Search for new physics in the final state with a single photon and large missing transverse momentum in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 137 fb$^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS experiment, this study finds no significant deviations from the Standard Model in events with a single photon and missing transverse momentum, thereby establishing the most stringent 95% confidence level limits to date on dark matter mediators, effective field theory suppression scales, and fundamental Planck scales.

The Gist

The Great Cosmic "Missing Person" Hunt

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed particle smasher. Scientists fire two beams of protons (tiny particles) at each other at nearly the speed of light. When they crash, it's like smashing two grand pianos together at full speed; the debris flies out in every direction, creating a chaotic explosion of new particles.

Usually, when you smash things, you can account for every piece of the debris. But in this paper, the CMS scientists are looking for a very specific, strange event: A "Monophoton" Mystery.

The Setup: The Perfect Crime Scene

The scientists are looking for an event where:

1. One Bright Flash: A single, high-energy photon (a particle of light) flies out of the crash.
2. The Missing Piece: A huge amount of "missing momentum" is detected.

Think of it like a game of billiards. If you hit the cue ball and it smashes into a rack of balls, you can see where all the balls go. But imagine if you hit the cue ball, it flew off to the left, and suddenly, the table seemed to recoil violently to the right, even though nothing was there to hit it.

In the world of physics, that "recoil" is called Missing Transverse Momentum ($p_T^{miss}$). It means something invisible flew out of the collision, carrying energy away, but our detectors couldn't see it.

The Suspects: What Could Be Missing?

The scientists are hunting for "New Physics"—things that don't fit our current rulebook (the Standard Model). They are testing three main theories about what might be hiding in that missing energy:

1. Dark Matter (The Invisible Ghost):

   • The Theory: Dark matter makes up most of the universe, but it doesn't interact with light. It's invisible.
   • The Analogy: Imagine a thief stealing a painting. You don't see the thief, but you see the empty frame on the wall and the hole in the wall where the painting used to be. In this experiment, the "thief" is a Dark Matter particle. It flies out of the collision unseen, but the "hole" (the missing momentum) tells us it was there. The single photon is the "flash" that alerted the security camera.

2. Extra Dimensions (The Secret Room):

   • The Theory: Our universe might have more than the three dimensions we know (up/down, left/right, forward/back). Some theories say gravity can leak into these "secret rooms."
   • The Analogy: Imagine a 2D drawing on a piece of paper. If you drop a ball on the paper, it stays there. But if the paper has a hole leading to a 3D room, the ball falls through and disappears from the 2D world. The scientists are looking for particles (gravitons) that fall through our 3D world into these extra dimensions, taking energy with them.

3. Contact Interactions (The Invisible Handshake):

   • The Theory: Dark matter might interact with normal matter in very subtle, short-range ways, like a secret handshake that only happens at extremely high energies.

The Investigation: How They Caught the Culprits

The CMS team analyzed data from 2017 and 2018, combining it with previous data from 2016. That's a massive dataset, equivalent to 137 "inverse femtobarns" (a unit of collision data). To put that in perspective, they watched trillions of proton collisions.

The Filter:
They had to be very picky. Most collisions produce messy debris (jets of particles) that look like missing energy by mistake.

• They looked for events with exactly one high-energy photon.
• They checked that the "missing energy" was real and not just a glitch in the detector (like a camera malfunction).
• They used "Control Regions" (like a practice field) to understand how normal background noise (like standard particle collisions) behaves, so they could distinguish it from a real mystery.

The Verdict: No New Suspects Found

After sifting through all that data, the result is a bit of a letdown for sci-fi fans, but a triumph for scientific rigor:

They found no evidence of new physics.

The number of "Monophoton" events they saw matched the predictions of the Standard Model perfectly. It's like checking the security footage and finding that every time the alarm went off, it was just a cat walking by, not a thief.

The Takeaway: Tightening the Net

Even though they didn't find the "thief," the hunt was incredibly successful because it ruled out many possibilities.

• Setting Limits: The scientists can now say, "If Dark Matter exists in the way we thought, it must be heavier than X" or "If Extra Dimensions exist, they must be smaller than Y."
• The Improvement: This new search is 10–14% better than their previous 2016 search. They have tightened the net. If the "thief" is still out there, they know exactly where not to look, which helps future experiments focus their search.

In Summary:
The CMS team looked for a single flash of light accompanied by a mysterious recoil in the particle smashers. They didn't find any new invisible particles or extra dimensions. Instead, they confirmed that our current understanding of the universe is still holding up, while simultaneously drawing a much tighter boundary around where the unknown might be hiding.

Technical Summary

1. Problem and Motivation

The search targets "monophoton" events (a single high-energy photon accompanied by large missing transverse momentum, $p_T^{\text{miss}}$) as a signature for physics beyond the Standard Model (SM). Since Dark Matter (DM) particles are expected to be weakly interacting and invisible to detectors, they would escape detection, manifesting as $p_T^{\text{miss}}$. The monophoton signature arises when a DM pair is produced in association with a photon (initial state radiation) or when a graviton is produced in models with extra dimensions.

The paper addresses three specific theoretical scenarios:

• Simplified Dark Matter Models: DM particles produced via a heavy mediator (vector or axial-vector boson) coupling to quarks and DM.
• Effective Field Theory (EFT) for Electroweak DM: Contact interactions between DM and electroweak gauge bosons ($Z/\gamma^*$), parametrized by a suppression scale $\Lambda$.
• Large Extra Dimensions (ADD Model): The Arkani-Hamed, Dimopoulos, and Dvali model, where gravity propagates into $n$ compactified extra dimensions, allowing for the production of Kaluza-Klein (KK) gravitons ($G$) which escape detection ($pp \to \gamma G$).

This analysis supersedes a previous CMS search using only 2016 data (36 fb$^{-1}$) by combining it with 2017 and 2018 data, resulting in a total integrated luminosity of 137 fb$^{-1}$.

2. Methodology

Data Sample and Trigger

• Dataset: Proton-proton collisions at $\sqrt{s} = 13$ TeV collected by the CMS detector.
• Luminosity: 101.3 fb$^{-1}$ from 2017–2018, combined with 36 fb$^{-1}$ from 2016 (Total: 137 fb$^{-1}$).
• Trigger: A single-photon trigger requiring $p_T^\gamma > 200$ GeV. The trigger efficiency for selected events is $\approx 95\%$.

Event Selection (Signal Region - SR)

Events are selected based on strict criteria to isolate the signal and suppress SM backgrounds:

• Photon: One isolated photon with $E_T^\gamma > 225$ GeV in the barrel region ($|\eta| < 1.44$).
• Missing Transverse Momentum: $p_T^{\text{miss}} > 200$ GeV.
• Isolation: The photon must be isolated (scalar sum of $p_T$ of charged hadrons, neutral hadrons, and photons in a $\Delta R < 0.3$ cone is below specific thresholds).
• Angular Separation:
  • $\Delta\phi(p_T^{\text{miss}}, p_T^\gamma) > 0.5$ rad (to reject QCD multijet backgrounds where $p_T^{\text{miss}}$ is a mismeasurement).
  • $\Delta\phi(p_T^{\text{miss}}, p_T^{\text{jet}}) > 0.5$ rad for the leading 4 jets (to reject $W/Z+\gamma$ and $\gamma$+jets).
• Ratio Cut: $E_T^\gamma / p_T^{\text{miss}} < 1.4$ (rejects $\gamma$+jets where $p_T^{\text{miss}}$ is spurious).
• Lepton Veto: No electrons or muons with $p_T > 10$ GeV (to suppress $W(\to \ell\nu)+\gamma$).
• Beam Halo Rejection: Specific cuts on calorimeter energy along beam paths and a split of the SR into "horizontal" ($|\phi| < 0.5$) and "vertical" regions to constrain beam halo backgrounds.

Background Estimation

A simultaneous maximum likelihood fit is performed across the Signal Region (SR) and Control Regions (CRs):

• Dominant Backgrounds:
  • $Z(\to \nu\nu) + \gamma$: Irreducible background. Estimated using a dilepton CR ($Z \to \ell\ell + \gamma$) with a transfer factor derived from simulation.
  • $W(\to \ell\nu) + \gamma$: Estimated using a single-lepton CR ($W \to \ell\nu + \gamma$).
  • Misidentification:
    • Electron $\to$ Photon: Estimated using a data-driven "tag-and-probe" method on $Z \to e^+e^-$ events.
    • Jet $\to$ Photon: Estimated using a low-$p_T^{\text{miss}}$ multijet sample with inverted shower shape and isolation criteria.
  • Beam Halo: Estimated by fitting the azimuthal distribution of calorimeter clusters.
• Systematic Uncertainties: Key sources include PDFs, higher-order QCD/EW corrections, jet/photon energy scales, luminosity (1.2–2.5%), and object identification efficiencies. Theoretical uncertainties in transfer factors are treated as uncorrelated between years, while experimental uncertainties (e.g., energy scales) are correlated.

Statistical Analysis

• A profile likelihood ratio test statistic is used to extract the signal strength ($\mu$).
• Limits are set using the CL$_s$ method at 95% confidence level (CL).
• The analysis combines 2016, 2017, and 2018 data in a single likelihood function.

3. Key Contributions

• Increased Dataset: The first CMS monophoton analysis to combine the full Run 2 dataset (2016–2018), significantly increasing statistical power.
• Improved Background Modeling: Refined treatment of beam halo backgrounds by splitting the SR based on azimuthal angle and improved data-driven estimation of misidentification rates.
• Comprehensive Model Coverage: Simultaneous constraints on Simplified DM models, EFT contact interactions, and ADD extra dimensions within a single analysis framework.
• Comparison with Direct Detection: Translation of collider limits into the DM-nucleon scattering cross-section plane ($\sigma_{SI}$ and $\sigma_{SD}$) to compare with direct detection experiments (e.g., LUX-ZEPLIN, XENONnT).

4. Results

Observation

• No significant excess of events over the Standard Model expectation was observed in the 2017–2018 data or the combined dataset.
• The observed data is consistent with the background prediction across the $E_T^\gamma$ spectrum in both the SR and CRs.

Exclusion Limits

1. Simplified Dark Matter Models:

   • For a DM mass ($M_{DM}$) < 50 GeV, mediator masses ($M_{\text{med}}$) up to 1085 GeV are excluded (observed).
   • The expected exclusion reach is up to 1300 GeV.
   • These limits are translated into the $\sigma_{SI}$ and $\sigma_{SD}$ plane, showing that for $M_{DM} < 2$ GeV (spin-independent) and $M_{DM} < 200$ GeV (spin-dependent), this search provides more stringent limits than current direct detection experiments.

2. Effective Field Theory (EW-DM Contact Interaction):

   • For $M_{DM}$ between 1 and 800 GeV, the suppression scale $\Lambda$ is excluded up to 940 GeV (observed).
   • This represents an 11% improvement over the 2016-only analysis.

3. Large Extra Dimensions (ADD Model):

   • For $n=3$ to $6$ extra dimensions, the fundamental Planck scale $M_D$ is excluded up to 3.2 TeV (observed) and 3.7 TeV (expected).
   • This represents a 10–11% improvement in the exclusion reach compared to the 2016 analysis.

5. Significance

• Stringent Constraints: This work establishes the most stringent constraints to date on the parameters of simplified DM models, electroweak contact interactions, and large extra dimensions using the monophoton channel at the LHC.
• Complementarity: The results are particularly significant for low-mass Dark Matter scenarios ($M_{DM} < 200$ GeV), where collider searches outperform direct detection experiments due to the latter's sensitivity thresholds.
• Methodological Benchmark: The analysis demonstrates the robustness of combining multiple years of data with varying trigger thresholds and systematic uncertainties, setting a standard for future Run 3 and High-Luminosity LHC (HL-LHC) searches.
• Physics Reach: Despite the lack of new physics discovery, the exclusion of mediator masses up to ~1.1 TeV and Planck scales up to ~3.2 TeV significantly narrows the parameter space for theoretical models attempting to solve the hierarchy problem and the nature of Dark Matter.