# How does one categorize antiparticles in flavor, family and generation?


The following terminology was introduced to me in the context of the basic six leptons:

• $\bf\A$: the (negatively) charged leptons
• $\bf\B$: the neutrinos, aka the neutral leptons
• $\textbf{1st}$: the first generation of leptons, aka the electronic leptons; least massive and most stable within respective rows
• $\textbf{2nd}$: the second generation of leptons, aka the muonic leptons; medium mass and medium stability within respective rows
• $\textbf{3rd}$: the third generation of leptons, aka the tauonic leptons; most massive and least stable within respective rows
• flavors: the six distinct categories into which a lepton can fall, as reflected by its symbol

In reality, however, this vocabulary is not comprehensive, because there are antileptons as well:

$$\begin{array}{|c|ccc|} \hline { } & \text{X} & \text{Y} & \text{Z} \\ \hline \text{A} & \rm e^- & \rm μ^- & \rm τ^- \\ \text{B} & \rm ν_e & \rm ν_μ & \rm ν_τ \\ \hline \text{C} & \rm e^+ & \rm μ^+ & \rm τ^+ \\ \text{D} & \rm \bar{ν}_e & \rm \bar{ν}_μ & \rm \bar{ν}_τ \\ \hline \end{array}$$

This is where I become unsure about which terms apply where, so I’ve identified some direct questions that should clear things up:

1. Are $\rm e^-$ and $\rm e^+$ the same flavor?
2. Are all four particles in column $\text Y$ considered muonic and in the same generation, or are there separate generations for leptons and antileptons?
3. Is there a situation in which one would need to say that $\rm τ^-$ and $\rm ν_τ$ are in a different “family” from $\rm τ^+$ and $\rm\bar{ν}_τ$, or is this a term that I have imagined in my own mind without actually encountering it?
4. Does the term neutrinos definitively exclude row $\text D$? I believe not, but it seems relevant to bring up here.

If you could provide a brief real-world example to justify each answer, that would be wonderful.

Are e− and e+ the same flavor?

I am not convinced that the term "flavor" is used in a consistent enough manner to provide an authoritative answer to this question.

I also see the term "flavor" used more frequently to describe neutrinos than to describe charged leptons, in part, because it is used in the context of neutrino oscillation which is a subject about which a great many papers are written, while flavor changing W boson interactions in charged leptons are well understood and hence do not produce many scientific articles.

Are all four particles in column Y considered muonic and in the same generation, or are there separate generations for leptons and antileptons?

All four particles in column Y are second generation leptons and second generation fermions. I do not see the term "muonic" used an an adjective to mean of the second generation of fermions, or of the second generation of leptons, very frequently.

Is there a situation in which one would need to say that τ− and ντ are in a different “family” from τ+ and ν¯τ, or is this a term that I have imagined in my own mind without actually encountering it?

I've seen the word "family" used in the literature, so you aren't imagining things. But, like "flavor", I am not convinced that the term "family" is used in a sufficiently consistent way for this question to have an authoritative answer.

Does the term neutrinos definitively exclude row D? I believe not, but it seems relevant to bring up here.

No. Ordinary neutrinos in row B have left parity. Antineutrinos in row D have right parity. Both neutrinos in row B and antineutrinos in row D interact via the weak force.

When someone refers to hypothetical "right handed neutrinos" they means leptons with neutral electrical charge for which right handed neutrinos have right parity, and right handed anti-neutrinos have left parity.

Hypothetical "right handed neutrinos"(not present in the Standard Model because they have no Standard Model interactions, but popular in extensions of the Standard Model, often as dark matter candidates) would not interact via the weak force, the electro-magnetic force, or the strong force, so they would need to have some new form of interaction of their own. Because they are not charged under any of these three forces, hypothetical "right handed neutrinos" are also known as "sterile neutrinos" in contrast to ordinary "active neutrinos". Sometimes people describe ordinary neutrinos, in a somewhat tongue in cheek manner, as "fertile neutrinos" in contrast to hypothetical "sterile neutrinos".