When determining if a decay is possible, is there a method to use?

[rwooduk]

Hi, I'm in the process of revision for upcoming exams, one likely question will give a number of decays (~5) and ask if they are possible.

I understand baryon number, lepton number (and parity, isospin, and strangeness) must be conserved, but for example for the following:

K+ -> neutral pion + positron + electron neutrino

K+ -> neutral pion + positive pion

p -> neutral pion + positron


What's the best way to determine if they are possible? Also it will ask about the force responsible for the decay, how do i determine this?

Thanks in advance for any guidance!

 

[Simon Bridge]

You just have to go through the conservation laws one at a time.
Make a chart for which interaction requires which laws.

 

[rwooduk]

You just have to go through the conservation laws one at a time.
Make a chart for which interaction requires which laws.

thanks for the reply.

the problem seems to be that for example:

K+ -> neutral pion + positron + electron neutrino

the pion doesn't have a lepton number, do i just take it as zero because it is not a lepton? how would i analyse this particular decay?

 

[rwooduk]

also i found this:

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/allfor.html

which talks say "One way to examine a decay is to list the quark content of each of the particles." , is there a way to say if it is possible by seeing if the quarks balance? the example it gives:

doesnt really help, how do the quark components balance in that image?

 

[Simon Bridge]

Also see:
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/parint.html

in $K^+\rightarrow \pi^0 + e^+ + \nu_e$

K and pi are mesons.
mesons have baryon and lepton number 0.

You can check the quarks just bear in mind the weak interaction.

 

[ChrisVer]

also i found this:

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/allfor.html

which talks say "One way to examine a decay is to list the quark content of each of the particles." , is there a way to say if it is possible by seeing if the quarks balance? the example it gives:

doesnt really help, how do the quark components balance in that image?

What do you mean by the quark components balance?
you will have that the u\rightarrow u and \bar{d}\rightarrow \bar{d}... one of the quarks will emit a gluon (by that you see the strong interaction) which will then give you the rest quark contents you need of a u\bar{u} or d\bar{d}...
So there is no need of a quark balance- one fast way to see that is by hadronization: you have one particle interacting with some other and you get jets of many particles coming out of such an interaction... so the quarks don't have to be balanced... This image can be helpful in seeing what kind of process you are having by knowing how quarks interact.
Also be careful with the weak interactions, since they can change flavors (turn an up quark into a down), which is illustrated by the beta decay:
udd (n) \rightarrow uud (p) + e^{-} + \bar{v}_{e}
the neutrino's down quark is changed to proton's up by emiting a W^{-} boson which decays to the electron+antineutrino
Also...
Strangeness can be violated by weak interactions... That's because all other interactions cannot mix the flavor components, while the weak can...The same goes for the isospin...
Parity can be violated by the weak interactions too...So given an interaction which violates parity, the only thing you have to check is whether weak interaction is possible or not.
CP can also be violated in certain weak interactions

 

[rwooduk]

Awesome replies as ever! Thanks guys, really appreciated!