Experimental setup
The KATRIN experiment measures the electron energy spectrum of tritium β-decay near the kinetic endpoint E 0 ≈ 18.6 keV. The 70-m-long setup comprises a high-activity gaseous tritium source, a high-resolution spectrometer using the MAC-E-filter principle and a silicon p-i-n diode detector2,30.
Molecular tritium gas with high isotopic purity (up to 99%; ref. 48) is continuously injected into the middle of the WGTS, in which it streams freely to both sides. At the ends of the 10-m-long beam tube, more than 99% of the tritium gas is pumped out using differential pumping systems. With a throughput of up to 40 g day−1, an activity close to 100 GBq can be achieved49,50. The β-electrons are guided adiabatically by a 2.5 T magnetic field through the WGTS51. Before entering the spectrometer, they traverse two chicanes, in which the residual tritium flow is reduced by more than 12 orders of magnitude through differential52 and cryogenic pumping53. The β-electrons flowing in the upstream direction of the beamline reach the gold-plated rear wall, where they are absorbed. Besides separating the WGTS from the rear part of the KATRIN experiment that houses calibration tools, the rear wall also controls the source potential by a tunable voltage of \({\mathcal{O}}\) (100 mV).
Electrons guided towards the detector are subjected to energy filtering by two spectrometers. A smaller pre-spectrometer first rejects low-energy β-particles. The precise energy selection with \({\mathcal{O}}\) (1 eV) resolution is then performed by the 23-m-long and 10-m-wide main spectrometer. In both spectrometers, only electrons with a kinetic energy above the threshold energy qU are transmitted (high-pass filter). The electron momenta \({\bf{p}}={{\bf{p}}}_{\perp }+{{\bf{p}}}_{\parallel }\) are collimated adiabatically such that the transverse momentum is reduced to a minimum towards the axial filter direction by gradually decreasing the magnetic field towards the so-called analysing plane. In the main spectrometer, the magnetic field is reduced by four orders of magnitude to B ana ≲ 6.3 × 10−4 T. Behind the main spectrometer exit, the magnetic field is increased to its maximum value of B max = 4.2 T, resulting in a maximum acceptance angle of \({\theta }_{\max }=\arcsin (\sqrt{{B}_{{\rm{S}}}/{B}_{\max }})\approx 5{1}^{^\circ }\), where θ is the initial pitch angle of the electron. The filtered electrons are counted by the FPD, which is a silicon p-i-n diode segmented into 148 pixels (ref. 40). This detector is regularly calibrated with a 241Am source to ensure stable performance. Its efficiency is about 95%, with only small variations between pixels that remain constant over time. Effects that do not depend on the retarding potential are accounted for by the free normalization combined fit across groups or patches of pixels54.
Background electrons are indistinguishable from tritium β-decay electrons and thus contribute to the overall count rate at the detector. There are different sources and mechanisms that generate the background events. The majority originates from the spectrometer section of the experiment. Secondary electrons are created by cosmic muons and ambient gamma radiation on the inner spectrometer surface55,56 but are mitigated by magnetic shielding and a wire electrode system30. The decay of 219Rn and 220Rn inside the main spectrometer volume is reduced by cryogenic copper baffles that are installed in the pumping ducts of the main spectrometer57. Another source of background is electrons from radioactive decays produced in the low-magnetic-field part of the spectrometer58. These primary electrons can be trapped magnetically, ionizing residual-gas molecules and producing secondary electrons that are correlated in time, leading to a background component with a non-Poisson distribution. The dominating part of the background stems from the ionization of neutral atoms in highly excited states, which enter the main spectrometer volume in sputtering processes (decay of residual 210Pb) at the inner surface of the spectrometer. The low-energy electrons emitted in this process are accelerated to signal-electron energies and guided to the detector. The magnitude of this background component scales with the flux tube volume in the re-acceleration part of the main spectrometer. A re-configuration of the electromagnetic fields in the main spectrometer, called the SAP setting, reduces the background by a factor of 2 by shifting the plane of minimal magnetic field from the nominal position in the centre of the spectrometer towards the detector while compressing the flux tube at the same time42,59. After successful tests, this configuration was set as the new standard (see the next section). There is also the possibility of a Penning trap being formed between the pre- and main spectrometer. The stored particles can increase the background rate. To counter this effect, a conductive wire is inserted between scan steps into the beam tube to remove the stored particles41. Because the duration of the scan steps differs, this creates a scan-time-dependent background. Reducing the time between particle removal events and lowering the pre-spectrometer potential enabled a full mitigation of the scan-step-duration-dependent background starting with the KNM5 measurement period. Moreover, the transmission and detection probabilities of background electrons may slightly depend on the retarding-potential setting, potentially causing a retarding-potential-dependent background. This effect is addressed in the analysis through an additional slope component, constrained by dedicated background measurements31.
KNM12345 dataset
The data collected by KATRIN is organized into distinct measurement periods, referred to as KATRIN Neutrino Measurement (KNM) campaigns. The integral β-spectrum is measured through a sequence of defined retarding-energy set points, which we refer to as a scan. Each dataset comprises several hundred β-spectrum scans, with individual scan durations ranging from 125 min to 195 min. The measurement time distribution (MTD), shown in Extended Data Fig. 1 (bottom), determines the time allocated for each qU i , optimized for maximizing sensitivity to a neutrino-mass signal, where the index i corresponds to different retarding energy settings. The energy interval typically spans E 0 − 300 eV ≤ qU i ≤ E 0 + 135 eV, following an increasing, decreasing or random sequence. The analysis presented in this work uses set points ranging from E 0 − 40 eV to E 0 + 135 eV and is based on the first five measurement campaigns (KNM1–KNM5), summarized in Extended Data Table 1. Extended Data Fig. 2 shows the electron energy spectra for each of the five individual campaigns.
The first measurement campaign of the KATRIN experiment, KNM1, started in April 2019 with a relatively low source-gas density of ρd = (1.08 ± 0.01) × 1021 m−2 compared with the design value of ρd = 5 × 1021 m−2. Here, ρ denotes the average density of the source gas, and d = 10 m is the length of the tritium source. The source was operated at a temperature of 30 K. The measurement in KNM1 lasted for 35 days, recording a total of about 2 million electrons. The sterile-neutrino analysis of this dataset was published in ref. 33.
After a maintenance break, the next campaign, KNM2, started in October of the same year and lasted for 45 days, only 10 days longer than KNM1. However, more than double the number of electrons was measured because of the increased source-gas density. The density was raised to ρd = (4.20 ± 0.04) × 1021 m−2, which corresponds to 84% of the design value. Although the background rate was reduced from 0.29 count per second (cps) in KNM1 to 0.22 cps, it was still above the anticipated design value of 0.01 cps (ref. 2). The sterile-neutrino analysis of this dataset, in combination with KNM1, was published in ref. 32.
To further reduce the background rate, a new electromagnetic-field configuration42 was tested in the next campaign, starting in June 2020. KNM3 was split into two parts to validate the new shifted-analysing-plane (SAP) setting in contrast to the nominal (NAP) setting. Before the start of the measurement, the source temperature was increased to 79 K. This allowed the co-circulation of gaseous krypton 83mKr with the tritium gas to perform simultaneous calibration measurements and β-scans60,61. In the first part of KNM3, KNM3-SAP, the β-spectrum was measured in the SAP setting for 14 days, and the background was subsequently reduced to 0.12 cps. Although the SAP setting reduced the background almost by a factor of 2, the increased inhomogeneities in the magnetic and electric fields require the segmentation of the detector analysis into 14 patches with 14 individual models59. In KNM3-NAP, it was demonstrated that switching between both settings works, and the background rate increased to 0.22 cps, as expected. The second part also lasted 14 days, and about 2.5 million electrons were measured in all of KNM3.
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