Calculation of proton's lifetime

[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.

 

[officialmanojsh]

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

 

[officialmanojsh]

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.

 

[officialmanojsh]

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! :(

 

[aylakadamk]

no problem :)

 

[mfb]

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".

We do not know the age of universe yet.

We know it very well. This has nothing to do with proton decays.

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.

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.

 

[aylakadamk]

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.

 

[jeffery_winkle]

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.

 

[stevendaryl]

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.