# Understanding the Particle Data Group review documents

Would someone mind outlining what each piece of semi-structured data means in these images taken of some PDG documents? As a newcomer it is very difficult to interpret the tables.

tl;dr

This question is mainly aimed at making it easy for newcomers to quickly get oriented in the world of particle physics and in reading through the PDG documents. Even though this is a bit long of a question, there are only a few key data elements in these PDG documents, so once those are explained briefly, it will be much easier for people to start reading through them.

Also, I am just beginning to learn more about particle physics, so am not very deep in it yet. The goal is to have a high-level idea of what's being summarized in these documents, so I know what specific topics in physics to dig into on my own.

Snapshot from a PDG document:

From the top to the bottom:

first section

• What is $I^G(J^P) = 1^−(0^−)$
• What is the $(S = 1.2)$ in $Mass\ m = 139.57018 ± 0.00035 MeV (S = 1.2)$.
• What is the $cτ = 7.8045 m$ just below and intented from $Mean\ life\ τ = (2.6033 ± 0.0005) × 10−8 s (S = 1.2)$. Along those lines, what does the indentation signify? (There's a few other places in the documents where indentation seems to be important, but I don't understand what it's saying).
• Is "$π± → ℓ± π νγ$ form factors" just some sort of decay equation?
• Where are the four variables ($F_V$, $F_A$, etc.) coming from? From the lines like $F_V = 0.0254 ± 0.0017$.

$π^±$ decay modes table

• What is the fraction $(Γ_i/Γ)$? I can get a sense of what the confidence level means from statistics (even though I haven't learned about that yet in physics).
• The first two lines in the table start like this:
• $µ^+ νµ$
•  $µ^+ ν_µγ$
• What does that indentation mean? $µ^+ ν_µγ$
• Are each of these "rows" in this table a "decay output"? So really you would write all of the equations like this:
• $π^±\toµ^+ ν_µ$
• $π^±\toµ^+ ν_µγ$
• $π^±\to e^+ ν_e$
• $π^±\to e^+ ν_eγ$
• $π^±\to e^+ ν_eπ^0$
• ...

All of these "decay output rows" (just what I'm calling them in this question for now) in the example seem pretty similar.

other examples

However, looking through some of the other "decay tables" in a document like http://pdg.lbl.gov/2014/tables/rpp2014-tab-mesons-light.pdf, you see other forms of values like these:

• $K^0_LK^0_S$
• $f_0(980)_γ$
• $ηU\to ηe^+e^-$ − $(ρ(1450)π)_S−wave$
• $a_0(980)π\ [ignoring\ a_0(980) \to K K]$
• $K K^*(892)+ c.c.$
• ...

Is all that stuff in the first column of the "decay tables" just the output/result of a decay equation like $π^± \to µ^+ ν_µ$, where the left-hand-side is whatever that section of the document is titled? (So in the first set of examples in the image, it would be $π^{+-}$).

• Almost every one of those 8+ questions should be separate. – dmckee Sep 14 '14 at 21:48
• I can separate them out if that is helpful, but really all I am looking for is a brief summary (like just a key term or a sentence or something) of what they are, and from there I can look for more detail on that particular topic on the web. If everything in that first column is just "decay output" or something like that, then that at least limits my confusion about it so I know where not to start looking. It would be good to know if there are a finite set of ways you can write decay equations, etc. I'm not asking what each equation means, just what it's generally talking about. – Lance Pollard Sep 14 '14 at 21:51
• @dmckee would you prefer I separate them out knowing that? – Lance Pollard Sep 14 '14 at 21:52
• Also, I have to ask: Have you read the footnotes? Many of the subquestions are answered in plain language in them. – dmckee Sep 14 '14 at 21:53
• I've looked through some of them, but in the first few documents I've seen so far not all of them were answered by the footnotes. Realistically it would take me at least a few hours, if not days, to find all the answers on my own. So I thought it would be nice to ask this question so myself and others could save that time in the future. – Lance Pollard Sep 14 '14 at 21:55

Briefly, but perhaps less briefly than the footnotes to the tables, and reflecting my own personal biases:

• The strings like $I^G(J^P) = 1^-(0^-)$ represent the quantum numbers of the particle. $I$ is isospin: the pion, with isospin 1, is a member of an isospin triplet ($\pi^+,\pi^0,\pi^-$). $J$ is spin: the pion is spinless. $P$ is spatial parity: the pion wavefunction changes sign under parity inversion, so its eigenvalue under the $P$ operator is $-1$. $G$-parity is another discrete symmetry that I personally have never used; about every two years I look it up out of curiosity. Neutral particles may also be eigenstates of the charge conjugation operator $C$ (if you look ahead to the $\pi^0$ entry you'll find it has eigenvalue $+1$ under $C$), but since $C$ changes the $\pi^+$ to a $\pi^-$ there's no eigenvalue to list.

• Values with a scale factor $S$ near an uncertainty have several recent competitive measurements which disagree by more than their individual uncertainties would predict. There's a long note about this in the full Review.

• $\tau$ is the decay lifetime. $c\tau$, which has units of length, is the distance that a particle can travel during its lifetime if you neglect length contraction and time dilation. Many discussions of special relativity use the muon's $c\tau = 650\,\mathrm m$ to argue that muons produced in the upper atmosphere should decay in the upper atmosphere rather than being detectable at sea level, then go on to derive the time dilation factor for relativistic cosmic ray muons. I suppose $c\tau$ is indented because it is a useful quantity but not something that is directly measured.

• The decay "form factors" $F_V,F_A$ have to do with the angular distribution of the decay products. You would need those if you were trying to simulate pions decaying in some detector. The use of $\ell$ (for "lepton") suggests that the same form factors can be used for pion decays to muons and for (rarer) pion decays to electrons.

• The decay width $\Gamma$ is related to the lifetime $\tau$ by $\tau = \hbar/\Gamma$ (perhaps with a factor of 2 or 2$\pi$ or $\log2$ somewhere). Decay widths have the nice property of adding linearly, while lifetimes add in inverse, like resistors in parallel. If I have a particle with two decay modes $a$ and $b$ with partial lifetimes $\tau_a$ and $\tau_b$, its observed lifetime will be reduced to $\tau = \left( \frac1{\tau_a} + \frac 1{\tau_b} \right)^{-1}$, but its observed width will be $\Gamma = \Gamma_a + \Gamma_b$. The PDG's notation $\Gamma_i/\Gamma_\text{total}$ simply suggests that all the decay modes should add up to 100%.

• As the footnotes explain, there is not a hard cutoff between the purely leptonic decay $\pi^+\to\mu^+\nu$ and the radiative decay $\pi^+\to\mu^+\nu\gamma$. If you like, you can think of the photon there as bremsstrahlung, and the question is whether it gets detected and whether it has enough energy to make a measurable difference in the decay energy spectrum. The related reactions are grouped as they are to aid people who want to make sure their different sub-reactions add up to 100%.

• Your stranger-looking decays are for heavier particles --- it looks like the first three examples are decay modes for the $\phi(1020)$, which is heavy enough to make strange quarks (bound in $K$ mesons) and shorter-lived unflavored mesons like the $a_0$.

One of the nice things about the enormous paper Review is that the introductory material which explains these things is much easier to find than in the online summary tables. It's really quite clear, and I suggest you look for it and digest it.

• This is amazing! Thank you so much, this helps tie a bunch of stuff together and gives me a great starting point to start digging into stuff. What is that Review paper, is it from PDG too? – Lance Pollard Sep 14 '14 at 23:55
• $c\tau$ for pions and kaons is particuarly useful to beam neutrino experimenters as a rule of thumb number. Beam energy/mass times $c\tau$ is the proper length scale for the decay pipe. And there are a few other cases where those kinds of approximations are handy. – dmckee Sep 15 '14 at 0:06
• The Particle Data Group's main product is the Review of Particle Physics, a 1600-page journal article which is updated and republished every couple of years. Excerpts from the Review, including the Summary Table you've excerpted here, are published as a smaller paper booklet. All of the content from the Review is available on the PDG website, somewhere, but I can never find the introductory stuff online when I want it. You can request to have the paper versions sent to you at no charge; the 2014 edition was completed this summer and will be shipping "soon". – rob Sep 15 '14 at 0:08
• Apropos of the full review: the PDG is considering stopping the paper publication of that document (it costs a mint, after all) and have sent out a survey through various channels to their core audience. If you have gotten one of those links I'd suggest that you fill it out with care and consideration. They are also considering cutting some of the material currently in the booklet to bring down both the size of the booklet and cost of that publication run as well. – dmckee Sep 15 '14 at 0:08
• @dmckee I voted for a full-sized paper Review and a smaller Booklet; thanks for the announcement. – rob Sep 15 '14 at 0:12