Decoding the Mystery of Branching Ratios and Decay Rates

[unscientific]

Homework Statement

(a) What are the branching ratios for EM decay only?
(b) What does this reveal about the strength of strong interaction?
(c)What are the relative rates of decay?

Homework Equations

The Attempt at a Solution

Part (a)
[/B]
For EM-only decay, the branching ratio would be 50% and 50%.

Part (b)
Strong interaction is more likely to occur, since only 12% of total reaction can be attributed to EM interaction.

Part (c)
Not too sure how to approach this part..

 

[mfb]

For EM-only decay, the branching ratio would be 50% and 50%.

There are more decay modes that can happen via the electromagnetic interaction.

Strong interaction is more likely to occur, since only 12% of total reaction can be attributed to EM interaction.

More than 12%, as a correct solution for (a) will show.

(c) did you draw the leading Feynman diagrams? What is the difference between them?

 

[unscientific]

There are more decay modes that can happen via the electromagnetic interaction.
More than 12%, as a correct solution for (a) will show.

(c) did you draw the leading Feynman diagrams? What is the difference between them?

The J/psi meson is composed of a charmed and anti-charm quark.Since electromagnetic interactions are classified under weak interactions, they decay to leptons, right?

So the possible leptons are $e^+e^-, \mu^+\mu^-, \tau^+\tau^-$. So proportion is $\frac{1}{3}$?

Also what is $\Psi~ ''$?Part (c)

The first feynman diagram is given by:

The second feynman diagram is given by:

The only difference between these two is the decay of $W^+$ lepton to either $\bar u s$ or $e^+ \nu_e$. Which has a higher decay width $\Gamma$, the hadronic or leptonic decay?

 

[mfb]

Since electromagnetic interactions are classified under weak interactions, they decay to leptons, right?

They are not, and even if they would the conclusion would be wrong. There are weak processes without any leptons (you have one example in (c)).
Did you draw a Feynman diagram for one of the decays? What else can get produced apart from leptons?
Concerning taus, what is their mass? Does that work?

Also what is $\Psi~ ''$?

See the particle data group, for example. Or Wikipedia, or various other lists of particles.

The only difference between these two is the decay of $W^+$ lepton to either $\bar u s$ or $e^+ \nu_e$. Which has a higher decay width $\Gamma$, the hadronic or leptonic decay?

That's what you have to find out.

 

[unscientific]

They are not, and even if they would the conclusion would be wrong. There are weak processes without any leptons (you have one example in (c)).
Did you draw a Feynman diagram for one of the decays? What else can get produced apart from leptons?
Concerning taus, what is their mass? Does that work?

See the particle data group, for example. Or Wikipedia, or various other lists of particles.

That's what you have to find out.

Masses of electron, muon and tau leptons are 0.0005, 0.1 and 1 GeV. Tau muons are much heavier, so I suppose they are not produced as much?

Part(c)
Their vertex factors are definitely different for hadron and lepton decays. For hadron decays it will be $g_{em} \times q\bar q = \frac{2}{9} g_{EM}$ while for lepton decay to positron, the vertex factor is $+1 \times g_{EM}$. So the lepton decay has higher decay width?

 

[mfb]

The mass of a tau is not 1 GeV.

(c) you have a W not a photon, I don't think your approach works for those (you'll need it for (a)!).

 

[unscientific]

The mass of a tau is not 1 GeV.

(c) you have a W not a photon, I don't think your approach works for those (you'll need it for (a)!).

Mass of Tau particle is about 1.7 GeV according to wikipedia: http://en.wikipedia.org/wiki/Tau_(particle)

True. That vertex factor thing only works for photon coupling. I'm guessing the hadronic decay is suppressed, since they are much heavier than lepton decay products (positron, neutrino)?

 

[mfb]

Mass of Tau particle is about 1.7 GeV according to wikipedia: http://en.wikipedia.org/wiki/Tau_(particle)

About 1.8, and not 1, and that makes a huge difference if look at the decay of a particle with 3.1 GeV into two lighter particles. What is the maximal mass for those lighter particles?

True. That vertex factor thing only works for photon coupling. I'm guessing the hadronic decay is suppressed, since they are much heavier than lepton decay products (positron, neutrino)?

Pions are relatively light compared to the available decay energy.

 

[unscientific]

About 1.8, and not 1, and that makes a huge difference if look at the decay of a particle with 3.1 GeV into two lighter particles. What is the maximal mass for those lighter particles?

Pions are relatively light compared to the available decay energy.

Heaviest lepton is the muon, with a mass of 0.1GeV.

What else would suppress the decay of hadrons?

 

[mfb]

Heaviest lepton is the muon, with a mass of 0.1GeV.

The heaviest lepton pair a J/Psi can decay into: right.

What else would suppress the decay of hadrons?

Why do you think it is suppressed?
Did you check the actual branching ratios?

 

[unscientific]

The heaviest lepton pair a J/Psi can decay into: right.

Why do you think it is suppressed?
Did you check the actual branching ratios?

I thought J/Psi is a meson?
How do I calculate the branching ratio?

 

[mfb]

I thought J/Psi is a meson?

No one disagreed with that?

How do I calculate the branching ratio?

I mean: did you look it up? You seem to expect a suppression of some sort: why?

 

[unscientific]

No one disagreed with that?

I mean: did you look it up? You seem to expect a suppression of some sort: why?

What's the branching ratio if it's only EM decay? Since tau muons are too heavy, only e+/e- and mu+/mu- pairs are produced at 50% branching ratio.

For hadronic decay from J/PSI, I looked it up there's something called the OZI rule that suppresses it. It is definitely beyond the scope of the course.

 

[mfb]

What's the branching ratio if it's only EM decay? Since tau muons are too heavy, only e+/e- and mu+/mu- pairs are produced at 50% branching ratio.

What about quarks as product of EM decays?

For hadronic decay from J/PSI, I looked it up there's something called the OZI rule that suppresses it. It is definitely beyond the scope of the course.

This applies to QCD decays only, not all hadronic decay processes.

 

[unscientific]

What about quarks as product of EM decays?

This applies to QCD decays only, not all hadronic decay processes.

Do all kinds of quarks get produced? ($u \bar u, d \bar d, s \bar s, c \bar c, b \bar b ,t \bar t$)

 

[mfb]

Do you have enough energy to produce all those?
Didn't we have that problem before?

 

[unscientific]

Do you have enough energy to produce all those?
Didn't we have that problem before?

The J/psi meson has about 3GeV mass, so possible EM decays are:

Hadronic: u,d,s,c
leptonic: electron, muon and tau

Mass of tau is about 1.8 GeV.

 

[mfb]

Hadronic: u,d,s,c

J/Psi is a bound state of two charm mesons, which means its energy is lower than the combined masses. And a more technical detail: quarks don't appear in isolation, so you actually have to make the lightest hadrons with charm quarks: D⁰. And two times their mass is above the J/Psi mass, therefore the decay to charm+anticharm does not work.

leptonic: electron, muon and tau

Mass of tau is about 1.8 GeV.

How exactly do you imagine a decay to tau+antitau? You said in post #13 that they are too heavy already.

 

[unscientific]

J/Psi is a bound state of two charm mesons, which means its energy is lower than the combined masses. And a more technical detail: quarks don't appear in isolation, so you actually have to make the lightest hadrons with charm quarks: D⁰. And two times their mass is above the J/Psi mass, therefore the decay to charm+anticharm does not work.
How exactly do you imagine a decay to tau+antitau? You said in post #13 that they are too heavy already.

Ok. so number of possibilities are : 3 x (1 + 1 + 1) for u,d,s and 1 + 1 for electron and muton so $\frac{1}{11}$.

 

[mfb]

Looks right. And 1/11 is not far away from 6%.