Branching ratio for one decay channel

[zaman786]

TL;DR

how can we find the branching ratio - after do calculation for one channel

hi, for studying one decay channel of particle - and measuring its decay width or life time - after this how do we proceed to find the branching ratio -
do we need to find the decay width of all possible channel - because its possible even by experiment we are missing some possible decay mode.
kindly help

 

[Vanadium 50]

Where are you starting from? Can't give you directions from here to there without knowing where "here" is.

 

[zaman786]

Where are you starting from? Can't give you directions from here to there without knowing where "here" is.

for example D0 meson has several semi-leptonic decay - i want to find its branching ratio for k-, positron and electron neutrino , i can find its decay width
but it has different mode or channel also exist as mention in PDG , so do i have to find decay width for all of these modes and get total decay width. than by using formula : Branching ratio = partial decay width/ total decay width
or there exist some easiest approach

 

[mfb]

If you want to do this purely theoretically then you need to calculate all decay modes, or at least all major decay modes and then neglect the rare ones. Typically theoretical results will compare one branching fraction to another, the ratio won't be affected by other decay modes. That is easier to measure experimentally as well.

 

[zaman786]

If you want to do this purely theoretically then you need to calculate all decay modes, or at least all major decay modes and then neglect the rare ones. Typically theoretical results will compare one branching fraction to another, the ratio won't be affected by other decay modes. That is easier to measure experimentally as well.

thanks a lot for clearing my confusion

 

[ohwilleke]

do we need to find the decay width of all possible channel - because its possible even by experiment we are missing some possible decay mode.

Calculating all possible channels is how you would make the theoretical calculation.

You could also do an inclusive measurement of the decay width of the entire hadron (looking at its resonance) which would measure the total decay width, including decays that are rare enough to not be detected individually.

Rare decays are so uncommon, and the measurements of total decay width and single channel decay widths have sufficient uncertainty (often 10^-3 or worse), that missing a few rare decays (which often have branching fractions of 10^-5 or less), doesn't change the branching fraction enough to be distinguishable given the uncertainties involved in your other calculations and measurements. So, you can safely omit rare decays from the theoretical total decay width without materially changing the accuracy of your calculation.

 

[zaman786]

surely, you have given hint - looking at its resonance - thanks , i will look into it-
thanks a lot