Neutral Kaon Decay

Factual Questions
1

So I was reading Robert L. Forward’s book Indistinguishable from Magic (which my wife and I call the “Ebert book” because of the guy on the cover) and in the final chapter Forward claims that there are experiments which show that a neutral kaon decays into two pions at a different rate than two pions turn into a neutral kaon.

Now, I had vaguely heard of these experiments before, but I didn’t know the details. But it seems to me that while a neutral kaon (strangeness=1) will decay into pions (strangeness=0) via the weak nuclear force, pions have to combine into kaons via the strong nuclear force. Since strangeness is conserved in strong force interactions, then the reaction would have to form two strange particles, one with strangeness=1 and the other with strangeness=-1. (I happen to be reading a particle physics book right now, but the section on strangeness didn’t mention the experiments which Forward describes.)

So what gives?

-Ben

2

Perhaps this is why kaon decay is not time symmetric?

3

This site, notes:

4

A-ha!
http://hyperphysics.phy-astr.gsu.edu/hbase/particles/kaon.html#c1
It seems that there are kaons which have a strangeness of 0.

5

The chart at that site lists all kaons as having a strangeness of +1.

-Ben

6

I’m not sure what the question is, but it sounds like “How can we produce [sym]K[/sym] particles, given that you need to conserve strangeness in a strong interaction?”

The answer is, as you already know, is that we need to produce one of each strange and anti-strange. Fortunately, it is relatively ‘easy’ to induce such a reaction if you have the energy to do it. A typical way to produce kaons is to shoot a baryon or nucleon (a collection of baryons) at another baryon or nucleon with sufficient energy.

Let’s look at baryon-baryon because that’s simpler to talk about, and I’m far from an expert. Let’s collide two protons. A proton is made of two up quarks and one down. Let’s do the simplest reaction that just produces the strange quarks. So, we have:

uud + uud + E[sub]0[/sub] -> uds + us + uud + E[sub]1[/sub]

where E is energy and underlining indicates an anti-particle. Assuming that neither of the resulting baryons are excited, that would be

[sym]L[/sym][sup]0[/sup] + [sym]K[/sym][sup]+[/sup] + proton (here, underlining is hyperlink, not anti-particle.)

One thing you can do to increase the rate of production, or ‘cross-section’, for this reaction, is to tune your energy (meaning 2 * proton mass + E[sub]0[/sub]) to approximately the mass of the resulting particles - production of a particular reaction spikes around that energy, and this is called a ‘resonance’. So, if you have a tunable accelerator, you can reliably create a given reaction and a decent rate.

Note that E[sub]0[/sub] - E[sub]1[/sub] is not just the energy of creating a strange-antistrange pair, but also involves other factors such as the binding energy the resulting baryons have. So, different reactions that also only create a strange-antistrange pair will have different resonance energies. This is reflected by the different masses of even baryons with the same quark composition - see Table of baryons and notice that [sym]L[/sym][sup]0[/sup] and [sym]S[/sym][sup]0[/sup] have the same quark composition but different masses.

Now, I hope that’s at least somewhat clear. Let me know if I can try to clarify anything, and perhaps we can get participation from those who either took more particle physics than I did or who did it more recently.

7

(create a given reaction at a decent rate…)

8

Er, yeah. right under the colums with the “S” on top.

sigh

9

This has never been directly measured, because although two pions can form a neutral kaon, there’s a lot of other things they can form much more easily, so you’ll have a lot of noise in your experiment. What we actually have measured is a bit more complicated. Let me try to start from the beginning:

There’s three important symmetries in particle physics, called C (charge), P (parity), and T (time). Charge symmetry means that if you replace all particles in a reaction with their antiparticles, the reaction will still occur in the same way. Parity symmetry means that if you look at the reaction in a mirror, what you see in the mirror will also be a valid reaction. Time symmetry means that if you run the tape of a reaction backwards, you’ll see a valid reaction.

Now, it turns out that the weak interaction really does a number on both C and P symmetries (beta decay, for instance, is 100% asymmetric), but if you combine the two, then CP turns out to still be a pretty good symmetry: If you replace all particles with their antiparticles, and look at the whole works in a mirror, you’ll see something valid.

Except, as it turns out, in a few oddball cases like the neutral kaon (I think the only other known example is the B[sup]0[/sup] meson). With neutral kaon decay, there’s a deviation from perfect symmetry of about one part in a thousand. What’s this have to do with the OP? Well, it’s been mathematically proven that if anything we know about quantum mechanics is even remotely close to true, then CPT must be a perfect symmetry. This means that if there’s a violation of CP to one part in a thousand, then there must also be a corresponding violation of T of the same amount. This means, in turn, that the reaction K[sup]0[/sup] --> [sym]p[/sym][sup]+[/sup] + [sym]p[/sym][sup]-[/sup] does not have the same amplitude as the reaction [sym]p[/sym][sup]+[/sup] + [sym]p[/sym][sup]-[/sup] --> K[sup]0[/sup].

To answer a tangential question, by the way: There are no kaons with zero strangeness. There are, however, kaons that don’t have a strangeness at all. The K[sup]0[/sup] is composed of ds, having a strangeness of +1, and its antiparticle the K[sup]0[/sup] is ds, having a strangeness of -1. You can also talk about the K[sub]1[/sub] and the K[sub]2[/sub], which are mixtures of the other two states (think Schroedinger’s Cat), and which therefore don’t have any particular definite strangeness. If you do something to measure the strangeness of a K[sub]1[/sub], say, you’ll find either +1 or -1, and the particle won’t be a K[sub]1[/sub] anymore, but rather a K[sup]0[/sup] or a K[sup]0[/sup].

10

The question concerns the fact that Robert L. Forward described a reaction in which two pions combine to make a neutral kaon. So far as I know, such a reaction is impossible, because strangeness is conserved under SNF reactions.

So, did Forward describe the experiment inaccurately? If so, then what is the real reaction which is observed? If not, then how can the reaction proceed when it creates a net strangeness out of nowhere?

-Ben