# What does the first column in the "decay modes" table mean (in Particle Data Group documents)?

As a follow-up to this more general question, what are the values in the first column of each of the "decay tables" in a PDG document describing?

What are those things in the first column? Are they just decay equations? That is, could you rewrite all of those like this?

• $f_0(1370) \to ππ$
• $f_0(1370) \to 4π$
• $f_0(1370) \to 4π^0$
• $f_0(1370) \to 2π^+2π^-$
• $f_0(1370) \to π^+π^-2π^0$
• $f_0(1370) \to ρρ$
• $f_0(1370) \to 2(ππ)_{S-wave}$
• ...

Or do they mean something different? Basically, what are they saying in general? Looking through the the document linked to in the image above, there are many different forms those values in the first column of the "decay modes" table take. Is there a standard sort of "syntax" for writing these things out?

Also, what does the indentation signify? That is, why is there a bunch of stuff nested under $4π$ and stuff under $6π$?

I addressed this a little at your other question but this one is more like physics.

Yes, they're decay product lists. Beware that if all the modes are only "seen" or "not seen," you are sort of looking at the hairy edge of what's experimentally accessible.

The indented lines are subtypes of the same reaction. Using your example, a neutral particle can decay to four pions by emitting

• four neutral $\pi^0$,
• two each $\pi^+$ and $\pi^-$,
• or a charged pair and two neutrals.

• Since the $\rho$ meson also mostly decays to two pions, in much less time than it takes to reach a detector, a decay to $\rho\rho$ will also show up in the four-pion data set.

• You might also decay to two bound $\pi\pi$ "molecules", or to a pion coupled with a heavier meson like the $\pi(1300)$ or $a_1(1260)$ which turns into three pions before reaching the detector.

These all get lumped together because they all look like four pions at the final detector; to distinguish them you have to reconstruct the energies and momenta of the individual pions in each decay and decide whether they are distributed like a real four-body decay or like a series of fewer-body decays.