# Measuring characteristic time of strong and weak interaction

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• crick
In summary, the conversation discusses a scattering event between particles a and b that produces particles c and d, with c decaying into particles e and f. The first interaction is by strong force with a time of interaction of approximately 10^-23 seconds, while the second interaction is weak with a decay time of approximately 10^-8 seconds. The purpose is to measure the times of interaction and decay using cross section measurements. The cross section is a function of the mass of the c state and the energy and momentum of particles e and f. It is hypothesized that the time of weak decay is linked to the decay width, while the time of interaction is linked to the integral of the cross section curve around the mass of the c state.
crick
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.----------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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The weak interaction is fine. I don't understand your argument for the second one. The cross section for this process depends on many different things.

crick

## 1. What is the characteristic time of strong and weak interaction?

The characteristic time of strong and weak interaction refers to the time it takes for an interaction between two particles, such as protons and neutrons, to occur. It is a measure of the strength of the interaction between these particles.

## 2. How is the characteristic time of strong and weak interaction measured?

The characteristic time of strong and weak interaction can be measured using a variety of experimental techniques, such as scattering experiments or particle colliders. These techniques involve observing the behavior of particles and measuring the time it takes for interactions to occur.

## 3. What factors affect the characteristic time of strong and weak interaction?

The characteristic time of strong and weak interaction is affected by several factors, including the masses of the particles involved, the distance between them, and the strength of the interaction between them. Additionally, the presence of other particles in the environment can also affect the characteristic time.

## 4. How does the characteristic time of strong and weak interaction impact particle behavior?

The characteristic time of strong and weak interaction plays a crucial role in determining the behavior of particles. For example, particles with a longer characteristic time will have a greater chance of interacting with other particles, leading to changes in their trajectory and overall movement.

## 5. What are some applications of measuring the characteristic time of strong and weak interaction?

Measuring the characteristic time of strong and weak interaction has many practical applications, such as in nuclear energy production, medical imaging, and particle physics research. Understanding these interactions and their characteristic times can also help us better understand the fundamental forces of nature.

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