## Sunday, October 23, 2016

### About Time Scale In The Standard Model

The linked video is a powerful illustration of the notion of different orders of magnitude of scale from the human scale on up.

It doesn't go the other direction and only looks at distance, however.

Since I am often guilty of lumping all small time intervals into the tiny "ephemeral" category, I'll do penance by touching on the remarkable orders of magnitude differences is decay rates in particle physics.

There are actually huge disparities of scale between the mean lifetimes of various fundamental particles and hadrons (27 orders of magnitude from the shortest lived to the longest lived unstable particle to be exact). It is hard to get you head around numbers like that. It is particularly hard to do when humans have no ability to consciously distinguish between all but the two or three longest time periods involved.

To help you do so, let's look at all of mean lifetimes for fundamental particles and hadrons that have been measured experimentally, from longest to shortest in mean lifetimes (all data via Wikipedia) in terms of a scale where the mean lifetime of a W boson (the shortest lived particle, tied with the Z boson) is set arbitrarily at 1 W second, which can make this easier to understand (below the break).

 Particle name Symbol Quark content Multiples of W Boson Lifetime = 1 W second Nucleon/proton p  /  p+  /  N+ Stable Not Applicable Nucleon/neutron n  /  n0  /  N0 8.800×10+2 92 sextillion W years Muon μ− not applicable 2.1969811×10−6 232 billion W years K-Long complex{\displaystyle \mathrm {\tfrac {d{\bar {s}}+s{\bar {d}}}{\sqrt {2}}} \,}Coocomplc 5.116×10−8 5 billion W years Pion 2.6033×10−8 3 billion W years Kaon 1.2380×10−8 1 billion W years K-Short complex{\displaystyle \mathrm {\tfrac {d{\bar {s}}-s{\bar {d}}}{\sqrt {2}}} \,} 8.954×10−11 10 million W years Omega 8.21×10−11 9 million W years B meson 1.638×10−12 173,022 W years B meson 1.519×10−12 160,452 W years Strange B meson 1.512×10−12 159,712 W years bottom Omega 1.13×10−12 119,362 W years D meson 1.04×10−12 109,855 W years strange D meson 5.00×10−13 52,815 W years Charmed B meson 4.52×10−13 47,745 W years D meson 4.101×10−13 43,319 W years Tau lepton τ− not applicable 2.906×10−13 30,696 W years double charmed Xi 3.3×10−14 3,486 W years Pion complex 8.52×10−17 9 W years Eta meson complex{\displaystyle \mathrm {\tfrac {u{\bar {u}}+d{\bar {d}}-2s{\bar {s}}}{\sqrt {6}}} \,} 5.02×10−19 19 W days Sigma 7.4×10−20 69 W hours Upsilon meson ϒ (1S) 1.22×10−20 11 W hours D meson D∗+ (2010) 7.89×10−21 7 W hours J/Psi 7.09×10−21 7 W hours Eta prime meson η′ (958) complex{\displaystyle \mathrm {\tfrac {u{\bar {u}}+d{\bar {d}}+s{\bar {s}}}{\sqrt {3}}} \,}complex 3.32×10−21 3 W hours Strange D meson 3.4×10−22 18 W minutes bottom Xi 3.1×10−22 17 W Minutes D meson D∗0 (2007) 3.1×10−22 17 W minutes charmed Xi Ξ∗+ c(2645) 2.1×10−22 11 W minutes Phi meson ϕ (1020) 1.54×10−22 8 W minutes charmed Sigma 3.05×10−22 17 W minutes charmed Sigma 2.91×10−22 16 W minutes charmed Sigma 1.43×10−22 8 W minutes bottom Sigma 1.34×10−22 7 W minutes charmed Xi Ξ∗0 c(2645) 1.2×10−22 7 W minutes bottom Sigma 8.8×10−23 5 W minutes Omega meson ω (782) {\displaystyle \mathrm {\tfrac {u{\bar {u}}+d{\bar {d}}}{\sqrt {2}}} \,}complex 7.75×10−23 4 W minutes Ξ∗0 (1530) 7.23×10−23 4 W minutes bottom Sigma 6.8×10−23 4 W minutes Xi Ξ∗− (1530) 6.6×10−23 4 W minutes bottom Sigma 5.7×10−23 3 W minutes charmed Sigma Σ∗0 c(2520) 4.54×10−23 3 W minutes charmed Sigma Σ∗++ c(2520) 4.42×10−23 148 W seconds charmed Sigma Σ∗+ c(2520) 3.87×10−23 129 W seconds Kaon 3.26×10−23 110 W seconds Charmed eta meson η c(1S) 2.04×10−23 68 W seconds Sigma Σ∗+ (1385) 1.839×10−23 61 W seconds Sigma Σ∗0 (1385) 1.83×10−23 61 W seconds Sigma Σ∗− (1385) 1.671×10−23 56 W seconds Kaon 1.39×10−23 46 W seconds Delta Δ++ (1232) 5.63×10−24 19 W seconds Delta Δ+ (1232) 5.63×10−24 19 W seconds Delta Δ0 (1232) 5.63×10−24 19 W seconds Delta Δ− (1232) 5.63×10−24 19 W seconds Neutral rho meson ρ0 (770) complex{\displaystyle \mathrm {\tfrac {u{\bar {u}}-d{\bar {d}}}{\sqrt {2}}} \,} 4.45×10−24 15 W seconds Charged rho meson ρ+ (770) 4.41×10−24 14 W seconds Top quark t t 5×10−25 2 W seconds W+/- boson W+/W- not applicable 3×10−25 1 W second Z boson Z not applicable 3×10−25 1 W second

Notes on The Table

1. For these purposes, I have disregarded experimental uncertainties (which generally do not change the order of magnitude of the time frame involved).

2. When a particle has a mean lifetime less than a given value have used the maximum value for that particle without annotation.

3. The W second based times in the table were rounded to remove all decimal quantities, after the mean lifetime in seconds shown in the table for each entry was converted to W second units.

4. Mesons with complex quark content are blends of mesons with different quark contents or with different kinds of blending.

5. The term "not applicable" in the fundamental particle column applies to particles treated as fundamental in the Standard Model.

6. The common names of the hadrons given is sometimes ambiguous because they omit designations of electric charge and spin, but the symbols are generally unambiguous.

7. Anti-mesons of the types shown (which are identical for electrically neutral mesons) have been omitted because they have the same mean lifetimes as the meson shown.

8. The table inadvertently omitted the Higgs boson which has a mean lifetime of 1.56×10−22 seconds, which is about 9 W minutes.

9. The table also omits electrons, photons, gluons and neutrinos. Electrons, photons and gluons are "stable" in the Standard Model, although in practice, gluons are short lived because they tend to interact with other particles at very short ranges and travel at the speed of light (apart from dynamically acquired mass). Neutrinos in the Standard Model oscillate but do not decay in the sense relevant to determining a mean lifetime.

10. Mean lifetime can be converted to half-life by dividing the mean lifetime by approximately 1.44 (more precisely the natural logarithm of 2).

Incidentally, don't assume that you can advance science by decoding the patterns in this chart, because that is a problem that has already been solved by the Standard Model of Particle Physics. Mean lifetimes are derived quantities in the Standard Model (even in the case of fundamental particles like the Higgs boson) that can be calculated from first principles without too much difficulty. Essentially, you just add up the decay times of every possible path of decay in the appropriate way.

Composite particles with decay products that can be formed without W boson interactions are generally much shorter lived than those that can only be formed with a W boson flavor changing interaction.  The weak force and strong force coupling constants drive the speed of the respective decay paths.