What is the phenomena of Mixing?

[HeavyWater]

I absolutely do not get it. I have read the boards in this section. What is the phenomena of mixing? I am just asking a simple question. I don't need to know about the CKM matrix (at least not yet) or D-zero mesons. What is a simple example (if there is one) of mixing? What do I start with? What do I end with? What do we end up with something is mixed? Are we making something that doesn't already exist? I just don't understand the basic idea. ( I've looked in Sakuri, Messiah, Park, Segre)

Thanks for your patience,

 

[mfb]

What is a simple example (if there is one) of mixing? What do I start with? What do I end with?

A simple example: you start with $D^0$ and end with $\overline {D^0}$.
A particle transforms into its own antiparticle. That is the basic idea.

 

[Orodruin]

A simple example: you start with $D^0$ and end with $\overline {D^0}$.
A particle transforms into its own antiparticle. That is the basic idea.

I would not say that this is the basic idea with mixing, there is no requirement that the mixing occurs between particle and anti-particle. Instead, the point is that you have particles with the same quantum numbers, resulting in the possibility that the mass basis and the interaction basis are not simultaneously diagonalisable. Depending on the mass differences, this will lead to effects such as oscillations or interactions breaking flavor.

 

[vanhees71]

"Mixing" in the here given context is the phenomenon that the interaction Hamiltonian is not diagonal in the basis of mass eigenstates. That's the case for the quarks in the Standard Model. While in the strong interaction (QCD) the the interaction is diagonal in mass eigenstates, the weak interaction (QFD) is not, i.e., the weak-isospin (flavor) eigenstates defined through the coupling of the gauge fields to the currents (with the famous "V minus A" structure) are not the mass eigenstates of the quarks.

Now the weak interaction is treatable as a perturbative correction of the strong interaction, and thus the weak interaction is "flavor changing" from the point of view of the strong interactions.

This manifests itself also in the CP-violating transitions between the particle-antiparticle states of the neutral pseudoscalars. It was first discovered in the $\mathrm{K}_0 \bar{\mathrm{K}}_0$ system (Nobel prize for Cronin and Fitch 1964).

In the neutrino sector it's the only clear manifestation of physics beyond the Standard Model (Nobel prize 2015 for Kajita and McDonald/(Super)Kamiokande+SNO).

 

[mfb]

I would not say that this is the basic idea with mixing, there is no requirement that the mixing occurs between particle and anti-particle. Instead, the point is that you have particles with the same quantum numbers, resulting in the possibility that the mass basis and the interaction basis are not simultaneously diagonalisable. Depending on the mass differences, this will lead to effects such as oscillations or interactions breaking flavor.

Hmm right, and for neutrinos it is not mixing to antiparticles. The CKM matrix and D⁰ were mentioned, so I was thinking about hadrons only, where all the mixing happens between particle/antiparticle pairs.

 

[HeavyWater]

First, "thank you" to each of you: mfb, Orodruin, and Vanhees71.

"mfb"--I've been waiting for an answer like yours all my life (which sounds something like what Woody Allen said in "Play It Again Sam"). Your response hit a few chords and got me moving. Yes, I can see where its about a particle transforming into its anti particle. You got me thinking and I went back and looked up my Feynman lectures where he talks about the K-zero and K-zero-bar. You got my enthusiasm and curiosity moving.

Orodruin; your mention of phrases like mass basis, interaction basis, and "same quantum numbers" all make more sense now.

Vanhees71; your comments about mass eigenstates and diagonalization of the Hamiltonian make a lot more sense--but I clearly have some learning to do too.

Thanks to all 3 of you.