Wait, you say… how can we tell the difference between B → D e ν and B → D τ ν if the τ then decays to an e plus undetected neutrinos?! The reason is that on average the electron from the τ decay has lower energy (and there are other tricks too.) Even better, an electron-positron collider is a precision machine, unlike a hadron collider like the LHC, so the total energy and total momentum of the undetected neutrinos can be inferred from the measurement of everything that is detected. In this measurement, they are detected only when they decay to electrons or to muons, plus a neutrino and anti-neutrino that go undetected.
τ leptons can’t be measured directly, because they decay very quickly. The real story is quite a bit longer, as always.įirst, this is not a completely straightforward measurement. And recently the relative probabilities have been measured, by the BABAR experiment (which studied B mesons produced in the collisions of electrons and positrons at the Stanford Linear Accelerator Center in California the experiment was shut down in 2008, but data analysis continues.) The measurement differs from the prediction, coming in too high by what can arguably be said to be 3.4 standard deviations (3.4 “σ”.) But, with some difficulty, the difference in these probabilities can be predicted using the Standard Model’s equations. As a result, although the probability of B → D e ν and B → D μ ν are expected to be (and are measured to be) the same, the probability for B → D τ ν is not expected to be the same as for B → D e ν. Whereas a W particle has a mass of 80 GeV/c 2, so big that the tau lepton’s 1.8 GeV/c 2 mass is too small to play any role in the W’s decay, the B and D mesons have masses around 5.3 and 1.9 GeV/c 2 respectively, and the difference in those masses is not that much bigger than the tau’s mass. However, testing lepton universality in this particular context is a little tricky, because the masses of the three leptons are different - because their interactions with the Higgs field are not universal - and in this class of decays, the difference matters. The meson with a bottom quark is called a B, the meson with a charm quark is called a D, so for shorthand the decays to the three leptons and their corresponding anti-neutrinos are called B → D e ν, B → D μ ν and B → D τ ν. These decays occur via the weak nuclear force (more precisely, through the effect of a W “virtual particle” ) so the probability for such a decay in which a tau is produced should be related to the probability for the case where a muon or electron is produced. Only the bottom and charm quarks in the mesons are shown, but the mesons also contain an up and down anti-quark, along with many gluons and quark-antiquark pairs. The D meson will also rapidly decay to other particles (not shown) these must all be experimentally detected in order to know a D meson was present. The tau will rapidly decay, sometimes to an electron or muon, along with an undetectable neutrino and anti-neutrino. 1: Lepton universality predicts that the two processes shown - the decay of a B meson to a D meson, an anti-neutrino and a tau or electron, involving the weak nuclear force via a W `virtual particle’ - should differ in probability only through the calculable effect of the tau lepton’s mass, which makes the tau decay a bit less likely. (Specifically, the focus here is on hadrons called “mesons” which contain a bottom quark or charm quark, an up or down anti-quark,and, as for all hadrons, lots of gluons and quark-antiquark pairs.)įig.
This expectation has been tested many times for instance, the probability that a negatively charged W particle decays to an electron plus an electron anti-neutrino is the same as for it to decay to a muon plus a muon anti-neutrino, and the same for a tau plus a tau anti-neutrino, to very good precision.Īnother place (see Figure 1) to test “lepton universality” is in the decay of a hadron containing a bottom quark to a hadron containing a charm quark plus a lepton plus a corresponding anti-neutrino. Within the Standard Model of particle physics (the equations that describe and predict the behavior of all of the known particles and forces), the effects of the weak nuclear force on the three leptons - the electron, the muon and the tau - are all expected to be identical. The Basic Story (Slightly Oversimplified) A brief mention today of a new measurement from the BABAR experimental collaboration, which tests lepton universality (to be explained below) and finds it wanting.