As I discussed a BaBar result previously, it only seemed fair that I spend a post discussing a Belle one. For those of you who only associate the words BaBar and Belle to cartoon characters, they are also the names of two competing \(B\) physics experiments, both of which have finished data taking but are still producing results.
So which Belle result have I decided to discuss today? I’m going to talk about the updated measurement of the \(B^- \rightarrow \tau^- \overline{\nu}_\tau\) branching ratio that was first presented by Youngmin Yook in a parallel session at ICHEP and now can be found on arXiv.
Why would I choose this measurement you ask? Let’s have a look at the Feynmann diagram of the process on the right here. In the Standard Model, the decay can only proceed via the exchange of a \(W^-\) boson and so the branching ratio can be translated to a measurement of \(V_{ub}\), one of the CKM quark mixing matrix elements. However, new physics could significantly modify the branching ratio via the exchange of a new charged particle, like a charged Higgs boson.
An updated result of the branching ratio is even more interesting than that though, because the average of the previous consistent experimental measurements from Belle and BaBar, \((1.67 \pm 0.30)\times10^{-4}\), is higher than the prediction from CKM fit, \((0.733^{+0.121}_{-0.073})\times10^{-4}\) and the Standard Model \((1.2 \pm 0.25)\times10^{-4}\). This is what is shown on the left here, where the blue point is the average of the previous results, and the green area is the CKM fit prediction. Could this be due to new physics?
Experimentally, it is quite difficult to measure \(B^- \rightarrow \tau^- \overline{\nu}_\tau\) decays, due to the multiple undetectable neutrinos in the final state (as well as the one from the \(B^-\) decay, there is also at least one from the \(\tau^-\) decay). In fact, I’m pretty sure that we can’t perform this measurement at LHCb at all.
Belle and BaBar are able to as their \(B\) meson pairs are produced through the well defined process \(e^+e^− \rightarrow \Upsilon(4S) \rightarrow B\overline{B}\) and their detectors cover a larger solid angle, which allows them to make a fairly accurate estimate of neutrinos produced in decays. To the right, here is a plot of the extra detected energy in selected events, where the points are the data, the red dotted line shows the signal, the dashed blue line shows the background and the red solid line shows the total fit. They expect the signal to peak at zero, since neutrinos can’t be detected.
For the full details of the analysis, I encourage you all to look at the paper, here I’m only going quote the result: \([0.72^{+0.27}_{-0.25}(stat) \pm 0.11(syst)] \times 10^{−4}\) and then discuss the implications…
Firstly, does this new result bring the experimental average closer or further away from the predictions? As presented by Mikihiko Nakao in a plenary session at ICHEP, the plot below shows that the new Belle average (bottom blue point) and the new experimental average (red point) are both consistent with the CKM fit and Standard model predictions (pink and yellow bands respectively). So no hint for new physics here…
Secondly, since this result doesn’t seem to point to new physics, what does it say about \(V_{ub}\), the Standard Model parameter describing the mixing between the \(u\) and \(b\) quarks? As presented by Phillip Urquijo, also in a plenary session at ICHEP, below is a comparison of the various measurements of \(V_{ub}\), which has historically been an area of \(B\) physics which requires further investigation. This is because there are two different methods to measure \(V_{ub}\), called inclusive and exclusive, depending on what type of \(B\) decays are used, and there is currently a discrepancy between the two, which people have been trying to understand. And interestingly… the \(V_{ub}\) measurement from \(B^- \rightarrow \tau^- \overline{\nu}_\tau\) is in agreement with both methods…
