Longitudinal Decay Width

In summary, calculating the longitudinal width in this decay process involves understanding the polarization of the W boson and its relationship to the total width. This can be done by using the equations for the polarization vector in different frames and integrating over all possible polarizations of the W boson.
  • #1
PLuz
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Homework Statement


Hello,

Given the decay: [itex]H \rightarrow W^{-} + \bar{s} + c[/itex], where it only matters that [itex]\bar{s}[/itex] and [itex]c[/itex] are fermions and [itex]W^{-}[/itex] is the W boson. If one knows the total width of the process how can we calculate the longitudinal width?




Homework Equations


In the frame where de boson has velocity zero the longitudinal polarization vector is given by: [itex]\epsilon_{\mu}(k)=(0,0,0,1)[/itex]

In the frame where [itex]W^{-}[/itex] moves at velocity [itex]\overrightarrow{\beta}[/itex]:
[itex]\epsilon_{\mu}(k)=(\gamma \beta, \gamma \frac{\overrightarrow{\beta}}{\beta})[/itex]


The Attempt at a Solution



I'm completely clueless of how to even start. Can anyone help me?


Thank you
 
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  • #2
for your question. Calculating the longitudinal width in this decay process involves understanding the polarization of the W boson and its relationship to the total width. The longitudinal width is related to the polarization of the W boson in the frame where it has zero velocity, and in the frame where it is moving at a velocity \overrightarrow{\beta}.

To start, we can use the equation for the polarization vector in the frame where the W boson has zero velocity: \epsilon_{\mu}(k)=(0,0,0,1). This means that the W boson is polarized only in the z-direction, which is the direction of motion for the decay products \bar{s} and c.

Next, we can use the equation for the polarization vector in the frame where the W boson is moving at a velocity \overrightarrow{\beta}: \epsilon_{\mu}(k)=(\gamma \beta, \gamma \frac{\overrightarrow{\beta}}{\beta}). This equation takes into account the relativistic effects of the W boson's motion.

To calculate the longitudinal width, we need to integrate over all possible polarizations of the W boson. This means we need to integrate over the angles \theta and \phi, which represent the direction of the W boson's motion. The result of this integration will give us the longitudinal width.

I hope this helps to get you started on your solution. Let me know if you have any further questions. Good luck!
 

1. What is longitudinal decay width?

Longitudinal decay width is a measure of the rate at which a particle decays in the direction of its momentum. It is a fundamental property of subatomic particles and is used to describe the probability of a particle decaying in a specific direction.

2. How is longitudinal decay width calculated?

Longitudinal decay width is calculated using the formula ΓL = ħc/τ, where ΓL is the longitudinal decay width, ħ is the reduced Planck's constant, c is the speed of light, and τ is the mean lifetime of the particle.

3. What is the significance of longitudinal decay width in particle physics?

Longitudinal decay width is an important quantity in particle physics as it provides information about the decay processes of subatomic particles. It is used in calculations to predict the lifetimes and decay modes of particles, and can also reveal insights about the fundamental forces of nature.

4. How does longitudinal decay width differ from transverse decay width?

Longitudinal decay width is a measure of the decay rate in the direction of a particle's momentum, while transverse decay width is a measure of the decay rate perpendicular to the particle's momentum. Transverse decay width is typically smaller than longitudinal decay width and is affected by the spin of the particle.

5. Can longitudinal decay width be experimentally measured?

Yes, longitudinal decay width can be measured experimentally by studying the decay products of a particle and analyzing their momentum distribution. This allows for the calculation of the decay width, providing valuable information about the properties of the particle.

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