# Branching ratio and decays

Tags:
1. Mar 16, 2015

### unscientific

1. The problem statement, all variables and given/known data

(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?

2. Relevant equations

3. The attempt at a solution

Part (a)

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..

2. Mar 17, 2015

### Staff: Mentor

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?

3. Mar 18, 2015

### unscientific

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?

Last edited: Mar 18, 2015
4. Mar 18, 2015

### Staff: Mentor

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.

5. Mar 18, 2015

### unscientific

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?

6. Mar 18, 2015

### Staff: Mentor

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)!).

7. Mar 18, 2015

### unscientific

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)?

8. Mar 18, 2015

### Staff: Mentor

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.

9. Mar 18, 2015

### unscientific

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

What else would suppress the decay of hadrons?

10. Mar 18, 2015

### Staff: Mentor

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?

11. Mar 19, 2015

### unscientific

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

12. Mar 19, 2015

### Staff: Mentor

No one disagreed with that?

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

13. Mar 19, 2015

### unscientific

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.

14. Mar 19, 2015

### Staff: Mentor

What about quarks as product of EM decays?

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

15. Mar 20, 2015

### unscientific

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

16. Mar 22, 2015

### Staff: Mentor

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

17. Mar 22, 2015

### unscientific

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

leptonic: electron, muon and tau

Mass of tau is about 1.8 GeV.

18. Mar 22, 2015

### Staff: Mentor

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.

19. Mar 22, 2015

### unscientific

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

20. Mar 23, 2015

### Staff: Mentor

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