# Branching Fraction of b -> s γ Decay

• Safinaz
In summary, the conversation discussed the concept of branching fraction and its relation to decay width. The branching fraction is the ratio of a specific decay's width to the total width of the particle. The decay width of b→sγ can be calculated by multiplying the branching fraction by the total width of the B meson. The conversation also mentioned the calculation of the partial decay width using FormCalc and LoopTools, with some discrepancies in the results.

#### Safinaz

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 !

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

## What is the branching fraction of b -> s γ decay?

The branching fraction of b -> s γ decay is the probability that a b quark will decay into a s quark and a photon (γ). It is expressed as a percentage and represents the fraction of all b -> s γ decays out of all possible b quark decays.

## Why is the branching fraction of b -> s γ decay important?

The branching fraction of b -> s γ decay is important because it provides valuable information about the fundamental forces and interactions within the Standard Model of particle physics. It also helps to test the predictions of this model and can provide insights into potential new physics beyond the Standard Model.

## How is the branching fraction of b -> s γ decay measured?

The branching fraction of b -> s γ decay is measured through experiments using particle accelerators, such as the Large Hadron Collider (LHC). By studying the decay products of b quarks, scientists can determine the number of b -> s γ decays and compare it to the total number of b quark decays to calculate the branching fraction.

## What is the current value of the branching fraction of b -> s γ decay?

The current value of the branching fraction of b -> s γ decay is approximately 3.15%, as determined by the LHCb experiment at CERN in 2019. This value is consistent with the predictions of the Standard Model and previous measurements by other experiments.

## Can the branching fraction of b -> s γ decay change over time?

Yes, the branching fraction of b -> s γ decay can change over time as more precise measurements are made and new theories are developed. Any significant deviation from the predicted value could indicate the presence of new particles or interactions, which would require further investigation and could lead to revisions of the Standard Model.