2
$\begingroup$

I have a particle (A) which undergoes a two-body, on-shell decay to particle (B). The associated width of the process is $\Gamma_{ABB}$.

Particle B under goes a two-body, on-shell decay to particle C and the associated width of the process is $\Gamma_{BCC}$.

Since the particles are all produced on shell I can use the narrow-width approximation. See below for roughly drawn diagram.

Is the width of the process $A\rightarrow B B \rightarrow CCCC$ approximately given by $\Gamma_{ABB}+\Gamma_{BCC}$? i.e can I simply sum the widths?enter image description here

$\endgroup$
1
  • $\begingroup$ 1. Is the internal line in the third diagram supposed to be on-shell/resonant or not? I.e. do you want to compute a Feynman diagram for the process "A decays into CCCC mediated by B" or the actual sequence of events "A decays into BB, then each B decays into CC"? 2. Since the width is essentially a decay rate (cf. physics.stackexchange.com/q/269852/50583), you could think yourself a bit about whether or not it makes sense to add the decay rate of two subsequent processes. $\endgroup$
    – ACuriousMind
    Sep 4, 2017 at 10:57

1 Answer 1

2
$\begingroup$

No. The width of process $A\to BB\to CCCC$ is given by $\Gamma_{ABB}\times(\textrm{BR}_{BCC})^2$, where BR is the branching ratio of $B\to CC$.

Since the $B$ particles are on-shell, the width of the process $A\to BB\to CCCC$ does not depend on the $B\to CC$ width, but rather on the branching ratio.

$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.