# Calculation of proton's lifetime

• aylakadamk
In summary, the conversation is about calculating the lifetime of a proton in Particle Physics class. While there are some sources stating its lifetime is ~10^32 years, there are no basic calculations to support this claim. The article provided for calculation is too complex for the classroom level, so a simpler calculation is requested. The use of the radioactive decay formula is suggested as an alternative, but it can only be used if the lifetime or the number of decays is known. The experts explain that the lifetime of a proton cannot be calculated because it is unknown if the proton is stable or not. There is an experimental lower limit on its lifetime, but even if it decays, it would take a very long time due to the properties of the particles
aylakadamk
Hi,

In a Particle Physics class, our instructor requested me to calculate the life time of proton. There are some sources telling that its life time is ~10^32 years, however there are no basic calculations. There is this article about calculation: http://journals.aps.org/prd/abstract/10.1103/PhysRevD.23.1580

However, its level is pretty higher than our classroom. Could provide a simpler calculation?

Thanks in advance.

Sorry I din't get any idea from that journal. We do not know the age of universe yet. But, according to me, as quarks are fundamental particles in the protons, the age of the quark from when it combined with other quarks to form a proton will be the age of proton. And mathematically I don't think there are equations to calculate age of proton exactly. :)

aylakadamk
Thanks for your reply. The calculation in the article is difficult to grasp for me too. I'm looking a way to solve the problem via radioactive decay formula: http://en.wikipedia.org/wiki/Exponential_decay

aylakadamk said:
Thanks for your reply. The calculation in the article is difficult to grasp for me too. I'm looking a way to solve the problem via radioactive decay formula: http://en.wikipedia.org/wiki/Exponential_decay
Welcome and Thanks for the link :)
Better you study about alpha decay as alpha particle had 1 proton and a neutron. :)

aylakadamk
Thanks for the advice :) As far as i know, it has two protons and two neutrons.

aylakadamk said:
Thanks for the advice :) As far as i know, it has two protons and two neutrons.
I forgot to mention pair of 2neutrons and a pair of 2protons. Sorry! :(

no problem :)

aylakadamk said:
Hi,

In a Particle Physics class, our instructor requested me to calculate the life time of proton. There are some sources telling that its life time is ~10^32 years, however there are no basic calculations. There is this article about calculation: http://journals.aps.org/prd/abstract/10.1103/PhysRevD.23.1580

However, its level is pretty higher than our classroom. Could provide a simpler calculation?

Thanks in advance.
It is unknown if the proton is stable or not. That also means you cannot calculate its lifetime. You can make some specific assumptions and ask "if those things are true, does it lead to proton decay and what is its lifetime?", but as you noted, those calculations are complicated.

There is an experimental lower limits on the lifetime. This means "if the lifetime would be lower than this value, we would have seen decays".

officialmanojsh said:
We do not know the age of universe yet.
We know it very well. This has nothing to do with proton decays.
officialmanojsh said:
But, according to me, as quarks are fundamental particles in the protons, the age of the quark from when it combined with other quarks to form a proton will be the age of proton.
This is not true. You cannot combine lifetimes like that. Also, "the lifetime of a quark" is not a meaningful concept, as quarks do not occur on their own.

aylakadamk said:
Thanks for your reply. The calculation in the article is difficult to grasp for me too. I'm looking a way to solve the problem via radioactive decay formula: http://en.wikipedia.org/wiki/Exponential_decay
That formula will tell you how many atoms decay within a specific time if you know the lifetime. Alternatively, it allows to find the lifetime if you know how many atoms decayed within a specific time. The formula does not help if you know neither.

bhobba and aylakadamk
mfb said:
It is unknown if the proton is stable or not. That also means you cannot calculate its lifetime. You can make some specific assumptions and ask "if those things are true, does it lead to proton decay and what is its lifetime?", but as you noted, those calculations are complicated.

There is an experimental lower limits on the lifetime. This means "if the lifetime would be lower than this value, we would have seen decays".

We know it very well. This has nothing to do with proton decays.This is not true. You cannot combine lifetimes like that. Also, "the lifetime of a quark" is not a meaningful concept, as quarks do not occur on their own.

That formula will tell you how many atoms decay within a specific time if you know the lifetime. Alternatively, it allows to find the lifetime if you know how many atoms decayed within a specific time. The formula does not help if you know neither.

Thanks a lot for the valuable information you've provided.

According to grand unified theory, which is an extension of the standard model, when two quarks get close enough, they exchange an X or Y boson, which are gauge bosons in grand unified theory, the quarks will be converted into leptons, and if they are parts of a proton, the proton will decay. Since the X and Y bosons, if they exist, are very heavy, they would be very short range, so it would be rare that two quarks within a proton would stray that close, which means the proton lifetime would be very long. The proton lifetime would be even longer if you take supersymmetry into account.

aylakadamk
Thanks a lot for your help.

Just a tidbit about proton decay that I read once upon a time. For protons to decay in a reasonable amount of time depends on whatever grand unified theory you have. However, there is an argument that protons must decay, regardless of the GUT, given by tHooft (I believe). I don't remember the details of the argument, but the upper bound on the proton's lifetime given by his calculation is so huge as to make the decay essentially unobservable, but it is interesting that there IS an upper bound.

I suppose there is another argument that uses semi-classical GR: Black holes are completely characterized by their mass, charge and angular momentum. So the formation of a black hole and its subsequent destruction through Hawking radiation will not preserve baryon number.

aylakadamk
Thanks a lot for your help.

## 1. How is the proton's lifetime calculated?

The proton's lifetime is calculated by using quantum field theory and the Standard Model of particle physics. This involves analyzing the interactions between protons and other particles, such as electrons, photons, and W and Z bosons.

## 2. Why is calculating the proton's lifetime important?

Calculating the proton's lifetime is important because it helps us understand the fundamental properties of matter and the behavior of subatomic particles. It also has implications for the stability of the universe and can provide insights into the nature of dark matter and energy.

## 3. What is the current estimated lifetime of a proton?

The current estimated lifetime of a proton is on the order of 10^33 to 10^35 years. This is an extremely long time, as the universe is only estimated to be around 13.8 billion years old.

## 4. How accurate are current calculations of the proton's lifetime?

The accuracy of current calculations of the proton's lifetime is limited by the precision of experimental data and the complexity of the calculations involved. However, these calculations are constantly being refined and improved upon as new data and techniques become available.

## 5. Are there any experiments being conducted to test the calculated proton's lifetime?

Yes, there are several experiments being conducted to test the calculated proton's lifetime. These include experiments at particle accelerators, such as the Large Hadron Collider, as well as experiments using natural sources of high-energy particles, such as cosmic rays. These experiments aim to observe proton decay, which would provide evidence for the calculated lifetime.

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