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Measurement of the branching ratio of the $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$ decay

The NA62 experiment has measured the branching ratio of the rare decay $K^+\to\pi^+\nu\bar{\nu}$ using data from 2016 to 2024, obtaining a result of $(9.6^{+1.9}_{-1.8})\times10^{-11}$ with 20% relative precision that is consistent with Standard Model predictions.

Original authors: NA62 Collaboration

Published 2026-07-21

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CC BY 4.0

Original authors: NA62 Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, bustling construction site where tiny building blocks called particles are constantly being assembled, broken apart, and rearranged. Most of the time, these blocks follow a very strict rulebook called the Standard Model, which is like the architect's blueprint for how matter should behave. But sometimes, the blueprint predicts that a very specific, incredibly rare event should happen: a tiny particle called a "kaon" should spontaneously transform into a "pion" and vanish into thin air, leaving behind only invisible ghosts called neutrinos. This is like watching a magician's assistant turn into a puff of smoke and disappear, but the trick is so rare that you'd have to watch a billion shows just to see it happen once. Scientists care deeply about this because if they see it happen more or less often than the blueprint predicts, it would mean the blueprint is wrong and there's a secret, hidden force of nature at work—something "new physics" that we haven't discovered yet.

This paper is a report from a team of scientists at CERN, the European Organization for Nuclear Research, who built a massive, high-tech "magic show" to catch this rare trick in the act. They used a machine called the NA62 experiment, which acts like a super-sensitive camera and a set of laser tripwires to track these tiny particles as they zoom through a vacuum. The team collected data over several years, but this specific report focuses on the fresh data they gathered in 2023 and 2024, combined with their earlier observations. They didn't just watch; they upgraded their equipment with "smart" computer brains (machine learning) to spot the right particles and ignore the noise, making their search much sharper.

The result? They caught the trick! In their 2023–2024 data, they found 33 events that looked exactly like the rare decay they were hunting for, while expecting only about 23 from the standard rules and 12 from background "noise" (like other particles mimicking the trick). When they combined this new data with their previous years of watching, they counted a total of 84 events. This is a huge deal because it confirms that the decay happens at a rate of about 9.6 events for every 100 billion kaons that decay. This number, written as $(9.6^{+1.9}_{-1.8}) \times 10^{-11}$ , matches the predictions of the Standard Model almost perfectly.

The scientists are very confident in this result. They calculated that the chance of this being a fluke or just random noise is less than one in a billion (a statistical significance exceeding 6 sigma). They explicitly ruled out the idea that they saw nothing or that the background noise was the only thing happening. While they didn't find any "new physics" breaking the rules in this specific experiment, they have now measured this rare event with a precision of 20%, which is a massive improvement over their previous measurements. They essentially doubled the size of their "audience" and cleaned up the view so clearly that they can now say with great certainty that the universe is behaving exactly as the current blueprint predicts for this particular trick. The team plans to keep watching until 2026, hoping to catch even more of these rare moments to see if the rules hold up under even closer scrutiny.

Technical Summary: Measurement of the Branching Ratio of the $K^+ \to \pi^+\nu\bar{\nu}$ Decay

Problem and Motivation
The decay $K^+ \to \pi^+\nu\bar{\nu}$ is an ultra-rare process in the quark-flavour sector, considered a "golden mode" for searching for physics beyond the Standard Model (SM). Recent SM predictions place the branching ratio, $\mathcal{B}(K^+ \to \pi^+\nu\bar{\nu})$ , at approximately $8 \times 10^{-11}$ with a theoretical precision better than 8%, limited primarily by experimental inputs and long-distance charm contributions. Several models involving new physics predict significant deviations from these values, often correlated with the $K_L \to \pi^0\nu\bar{\nu}$ decay and other flavour-changing neutral currents. While the NA62 experiment previously established the first observation of this decay using 2016–2022 data, this paper reports a refined measurement using data collected in 2023 and 2024, combined with the previous dataset to achieve higher precision.

Methodology and Experimental Improvements
The analysis utilizes data from the NA62 experiment at the CERN SPS, collected during 2023 and 2024. The dataset comprises $8.9 \times 10^5$ spills, collected at an average instantaneous beam intensity of 440 MHz, which is lower than the maximum design intensity used in 2021–2022. This reduction in intensity was found to optimize signal yield by minimizing dead time and accidental vetoes.

Key technical upgrades and methodological improvements implemented for this dataset include:

Beamline Upgrades: The KTAG differential Cherenkov counter was upgraded to use H $_2$ gas at 3.85 bar (previously N $_2$ at 1.71 bar). This reduced the material budget from 3.9% to 0.7% of a radiation length, decreasing scattered beam particles by 30% and improving $K^+$ identification efficiency to 99.7%.
Readout Systems: A new FPGA-based Time-to-Digital Converter (TDC) system, read out by ATLAS FELIX boards, replaced previous TEL62 boards for the veto counter (VC) and CHANTI detectors, improving data throughput and reliability.
Machine Learning in Reconstruction:
- Beam Tracking: The 4D beam particle tracking in the Gigatracker (GTK) spectrometer was updated from a conventional algorithm to a deep learning architecture based on a transformer encoder and a binary classifier. This reduced the false track rate from 13% to 4% and increased track purity from 87% to 97%.
- Particle Identification: A new classifier combining a Convolutional Neural Network (CNN) and a fully connected feed-forward network was implemented for calorimetric particle identification (using LKr and MUV1,2 detectors). This improved pion identification probability by ~2% and reduced the misidentification of muons as pions by 40% relative to the previous Boosted Decision Tree (BDT) classifier.
Trigger and Selection: The PNN signal trigger line incorporated improved online slewing corrections for the Large-Angle Veto (LAV), reducing veto windows from 6 to 4 ns. Upstream background rejection was enhanced by requiring no signals in the most upstream LAV station (LAV1) within 2 ns of the kaon time.

Background Estimation
Backgrounds arise from misreconstructed $K^+$ decays within the fiducial volume (FV) and from upstream decays or interactions.

In-Fiducial Volume Backgrounds: Kinematic tail fractions for dominant modes ( $K^+ \to \mu^+\nu$ , $K^+ \to \pi^+\pi^0$ , $K^+ \to \pi^+\pi^+\pi^-$ ) were determined using dedicated control samples. Radiative decays and rare modes like $K^+ \to \pi^+\pi^-e^+\nu$ were estimated via simulation and validated in control regions. The contribution from $K^+ \to \mu^+\nu\gamma$ was significantly reduced due to lower beam occupancy and the new calorimetric identification algorithm.
Upstream Backgrounds: A fully data-driven strategy was employed using an Upstream Reference Sample (URS). A template fit to the Closest Distance of Approach (CDA) distribution allowed for the extrapolation of upstream background events into the signal region. The accidental component was found to be dominant. The total estimated background for the 2023–2024 dataset is $12.0^{+2.9}_{-2.2}$ events.

Results

2023–2024 Dataset: After unmasking the signal regions, 33 candidate events were observed. The expected SM signal was $22.9 \pm 1.1$ events, with an estimated background of $12.0^{+2.9}_{-2.2}$ events. The measured branching ratio is:
$\mathcal{B}_{2023-2024}(K^+ \to \pi^+\nu\bar{\nu}) = \left( 7.2^{+2.3}_{-2.1} \right) \times 10^{-11}$
Combined Dataset (2016–2024): Combining the 2023–2024 data with the 2016–2022 dataset yields a total of 84 observed events against an expected background of $30^{+4}_{-3}$ and an expected SM signal of $43 \pm 1$ . This results in a significance for the rejection of the background-only hypothesis exceeding $6\sigma$ . The combined branching ratio is:
$\mathcal{B}_{2016-2024}(K^+ \to \pi^+\nu\bar{\nu}) = \left( 9.6^{+1.9}_{-1.8} \right) \times 10^{-11}$
This corresponds to a relative precision of 20%.

Significance and Claims
The paper claims that the combined measurement is consistent with Standard Model predictions. The inclusion of the 2023–2024 dataset, collected under optimized conditions, provided a major improvement in precision over the previous 2016–2022 measurement. Specifically, the effective sample size was doubled while the relative background contribution was significantly decreased. The result represents the first time the NA62 experiment has reached an expected significance for the SM observation exceeding $5\sigma$ using the combined dataset. The measurement provides current constraints on $K \to \pi\nu\bar{\nu}$ decay modes, consistent with the Grossman-Nir bound and the direct upper limits set by the KOTO experiment for the $K_L$ mode. The authors note that data taking continues through 2026, with the final dataset expected to increase the number of signal events by a further 50%.

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