The worst possible Flashlight

Why the Higgs boson is almost never emitted alongside dark matter, and why that makes it the cleanest place to look for it

A PPC spotlight on the CMS search “Search for dark matter particles produced in association with a Higgs boson in proton-proton collisions at √s = 13 TeV”, published as JHEP 03 (2020) 025 (arXiv:1908.01713, analysis CMS-EXO-18-011).

Every mono-X search follows the same basic strategy. If dark matter is produced, it leaves no direct trace in the detector, so one searches for a visible object recoiling against the missing momentum and labels that object X: a jet, a photon, a W or Z boson, or a top quark. The visible object serves as a flashlight pointed into the dark, and the brighter the flashlight, the better.

By that standard, the Higgs boson is a catastrophically poor choice. In a conventional mono-X search, X is radiated from an incoming quark, with a rate determined by its coupling to light quarks. The Higgs boson couples to light quarks through notoriously tiny Yukawa couplings and to gluons only through loop-induced interactions. Initial-state Higgs radiation is therefore so strongly suppressed that the Standard Model all but refuses to produce it.

That suppression is precisely what makes the Higgs appealing. There is essentially no Standard Model process with this signature to compete against, so any observed excess would almost certainly point to new physics rather than a subtle rate measurement. This paper presents the first CMS search to pursue that idea systematically across the full range of Higgs boson decay channels: five channels, h → bb, γγ, τ⁺τ⁻, W⁺W⁻, and ZZ, using 35.9 fb⁻¹ of proton-proton collisions from 2016. The last two had never been used for a mono-Higgs search by anyone, and no one had combined all five.

Two models, two very different boosts

The two benchmarks come from the ATLAS-CMS Dark Matter Forum. In the Z′-2HDM, a type-II two Higgs doublet model extended by a new U(1) group, a Z′ boson decays to a Higgs boson plus a pseudoscalar mediator A, which then decays to Dirac dark matter. In the baryonic Z′ model, which gauges baryon number, the Z′ boson is itself the mediator and radiates a Higgs boson before decaying to dark matter.

The difference that matters experimentally is kinematic rather than theoretical. In the Z′-2HDM, dark matter is produced through a resonant decay chain, yielding a hard missing transverse momentum spectrum and a highly boosted Higgs boson. In the baryonic Z′ model, no such resonance is present, so the missing transverse momentum spectrum is softer and the Higgs boson carries only a modest boost. The final state is the same, but the event topology in the detector is markedly different, and no single reconstruction strategy performs optimally for both. The paper is also refreshingly candid: for the benchmark couplings it adopts, the accessible Z′ mass range had already been excluded by dijet searches. The benchmark is retained nonetheless, simply because it has become the standard point of comparison used throughout the field.

The bb channel, and the jet radius that had to move

With a branching fraction of about 58%, h → bb carries the sensitivity, and with it the entire experimental problem: a Higgs boson with enough transverse momentum to be interesting produces two b jets that overlap and refuse to be reconstructed separately.

The response is to stop trying to resolve the two b quarks as separate jets. Instead, they are clustered into a single large-radius jet, soft wide-angle radiation is removed with the soft-drop algorithm, and the remaining jet is tested to see whether its mass is consistent with 125 GeV and its substructure is consistent with a two-b-quark decay. This is the language of jet substructure, and in this group it arrived by a very specific route. It was built for the top tagger in the CMS mono-top search, then carried across to h → bb.

The subtlety is the radius. Two decay products of a particle of mass m and transverse momentum pT are separated by roughly ΔR ≈ 2m/pT, which for a 125 GeV Higgs boson at 200 GeV is about 1.2, comfortably more than the standard AK8 jet can hold. So the analysis uses two different jets:

  • For the Z′-2HDM, where the boost is high, anti-kT jets have a distance parameter of 0.8. One or both subjets are required to be b tagged, and the two categories are kept separate because the two-tag category is the pure one. The groomed jet mass must lie between 105 and 135 GeV.
  • For the baryonic Z′, where the boost is low, Cambridge-Aachen jets with a distance parameter of 1.5. subjet tagging is the wrong tool at that radius, so a multivariate double b tagging discriminant is built instead from the primary and secondary vertices and the tracks inside the jet, trained to separate genuine h → bb jets from energetic light-flavor and gluon jets. It reaches 50% efficiency at a 10% misidentification rate, and the mass window widens to 100–150 GeV to match the coarser resolution.

Before either clustering step, every particle-flow candidate is weighted using the pileup-per-particle identification algorithm, the difference between measuring the jet mass and measuring the 2016 pileup. Events containing identified leptons or photons are vetoed, and those with additional b-tagged jets are rejected. These selections suppress the dominant W+jets and tt backgrounds while, as a side effect, making this channel nearly orthogonal to the other four.

Two models, two jet radii, two taggers, one final state. That is not elegance, it is honesty about what the detector can resolve.

The other four

The remaining channels trade rate for cleanliness in different ways. The γγ and ττ analyses, published earlier, have small branching fractions but tolerate soft missing transverse momentum, which turns out to matter. Of the two new ones, h → WW uses the fully leptonic eμ final state and a boosted decision tree, exploiting the low dilepton mass and small angular separation that follow from the scalar nature of the Higgs boson and its recoil against dark matter. Nothing about the Higgs boson itself can be reconstructed there. The h → ZZ → 4ℓ analysis has the opposite character: the Higgs boson is fully reconstructed with excellent resolution and the backgrounds are tiny, but so is the rate. Its benchmark signal expectations are 0.36 and 1.38 events against 112 observed, and looking for a third of an event does not set records. The WW channel alone excludes a 50 GeV strip of Z′ mass. That is the argument for a combination.

Combining the channels is only meaningful if no event is counted twice, and the paper verifies exactly that. With the event vetoes in place, the overlap between signal regions is zero, while the overlap between control regions remains below 0.01%. No excess is observed in any channel. At the 95% confidence level,

Z′-2HDM: 500 < mZ′ < 3200 GeV excluded for mA = 300 GeV.
Baryonic Z′: 100 < mZ′ < 1600 GeV excluded for mχ = 1 GeV.

The most significant plot

CMS-EXO-18-011 Figure 8, upper limits on the dark matter production cross section from the five individual Higgs boson decay channels and their combination, for the Z'-2HDM and the baryonic Z' model

Figure 8 (JHEP 03 (2020) 025): Upper limits at 95% CL on σ/σth for the Z′-2HDM (left) and the baryonic Z′ model (right), shown for the five individual Higgs boson decay channels and for their combination, as a function of mZ′. Solid lines are observed limits and dashed lines expected. The inner and outer bands show the 68 and 95% uncertainties in the expected limit of the combination.

Six curves appear in each panel, and it is immediately obvious which channel is carrying the search. Across most of the mass range, the h(bb) curve lies roughly an order of magnitude below the others, while the black combination curve is almost indistinguishable from it. A less candid presentation could have shown only the combined result.

Showing the decomposition invites the obvious question, and the answer is where the interesting physics lives. In the left panel below 800 GeV the h(bb) curve simply stops, because the Higgs boson is no longer boosted enough for the large-radius jet approach to function at all. There the combination is carried by h(γγ) and h(ττ), and the exclusion reaching down to 500 GeV is theirs. The dominant channel dominates most of the parameter space and is absent from the rest, which is why one combines rather than picks a winner.

The part that competes with underground laboratories

CMS-EXO-18-011 Figure 11, limits on the spin-independent dark matter-nucleon scattering cross section compared with direct-detection experiments

Figure 11 (JHEP 03 (2020) 025): Upper limits at 90% CL on the spin-independent dark matter-nucleon scattering cross section σSI as a function of mχ, from the combination of the five Higgs boson decay channels, compared with the CMS dijet analyses and with the CRESST-II, CDMSlite, PandaX-II, LUX, XENON1T, and CDEX-10 direct-detection experiments.

Translated into the language of direct detection through the simplified s-channel model, and with the health warning that it holds only for gq = 0.25 and gχ = 1, the combined result crosses below the direct-detection curves for mχ between 1 and 5 GeV. Dark matter in that mass range transfers too little recoil energy to a xenon or germanium target to produce a detectable signal, whereas the LHC is largely insensitive to the dark matter mass itself, provided the mediator is heavy enough to be produced.

The PPC angle

Benedikt Maier, a postdoc in the group, is the reason the bb channel looks the way it does. Jet substructure had been developed here for the top tagger in the CMS mono-top search, and carrying it into h → bb was the move that made a boosted mono-Higgs search viable at all. Beyond the idea, someone has to push a channel through: build the tagger, calibrate the groomed jet mass, defend a jet of radius 1.5 to reviewers who have never used one, and hold it together until publication.

Siddharth Narayanan, a graduate student, contributed on the substructure side and on the machine learning behind the double b tagging discriminant. Deciding what a jet containing two b quarks looks like, as opposed to a light-flavor jet that happens to have the right mass, is the difference between 50% efficiency at 10% misidentification and something much less useful.

Both contributions point in the same way, and it is one this group keeps choosing. When a signature cannot be reconstructed with conventional objects, the response is not to abandon it but to redefine what counts as an object. Two overlapping b jets cease to be two jets and instead become a single jet with internal structure. Once that shift is made, the tagger, the jet radius, and the mass window follow naturally. The result is a search that found nothing across five complementary channels, in a corner of phase space where any excess would have been difficult to mistake for anything other than new physics.

If you ever see a Higgs next to invisible particles, where the standard model refuses to hand you a Higgs, you will not have to argue about what it means. That’s worth a small rate.
// Christoph Paus / the PPC, MIT

References

  • CMS Collaboration, “Search for dark matter particles produced in association with a Higgs boson in proton-proton collisions at √s = 13 TeV”, JHEP 03 (2020) 025. DOI: 10.1007/JHEP03(2020)025. arXiv: 1908.01713. Report nos. CERN-EP-2019-141, CMS-EXO-18-011.
  • Public figures and additional material: CMS-EXO-18-011 public results.
  • The h → bb input for the baryonic Z′ model, using CA15 jets and the double b tagging discriminant: CMS Collaboration, “Search for dark matter produced in association with a Higgs boson decaying to a pair of bottom quarks in proton-proton collisions at √s = 13 TeV”, Eur. Phys. J. C 79 (2019) 280, arXiv:1811.06562, CMS-EXO-16-050.
  • The h → bb input for the Z′-2HDM, using AK8 jets with subjet b tagging: CMS Collaboration, “Search for heavy resonances decaying into a vector boson and a Higgs boson in final states with charged leptons, neutrinos and b quarks at √s = 13 TeV”, JHEP 11 (2018) 172, arXiv:1807.02826.
  • The h → γγ and h → ττ inputs: CMS Collaboration, “Search for dark matter produced in association with a Higgs boson decaying to γγ or τ⁺τ⁻ at √s = 13 TeV”, JHEP 09 (2018) 046, arXiv:1806.04771.
  • The mono-top search in which the group’s jet substructure tagging was first deployed: CMS Collaboration, “Search for dark matter in events with energetic, hadronically decaying top quarks and missing transverse momentum at √s = 13 TeV”, JHEP 06 (2018) 027, arXiv:1801.08427, CMS-EXO-16-051.
  • Benchmark models and their parameter choices: D. Abercrombie et al., “Dark matter benchmark models for early LHC Run-2 searches: report of the ATLAS/CMS Dark Matter Forum”, arXiv:1507.00966; A. Boveia et al., “Recommendations on presenting LHC searches for missing transverse energy signals using simplified s-channel models of dark matter”, arXiv:1603.04156.
  • Mono-Higgs as a signature: L. Carpenter et al., “Mono-Higgs-boson: a new collider probe of dark matter”, Phys. Rev. D 89 (2014) 075017, arXiv:1312.2592; J. M. No, “Looking through the pseudoscalar portal into dark matter”, Phys. Rev. D 93 (2016) 031701, arXiv:1509.01110.
  • The Z′-2HDM: A. Berlin, T. Lin, and L.-T. Wang, “Mono-Higgs detection of dark matter at the LHC”, JHEP 06 (2014) 078, arXiv:1402.7074.
  • Jet grooming: A. J. Larkoski, S. Marzani, G. Soyez, and J. Thaler, “Soft drop”, JHEP 05 (2014) 146, arXiv:1402.2657.
  • Pileup mitigation before clustering: D. Bertolini, P. Harris, M. Low, and N. Tran, “Pileup per particle identification”, JHEP 10 (2014) 059, arXiv:1407.6013.
  • Jet clustering algorithms: M. Cacciari, G. P. Salam, and G. Soyez, “The anti-kT jet clustering algorithm”, JHEP 04 (2008) 063, arXiv:0802.1189; Y. L. Dokshitzer, G. D. Leder, S. Moretti, and B. R. Webber, “Better jet clustering algorithms”, JHEP 08 (1997) 001, arXiv:hep-ph/9707323.
  • Heavy-flavor jet identification, including the double b tagging discriminant: CMS Collaboration, “Identification of heavy-flavour jets with the CMS detector in pp collisions at 13 TeV”, JINST 13 (2018) P05011, arXiv:1712.07158.
  • Direct-detection results shown in the comparison: CRESST-II, arXiv:1509.01515; CDMSlite, arXiv:1509.02448; PandaX-II, arXiv:1708.06917; LUX, arXiv:1608.07648; XENON1T, arXiv:1805.12562; CDEX-10, arXiv:1802.09016.
  • CMS dijet limits shown in the same comparison: JHEP 01 (2018) 097, arXiv:1710.00159; JHEP 08 (2018) 130, arXiv:1806.00843.
  • Local copy of the paper: 1908.01713.pdf (CC-BY-4.0, © 2020 CERN for the benefit of the CMS Collaboration).

Figures reproduced from CMS-EXO-18-011 under the CC-BY-4.0 license. Spotlight prepared for the MIT Particle Physics Collaboration (PPC).