## Friday, November 16, 2018

### Three Sigma Tension Seen In Standard Model Parameter Measurement

The Standard Model has lots of experimentally measured physical constants. One set of those physical constants describe the CKM matrix (the letters are the first initials of the surnames of the scientists who came up with it).

The CKM matrix measures the probability that a quark of one type will turn into a quark of another type, conservation of mass-energy permitting. (To be precise, the matrix elements themselves are the square roots of the relevant probabilities.)

There are eighteen possible transitions between quark types in W boson mediated interactions whose probabilities can are described in the Standard Model by four parameters. These parameters are measured by measuring how often the eighteen possible transitions take place in various kinds of experiments and using that data to fit the four parameters.

One of the eighteen possible transitions is the probability of a transition from an up quark to a strange quark. There are many ways that this can be measured. One way to measure it involves the decays of a compound particle knowns as a kaon. Another way to measure it, used in the most recent experiment, involves decays of a fundamental particle known as a tau lepton. It can also be measured directly, or determined indirectly, when you know that several quantities combined are equal to a known value and you know the value of the other amounts in the sum. In this case, the "sum" is the rule that the probabilities of all possible events should add up to 100%, when there are three possibilities and we know two of the probabilities are are trying to determine the third.

This is notable because the latest experimental measurement is three standard deviations from another measurement of the same quantity, given the respective margins of error of the measurements.

The key language is that: "The Vus determinations based on the inclusive branching fraction of τ to strange final states are about 3σ lower than the Vus determination from the CKM matrix unitarity."

This means that if you add up the three possible things that could happen to an up quark that transitions, the probabilities should add up to 100%. But, if you take the best available known values of Vud (which is use to determine the probability that an up quark transitions to a down quark) and Vub (which is used to determine the probability that an up quark transitions to a bottom quark) and subtract those from 100%, the probability that is left over is significantly bigger than the directly measured value of Vus (which is used to determine the probability that an up quark transitions to a strange quark).

So, either one of the three directly measured elements that give us transition probabilities (i.e. Vud, Vus, and Vub) is lower than the true value, or there is another possibility that the Standard Model does not permit (i.e. an up quark can transition into something other than a down quark, a strange quark or a bottom quark) that happens with a probability sufficient to make the total sum of the probabilities equal 100%.

This is a pretty notable anomaly, although sometimes three sigma results are still just statistical flukes, because so many different quantities are measured and we only pay close attention to the improbable ones. Also, sometimes the margins of error are modestly underestimated, making the discrepancies look more significant than they actually are in reality.

Any big anomaly could, of course, be a sign of beyond the Standard Model Physics and show that the Standard Model is wrong. But, because this anomaly is isolated, rather than fitting a pattern of multiple anomalous measurements that look like they could have a common source, and because there wasn't any strong theoretical prediction from any popular beyond the Standard Model physics theories that this would happen, it is premature at this case to speculate what kind of "New Physics" could give rise to this anomaly. A fluke or experimental error seems far more likely at this point.

The paper reporting the latest anomaly and its abstract are as follows (emphasis added):
We report the status of the Heavy Flavour Averaging Group (HFLAV) averages of the τ lepton measurements We then update the latest published HFLAV global fit of the τ lepton branching fractions (Spring 2017) with recent results by BABAR. We use the fit results to update the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vus measurements with the τ branching fractions. We combine the direct τ branching fraction measurements with indirect predictions using kaon branching fractions measurements to improve the determination of Vus using τ branching fractions. The Vus determinations based on the inclusive branching fraction of τ to strange final states are about 3σ lower than the Vus determination from the CKM matrix unitarity.