Lifetime & Branching ratio

  • #1
malawi_glenn
Science Advisor
Homework Helper
4,795
22
[SOLVED] Lifetime & Branching ratio

Hi!

In my book Particle Physics by Martin & Shaw, eq 2.15:

Lifetime:
[tex] \tau _l = \dfrac{B(l^- \rightarrow e^-\bar{\nu }_e\nu _l )}{\Gamma (l^-\rightarrow e^-\bar{\nu }_e\nu _l )} [/tex]

Where B is branching ratio and Gamma the decay rate and l is a lepton.

Why is B included? :S I thought the lifetime just was the inverse of the decay rate...
 

Answers and Replies

  • #2
nrqed
Science Advisor
Homework Helper
Gold Member
3,764
294
Hi!

In my book Particle Physics by Martin & Shaw, eq 2.15:

Lifetime:
[tex] \tau _l = \dfrac{B(l^- \rightarrow e^-\bar{\nu }_e\nu _l )}{\Gamma (l^-\rightarrow e^-\bar{\nu }_e\nu _l )} [/tex]

Where B is branching ratio and Gamma the decay rate and l is a lepton.

Why is B included? :S I thought the lifetime just was the inverse of the decay rate...

Because this decay rate is not the total decay rate, it's only the decay rat efor that particular mode. The lifetime is the inverse of the total decay rate.
 
  • #3
Hi!

In my book Particle Physics by Martin & Shaw, eq 2.15:

Lifetime:
[tex] \tau _l = \dfrac{B(l^- \rightarrow e^-\bar{\nu }_e\nu _l )}{\Gamma (l^-\rightarrow e^-\bar{\nu }_e\nu _l )} [/tex]

Where B is branching ratio and Gamma the decay rate and l is a lepton.

Why is B included? :S I thought the lifetime just was the inverse of the decay rate...

Well, assuming that;

[tex] \Gamma (l^-\rightarrow e^-\bar{\nu }_e\nu _l ) < \Gamma (l^-\rightarrow anything) [/tex]

you must compensate for the longer lifetime that would occur if you restricted the lepton to that one decay mode. Compensating will require you to consider the ratio of this decay mode versus any available decay mode, which is the branching ratio in the posted equation. Thus, dividing the branching ratio, which is less than or equal to one, by the partial width, which is less than or equal to the total width, is the logical solution.
 
  • #4
malawi_glenn
Science Advisor
Homework Helper
4,795
22
Ok i think I understand now, perhaps I have not understand the concept of lifetime proper yet. Thanx!
 

Related Threads on Lifetime &amp; Branching ratio

  • Last Post
Replies
2
Views
4K
Replies
7
Views
686
Replies
13
Views
449
Replies
3
Views
6K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
7
Views
5K
  • Last Post
Replies
6
Views
922
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
5
Views
1K
Top