The central challenge of any direct-detection dark matter experiment is separation. If weakly interacting massive particles, or WIMPs, exist, they should occasionally strike a xenon nucleus, producing a tiny recoil that scintillation light and ionization electrons record. But gamma rays and beta particles from residual radioactivity in detector materials produce electronic recoils that look superficially similar. LZ’s main line of defense has been charge-to-light discrimination, which exploits the fact that nuclear recoils and electronic recoils produce different ratios of ionization charge to scintillation light. That method already rejects electronic recoil backgrounds with high efficiency, but every additional layer of rejection translates directly into better sensitivity to the vanishingly rare signals the experiment is built to find.

Pulse shape discrimination offers a second, independent handle. When energy is deposited in liquid xenon, scintillation light emerges from excited xenon dimers that can occupy either a singlet or a triplet molecular state. These states decay with different lifetimes, and crucially, nuclear recoils preferentially excite the singlet state, producing a flash with a steeper rising edge, while electronic recoils favor the triplet state and produce a longer tail. In liquid argon detectors, where the two lifetimes differ by more than two orders of magnitude, this effect is so pronounced that it serves as the dominant background rejection method. In liquid xenon, however, the singlet and triplet lifetimes are only about 3 and 26 nanoseconds respectively, a difference so small that most experiments have treated pulse shape information as marginal at best.

The LZ team attacked this limitation with an unusually rigorous timing analysis. The first hurdle was instrumental: differences in cable lengths, electronics, and operating voltages mean that each of the 494 photomultiplier tubes lining the detector responds with its own timing offset. Using an embedded LED calibration system, the collaboration measured these channel-to-channel offsets to better than one nanosecond. The deeper challenge was that individual photomultiplier waveforms often contain multiple overlapping photons, each contributing a pulse roughly 60 nanoseconds wide. Rather than treating the waveform as a single lump, the team developed an N-photon model that fits the waveform as a sum of up to three single-photoelectron templates, using Bayes’ theorem to decide how many photons each waveform actually contains, while accounting for the roughly 23 percent chance that a single photon produces two photoelectrons.

With photon arrival times reconstructed event by event, the collaboration compared timing distributions from two calibration sources: tritiated methane, which produces electronic recoils, and deuterium-deuterium neutrons, which produce nuclear recoils. As expected, the nuclear recoil spectra showed photons clustered earlier in time, while electronic recoil events exhibited longer tails. To convert this difference into a usable discriminator, the team defined a tail fraction, the ratio of photons counted in an optimized early time window to the total number of photons in the pulse. Counting individual photons rather than integrating raw current eliminated the smearing effects of the photomultiplier response and improved resolution. The boundaries of the early window were then optimized for each pulse size using a raster scan followed by a stochastic gradient descent algorithm, with the data repeatedly split into optimization and verification sets to guard against overfitting.

The performance exceeded expectations for a xenon detector. For scintillation pulses above 20 detected photons, the fraction of electronic recoil events leaking into the region occupied by half of the nuclear recoils ranged from 15 to 35 percent, reaching as low as 14 percent for the largest pulses studied. For a specific and troublesome background, the double electron capture of xenon-124, whose suppressed charge yield causes it to masquerade as a nuclear recoil under charge-to-light analysis, simulations showed that pulse shape discrimination reduces leakage to roughly 5 percent and outperforms charge-to-light discrimination above 95 detected photons. The team also derived a position-dependent correction to account for the fact that photons generated deeper in the detector spend longer in transit, extending the technique across the full detector volume rather than just the upper third where neutron calibration data were available.

To understand the physics underlying these results and to project performance, the collaboration tuned the photon timing model of the NEST simulation framework against the calibration data. The fit confirmed the singlet and triplet lifetimes previously measured in smaller experiments and extracted recombination time constants of essentially zero for nuclear recoils and about 3.7 nanoseconds for electronic recoils, consistent with the field-dependent recombination model built into NEST. The transit of photons through the detector, including reflections and scattering, was modeled with a combination of direct and exponential components whose parameters vary smoothly with depth. The agreement between simulation and data validated the emission parameters and provided an estimate of the best possible pulse shape performance, while also confirming that the depth correction applies equally to both interaction types.

The most consequential result comes from combining the two methods. The team constructed a two-factor discriminator, a linear combination of the charge-to-light output and the corrected tail fraction, with the weighting between them optimized as a function of pulse size. Because calibration data contained too few leaking events for a traditional counting-based evaluation, the collaboration instead quantified the separation between electronic and nuclear recoil distributions using a Z-score approach, previously employed by Xenon10 and other pulse shape studies. In the largest pulse bin, the separation improved from 3.65 to 3.83 standard deviations, cutting the corresponding false positive rate from 1.3 times ten to the minus four to 0.6 times ten to the minus four, a factor of two reduction. Applied to the WIMP search data collected between March 2023 and April 2024, the combined discriminator halved the number of events falling in the nuclear recoil band, from four to two, and all four events in the charge-to-light band were classified as electronic recoils by their pulse shapes alone.

The implications reach beyond LZ. The demonstration that photon timing carries exploitable information in a detector of this scale establishes a feasibility case for next-generation liquid xenon experiments, where every increment in background rejection buys sensitivity to ever fainter dark matter signals. The technique may prove even more powerful at lower drift fields, where enhanced recombination lengthens the timing differences between interaction types. And for backgrounds like xenon-124 double electron capture, which will only grow more relevant as exposures increase, pulse shape discrimination offers a complementary tool precisely in the energy range where other methods weaken. For now, the null result from the WIMP search data stands, but the machinery built to interpret those flickers of xenon light has become measurably sharper, and the hunt for the universe’s missing mass has gained a second pair of eyes.

Subject of Research: Pulse shape discrimination for electronic recoil background rejection in the LUX-ZEPLIN liquid xenon dark matter detector

Article Title: Pushing the limits of pulse shape discrimination in a large liquid xenon detector

Article References: LZ Collaboration, Akerib, D. S., Al Musalhi, A. K., Alder, F., Almquist, B. J., Amarasinghe, C. S., Ames, A., Anderson, T. J., Angelides, N., Araújo, H. M., Armstrong, J. E., Arthurs, M., Baker, A., Balashov, S., Bang, J., Bargemann, J. W., Barillier, E. E., Beattie, K., Bhatti, A., … Zhou, Y. (2026). Pushing the limits of pulse shape discrimination in a large liquid xenon detector. The European Physical Journal C, 86(9), Article 1060. https://doi.org/10.1140/epjc/s10052-026-16216-8

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16216-8

Keywords: dark matter, LUX-ZEPLIN, liquid xenon, pulse shape discrimination, WIMPs, background rejection, scintillation, photon timing, NEST simulation, two-factor discrimination, xenon-124 double electron capture, direct detection