Tuesday, June 18, 2024

Measuring The Mean Lifetime Of A Short Lived Particle

The LHCb experiment has measured the mean lifetime of a particle called the bottom xi or cascade B baryon, a spin 1/2 baryon with a down quark, a strange quark, and a bottom quark as valence quarks, with a mass of 5,797.0 ± 0.6 MeV (between the mass of a helium atom and a lithium atom), which is the eighth most massive baryon ever observed (the most massive is the bottom omega baryon with a mass of 6,046.1 ± 1.7 MeV, which is a spin-1/2 baryon with two strange quarks and a bottom quark as valence quarks). 

Its mean lifetime is: 1.578 ± 0.018 ± 0.010 ± 0.011 ps which with a combined uncertainty is 1.578 ± 0.023 ps. A picosecond is 10-12 seconds (i.e. a trillionth of a second). As the linked article's abstract explains:

This measurement improves the precision of the current world average of the Ξblifetime by about a factor of two, and is in good agreement with the most recent theoretical predictions.

It is astounding that we can measure such a tiny span of time to better than 2% precision. The uncertainty in its lifetime is on the order of 40 trillionths of second. 

The measured value is about 0.2% less than the best theoretical prediction to date, and the theoretical prediction also has an uncertainty of about 2%, so the measured value is basically a perfect match to the theoretically predicted value.

There are at least fifteen possible decays of bottom xi baryons whose branching fractions are summarized by the particle data group. This history of this particle's discovery can be found here. The first experimental observation of this particle, which took place at Fermilab, was announced just over seventeen years ago, on June 12, 2007.

There are baryons which decay a trillion times faster, as little as 5.63 ± 0.14 x 10-24 seconds, usually to a pion and either a proton or a neutron, for the four kinds of spin-3/2 delta baryons which have only up and down quarks as valence quarks and masses of 1232 ± 2 MeV. 

There is nothing terribly notable about this most recent measurement of the mean lifetime of the bottom xi except that it was first publicly announced today in a preprint on arXiv.


neo said...

any theoretical principles to calculate this Mean Lifetime Of A fundamental Particle

andrew said...

Yes. It is rather straightforward.

Basically, you first list every possible path by which it could decay, while conserving baryon number, electromagnetic charge, lepton number, mass-energy, spin, etc. This is particularly easy for baryons since their valence quarks are well defined.

Then, you draw a Feynman diagram for each possible decay.

Then you do a fairly straightforward calculation that is easily constructed for each Feynman diagram, which will give you an electron volt value called the width of that decay path.

Then you add up the widths of all of the possible decay channels which is called the width of the particle.

Then you take one divided by the width and convert that to seconds using a unit conversion factor.

The measured value was about 0.2% less than the theoretically predicted value in the Standard Model, which itself has an uncertainty of about 2% (which is similar to the uncertainty in the measured value). This uncertainty is, in part, because the infinite series QCD calculations are hard to do precisely, and, in part, because some key parameters but especially the strong force coupling constant, are only known a little more precisely than that. It is more precise than some lighter baryons because the bottom quark mass is another key parameter and the measured value of the bottom quark mass has little relative error.

Of course, a bottom xi isn't a fundamental particle. It is, instead, a composite particle. But the formula in the Standard Model for calculating the mean lifetime of a fundamental particle and the formula in the Standard Model for calculating the mean lifetime of a composite particle is the same.

neo said...

so how would you calculate from first principles the mean lifetime of a muon or tau, or top or bottom quark, or neutrino ossicilation or w, z or higgs boson?

could these be adapted to calculate particle masses such as the koide mass formula for leptons?

andrew said...

This is how you calculated the mean lifetime of a muon or tau or top quark or W or Z or Higgs boson. You can't calculated the decay of a b quark separately since it is always confined in a hadron. A neutrino oscillation is different (since it isn't a decay).

"could these be adapted to calculate particle masses such as the koide mass formula for leptons?"

No. The mass is a key component of the calculation of the mean lifetime. It is an input that can't be reverse engineered without knowing all of the decay products (which indirectly contains the mass anyway) and the mean lifetime.