# Measuring characteristic time of strong and weak interaction

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## Main Question or Discussion Point

Consider a scattering between two particles a and b that produces two particles c and d: d is stable, while c decays in two other different particles e and f.

The first interaction is by strong force (time of interaction $t_1\sim 10^{-23}s$, which is also the time of generation of c and d), the second is weak (time of decay of c $t_2\sim 10^{-8}$).

$$a+b\to_{strong} c+d\to_{weak} (e+f)+d$$

Suppose that the pourpose is to measure the times of interaction and decay $t_1$ and $t_2$ above stated using the cross section measurements.

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By "measuring the cross section" I mean measuring the rate of particle detection of $e$and$f$ as a function of $W=M_c$, the mass of the $c$ state, which looks something like:

(For each value of $M_c$, $e$ and $f$ will have to satisfy conditions on energy and momentum).

Now, are the following two considerations true?

- The time of weak decay of c is only linked to $\Gamma$ as $$t_2 \sim \hbar/\Gamma$$
- The time of interaction by strong force in the scattering of a and b (i.e. the time of generation of c state) is only linked to the integral of the curve above in a region around $M_{c,0}$. Let's call this integral $I$ : then $$t_1 \sim 1/I$$

My reasoning is that, since c is generated by strong force in $t_1$, this is the time that determines also the rate of production of $e$ and $f$, which is the one I measure (c is not measurable in practice). But is this hypotesis correct?

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