The KOTO anomaly

Patrick Meade pointed out some new papers about an experimental anomaly, starting with his own. The KOTO experiment at J-PARC in Japan (where they are also building a \( g-2 \) experiment) has seen 3 events when looking for the rare process \( K_L \rightarrow \pi_0 + \mathrm{invisible} \), when they expect a background of \( 0.05 \pm 0.02 \) Update: it was pointed out to me that the effective background rate is \( 0.1 \pm 0.02 \) as in Meade's paper, because the Standard Model rate is \( 0.049 \pm 0.01 \). For more details see the slides of the talk where the results are reported; there is currently no paper about the excess. This is interesting as the Standard Model process \( K_L \rightarrow \pi \overline{\nu} \nu \) has a tiny branching ratio, two orders of magnitude too small to explain the number of events.

Assuming the anomaly is just statistics, the probability of observing three or more events would be of the order of one chance in \( 10,000 \) if we take the more generous estimate of the background. On the other hand, it is apparently only roughly two-sigma evidence for an anomalous \( K_L \rightarrow \pi_0 + \mathrm{invisible} \) signal. Moreover, the central value of the required signal is just above (but well within errors of) the Grossman-Nir bound, which says that if something generates \( K_L \rightarrow \pi \overline{\nu} \nu \), it should also generate \( K^+ \rightarrow \pi^+ \overline{\nu} \nu\) in the ratio $$ \frac{\mathrm{Br} (K_L \rightarrow \pi_0 \overline{\nu} \nu)}{\mathrm{Br}(K^+ \rightarrow \pi^+ \overline{\nu} \nu)} = \sin^2 \theta_c$$ where \( \theta_c \) is the Cabbibo angle, provided that the interactions respect isospin. Since the charged process is not observed, the observed anomaly might be in slight tension with this bound.

So far I can find three papers seeking to explain this anomaly, through light scalar extensions of the Standard Model (with masses less than 180 MeV) and the inevitable two-Higgs doublet model. Since such scalars must couple to quarks/mesons they look a bit like axion-like particles and there are many astrophysical and beam-dump experiments that exclude large swathes of the potential parameter space, but this is quite exciting as, if the anomaly is confirmed, it should also be possible to easily look for it in (many) other experiments.