Question

I cam across a question that stated the total decay width for the phi meson was 4300 kev and the partial decay of it into an electron-positron pair was 1.3kev. How would I estimate the partial width for the decay of upsilon meson into an electron-poistron pair knowing that its total decay width is 54kev? I know it must be small as strong force would dominate but is there a way i could make a good guess, or is it a case of just being able to say its small

Answer 1

A rough estimation of the partial decay width of the upsilon meson into an electron-positron pair can be made by applying the branching fraction from the phi meson's decay to the upsilon's total decay width, resulting in an approximate partial width of 0.0163 keV.

Step-by-step explanation:

To estimate the partial width for the decay of the upsilon meson into an electron-positron pair given the total decay width, we can use the branching fraction from a similar meson's decay into the same final state. The decay width ratio of the phi meson into an electron-positron pair (1.3 keV) to its total decay width (4300 keV) gives a branching fraction of about 0.000302, or 0.0302%.

Applying this fractional estimate to the upsilon meson's total decay width of 54 keV, you would get an estimated partial width for the electron-positron channel of about 0.0163 keV. This is a rough approximation and assumes that the branching ratios for similar meson decays are comparable, which is not always the case, but it can serve as a starting guide.