Looking at the Invisible Z

Turning the monojet most stubborn background into a precision measurement

A PPC spotlight on JHEP 05, 205 (2021) — CMS, “Measurement of the Z boson differential production cross section using its invisible decay mode (Z → νν̄) in proton-proton collisions at √s = 13 TeV” (arXiv:2012.09254, analysis CMS-SMP-18-003)

For years, the process Z → νν̄ has been the villain of the story. A Z boson recoiling against a jet and then decaying into two neutrinos leaves nothing behind but a jet and a gaping hole in the transverse momentum balance — the exact signature every dark-matter “monojet” search is hunting for. It is the dominant, irreducible background that stands between the LHC and a discovery of the dark sector.

This paper inverts the problem. Rather than treating invisible Z production as a background to suppress and subtract, the CMS collaboration reconstructs it as a signal. They have measured the differential cross section of the Z boson using only what the detector cannot see—the first such measurement of its kind.

The idea: measure a boson from its absence

The analysis selects events with a single energetic jet (leading jet pT > 100 GeV) and large pTmisss (> 250 GeV at reconstruction level), then infers the recoiling Z boson’s transverse momentum directly from that imbalance. No leptons, no reconstructed mass peak, only the momentum the neutrinos carry away.

That is a hard place to do precision physics, because the signal region swarms with mimics:

  • W(ℓν) + jets, where the charged lepton escapes or hides, dominates the background at roughly 85%
  • QCD multijet events, where jet energy mismeasurement masquerades as genuine missing momentum

The team constrained these not through simulation alone but with data-driven control regions: single-muon and single-electron samples enriched in W(ℓν)+jets, which directly anchor the lepton-loss rate and kinematics, and a low-Δφ region to extrapolate QCD multijet contamination in the signal space. This reflects a foundational principle of the PPC’s program: understand your backgrounds better than your signal. The control-region scaffolding that underpins the monojet dark-matter searches becomes, here, the measurement itself. The same kinematic constraints that set dark-sector limits now define a Standard Model precision observable.

The result: 6% precision on the unseeable

Working with the 2016 dataset (35.9 fb⁻¹ at 13 TeV), the analysis delivers the fiducial cross section for Z bosons with pT > 200 GeV decaying invisibly:

σ(pTZ > 200 GeV) = 3000 ⁺¹⁸⁰₋₁₇₀ fb

That is about a 6% total uncertainty on a boson identified purely by its absence: with the jet/missing-momentum scale (~4%) and luminosity (2.5%) as the leading systematic uncertainties. Statistical and background-modeling contributions remain subdominant which is a clear sign of the control-region strategy’s power. The differential spectrum is measured in five bins of Z pT, from 200 GeV all the way out to 1500 GeV, where the cross section falls to just 3.2 ± 0.3 fb. This exponential falloff is precisely where discovery potential lives: new particles coupling to the Z would distort this tail.

Here lies the crucial advantage: The neutrino channel’s branching fraction is six times larger than Z → e⁺e⁻ or μ⁺μ⁻. In the charged lepton channels, detector efficiency and trigger thresholds suppress the high-pT reach. But the invisible decay gains statistical power in the far tail—exactly where beyond-standard-model signals would first emerge. The channel deemed a background became the measurement’s secret weapon.

The most significant plot

The figure that captures the whole enterprise is Figure 3; the differential Z → νν̄ cross section as a function of the Z boson transverse momentum:

CMS-SMP-18-003 Figure 3 — measured absolute (left) and normalized (right) fiducial Z→νν differential cross section vs Z pT, compared to MadGraph5_aMC@NLO, FEWZ and NNLOJET predictions

Figure 3 (JHEP 05, 205 (2021)): The measured absolute (left) and normalized (right) fiducial cross section as a function of pTZ for the invisible decay Z → νν̄, compared with MadGraph5_aMC@NLO (with and without NLO electroweak corrections), FEWZ, and NNLOJET calculations. The lower panels show prediction/data ratios; the data span more than four orders of magnitude in cross section across the pT range.

Why this one? Because it is the measurement that should not exist: a full differential spectrum of a particle reconstructed from missing energy, laid over the best available QCD and electroweak predictions … and it agrees with them! within uncertainties. This agreement is not trivial. In the high-pT tail, the prediction/data ratio rises visibly; this uptick is where electroweak corrections (which suppress the cross section by about 10% around pTZ = 500 GeV) leave their fingerprint. And crucially: this is the exact corner of phase space a monojet dark-matter search inhabits. The measurement validates the electroweak background prediction at the kinematic frontier where new physics would hide.

The figures tell the story: Figure 3 shows the invisible Z spectrum—the measurement’s audacity. Figure 4 combines it with the Z → ℓ⁺ℓ⁻ channels to shrink error bars in complementary manner, yielding the best Z pT spectrum CMS has produced to date. The background becomes the benchmark.

The PPC angle

This is precision standard model physics extracted from pure missing energy and it bears the unmistakable hallmarks of the PPC group. Zeynep Demiragli led the analysis in the trenches; Guillelmo Gomez-Ceballos shaped its architecture and strategy. The signature is nothing but missing momentum. The methodology of data-driven control regions calibrated against dedicated sidebands is borrowed directly from the group’s dark-matter program. The result is a precision standard model benchmark that immediately becomes the calibration anchor for every monojet search that follows.

A significant deviation of this spectrum from the standard model at large transverse momenta would itself be a sign of new physics: so measuring the background this precisely is not a detour from the dark-matter hunt. It is the dark-matter hunt.
// Christoph Paus / the PPC, MIT

References

  • CMS Collaboration, “Measurement of the Z boson differential production cross section using its invisible decay mode (Z → νν̄) in proton-proton collisions at √s = 13 TeV,” JHEP 05 (2021) 205. DOI: 10.1007/JHEP05(2021)205.
  • Public figures and data: CMS-SMP-18-003 public results.
  • Companion charged-lepton measurement used in the combination: CMS Collaboration, “Measurements of differential Z boson production cross sections in proton-proton collisions at √s = 13 TeV,” JHEP 12 (2019) 061, arXiv:1909.04133.
  • Theory predictions compared to the data: MadGraph5_aMC@NLO (arXiv:1405.0301), FEWZ (arXiv:1011.3540), and NNLOJET (arXiv:1507.02850).

Figure reproduced from CMS-SMP-18-003 under the CMS public-results terms. Spotlight prepared for the MIT Particle Physics Collaboration (PPC).