# Branching fraction

Hi all,

I found that the branching fraction ## b \to s \gamma ## decay is given by
## B \to K \gamma ## ~ 10^-4 , but now I want to know if I calculate the decay width of ## b \to s \gamma ##, what it should equals ? In other words I don't understand what does a branching fraction mean ..

Bests.

The branching fraction of a certain decay ##A\to B+C## is simply defined as:

$$\mathcal{BR}(A\to B+C)=\frac{\Gamma(A\to B+C)}{\Gamma^{tot}_A},$$

where ##\Gamma_A^{tot}## is the total width of the particle A.

So the branching fraction is the same as the branching ratio.

But now what is the decay width of ## b \to s \gamma ##, if the b→sγ branching fraction has been calculated to be
## B \to K \gamma ## ~ 10^-4 ?

Last edited:
You simply have to multiply the branching fraction (or ratio) by the total width of the B meson.

I found in PDG that the mean life time of ## B_0 ## is ~ 10^-12 s, so its total decay width ## \Gamma = h / 2 \pi \tau ## ~ 10^-25 GeV.s. / 10^-12 s ~ 10^-13 GeV . Which means the partial decay width of s ## \gamma ## will be ~ 10^-17 GeV .

I think your calculation is wrong. The Plank constant is ##\hbar \simeq 6.58\times 10^{-16} eV\cdot s## and I would say:

$$\Gamma=\frac{\hbar}{\tau}\simeq6.6\times10^{-4} \;eV.$$

To be fair I don't know if this is a reasonable value for the total width but I think so. Anyways, in this case you obtain the partial width to be ##\sim10^{-8}\;eV##

Which means the partial width ~ ## 10^{-17} GeV ## ..

The problem is I calculate this width by FormCalc and LoopTools and I get it much larger !

mfb
Mentor
What is "much larger"? Factor 10? 10 orders of magnitude?
Is the result given in GeV or eV?