Why are there not up and down quantum numbers?


by center o bass
Tags: numbers, quantum
center o bass
center o bass is offline
#1
Mar21-12, 09:49 AM
P: 423
Hi. I am a bit confused by the fact that there are quantum numbers related to every flavour of quark except the up and down. A consequence of this is that the neutral pion is it's own anti-particle while the neutral kaon is not. Why is this so?
Phys.Org News Partner Physics news on Phys.org
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Mapping the road to quantum gravity
Chameleon crystals could enable active camouflage (w/ video)
Nabeshin
Nabeshin is offline
#2
Mar21-12, 11:32 AM
Sci Advisor
Nabeshin's Avatar
P: 2,194
A neutral pion is either [itex] u \bar{u} [/itex] or [itex] d \bar{d} [/itex]. In either case, the antiparticle gives the identical thing (remember, order isn't important!).

A neutral kaon, on the other hand, is [itex]d \bar{s} [/itex], whose antiparticle is [itex] \bar{d} s[/itex], clearly not the same thing.

A caveat is that you can have the kaon as a superposition, like [itex] \frac{1}{\sqrt{2}} \left( d \bar{s} \pm \bar{d} s \right) [/itex], in which case it IS its own antiparticle.
fzero
fzero is offline
#3
Mar21-12, 12:23 PM
Sci Advisor
HW Helper
PF Gold
P: 2,606
You can assign either upness or downness as a quantum number. These flavor quantum numbers can be viewed as the remnants of an [itex]SU(N_f)[/itex] flavor symmetry that would be present in the absence of quark masses. Maximally breaking this symmetry via quark masses leaves the [itex]U(1)^{N_f-1}[/itex] symmetry associated to the flavors. Typically we choose the up quark to be neutral, with each other quark having charge one under a separate factor.

Edit: I should add that downness isn't such an interesting quantum number since the electric charge already distinguishes between the up and down quark (so no analogy of the neutral kaon as already pointed out.)

AdrianTheRock
AdrianTheRock is offline
#4
Mar21-12, 04:30 PM
P: 136

Why are there not up and down quantum numbers?


Quote Quote by Nabeshin View Post
A neutral pion is either [itex] u \bar{u} [/itex] or [itex] b \bar{b} [/itex]...
I assume the latter is a typo, and what you meant was [itex] d \bar{d} [/itex].
Nabeshin
Nabeshin is offline
#5
Mar21-12, 06:00 PM
Sci Advisor
Nabeshin's Avatar
P: 2,194
Quote Quote by AdrianTheRock View Post
I assume the latter is a typo, and what you meant was [itex] d \bar{d} [/itex].
ty :)
tom.stoer
tom.stoer is offline
#6
Mar21-12, 06:05 PM
Sci Advisor
P: 5,307
the reason is simple; you don't call it up-ness or down-ness but isospin
samalkhaiat
samalkhaiat is offline
#7
Apr1-12, 05:43 PM
Sci Advisor
P: 817
Quote Quote by Nabeshin View Post
A caveat is that you can have the kaon as a superposition, like [itex] \frac{1}{\sqrt{2}} \left( d \bar{s} \pm \bar{d} s \right) [/itex], in which case it IS its own antiparticle.

You cannot have such superposition and the neutral Kaon can never be its own antiparticle! Because strong interaction conserves strangeness while the weak interaction does not, the neutral Kaon eigenstates with respect to these interactions are very different from each other; the strong-interaction eigenstates [itex]K_{0} \sim d \bar{s}[/itex] and [itex]\bar{K}_{0} \sim s \bar{d}[/itex] can MIX through weak transitions such as the one with two pions as intermediate state. In this [itex]K_{0}- \bar{K}_{0}[/itex] mixing, the [itex]\bar{K}_{0}[/itex] is the [itex]CP[/itex] conjugate of [itex]K_{0}[/itex],
[tex]|\bar{K}_{0}\rangle = CP|K_{0}\rangle .[/tex]
The mixing can be described by “effective Hamiltonian” having two eigenstates with very different lifetimes,
[tex]K_{S} = \frac{1}{\sqrt{2(1 + |\epsilon |^{2})}}\{ (K_{0} + \bar{K}_{0}) + \epsilon (K_{0} - \bar{K}_{0}) \}[/tex]
[tex]K_{L} = \frac{1}{\sqrt{2(1 + |\epsilon |^{2})}}\{ (K_{0} - \bar{K}_{0}) + \epsilon (K_{0} + \bar{K}_{0}) \}.[/tex]

Sam


Register to reply

Related Discussions
Quantum Numbers Introductory Physics Homework 3
quantum numbers High Energy, Nuclear, Particle Physics 0
Quantum Numbers Quantum Physics 6
about quantum numbers Quantum Physics 1
quantum numbers High Energy, Nuclear, Particle Physics 11