the expressions for processes such as the decay of the Z boson. The value of sin²?W is important for calculating the effective couplings in the model.

Electroweak Theory

Electroweak theory unifies the electromagnetic and weak interactions into a single theoretical framework based on the SU(2) x U(1) gauge symmetry. This concept introduces gauge bosons (W+, W?, and Z) whose interactions are governed by coupling constants that are functions of the weak mixing angle. It is central to predicting and understanding processes like the Z boson decay into neutrino pairs.

Z Boson

The Z boson is a neutral gauge boson that mediates the weak neutral current interaction in the Standard Model. Its interactions with fermions, including neutrinos, are characterized by specific coupling constants. Studying its decay properties, including partial decay widths, provides essential tests of electroweak theory and the underlying gauge symmetries.

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