Time-dependent signals of new physics at the LHC

This paper demonstrates that incorporating timing information into LHC searches for new physics, specifically interactions involving ultralight dark matter and quarks, can enhance sensitivity by up to a factor of two compared to traditional methods that assume time-invariant signals.

The Gist

The Big Idea: Listening for a Rhythm in the Noise

Imagine you are trying to hear a specific, faint song playing in a very loud, chaotic room (the Large Hadron Collider, or LHC). Usually, scientists try to find this song by looking for a specific pitch or volume (kinematic properties like energy or mass). They assume the song plays at a constant volume the whole time, while the background noise (Standard Model physics) is also constant.

This paper proposes a new way to listen. It suggests that if the "song" is actually a new type of physics driven by ultralight dark matter, it might not play at a constant volume. Instead, it might pulse or oscillate like a heartbeat, getting louder and softer over time.

The authors argue that if you can detect this rhythm, you can separate the song from the noise much better than if you just looked at the volume. Even if the song is very quiet, if you know when it gets loud, you can ignore the times when it's quiet and focus only on the peaks. This makes the search up to twice as sensitive as current methods.

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The Cast of Characters

1. The LHC (The Loud Room): A massive particle accelerator that smashes protons together. It produces a huge amount of data, most of which is just "background noise" (standard physics we already understand).
2. The New Physics (The Faint Song): A hypothetical signal from new particles.
3. Ultralight Dark Matter (The Conductor): The paper imagines that the universe is filled with a ghostly, invisible field of dark matter that is incredibly light. Because it is so light, it doesn't act like individual particles; it acts like a giant, smooth wave that ripples through the entire room.
4. The Interaction (The Volume Knob): The paper suggests this dark matter wave interacts with new, heavy particles. As the dark matter wave ripples, it turns the "volume knob" on the production of these new particles up and down.

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How the Search Works (The Analogies)

1. The "Pulsing" Signal

Imagine the background noise in the room is a steady hum of a refrigerator. It never changes.
Now, imagine the new signal is a light bulb that is connected to a dimmer switch controlled by the dark matter wave. The light bulb flickers on and off (or brightens and dims) in a predictable pattern.

• Old Method: You look at the room and say, "Is there a light brighter than the background?" If the light is dim, you might miss it because the background hum is so loud.
• New Method: You wait for the light to hit its brightest moment. You ignore the times when the light is dim. By focusing only on the "bright moments," the signal-to-noise ratio improves dramatically.

2. The Missing Energy Search (The Empty Seat)

The paper first looked at a real experiment by the ATLAS detector at the LHC. They were looking for "missing energy" (particles that disappear without a trace).

• The Scenario: They re-analyzed data from 36 months of running. They assumed the new physics signal pulses like the dark matter wave.
• The Result: By using the timing information, they could set stricter limits on how much new physics could exist. If the signal pulses, they found they could rule out more possibilities than if they assumed the signal was constant. In some cases, this made their search twice as powerful.

3. The Resonance Search (The Specific Note)

Next, they looked for "resonances" (new particles that appear as a spike in a graph of mass).

• The Problem: Sometimes the background noise has a weird shape (a bump or a dip) that looks like a signal. It's hard to tell if a bump is a new particle or just a glitch in the background.
• The Solution: If the new particle is a "pulsing" signal, you can look at the data in two dimensions: Mass and Time.
  • You can look at the times when the signal is supposed to be weak. This helps you map out exactly what the background noise looks like without the signal interfering.
  • Once you know exactly what the background looks like, you can subtract it out, leaving the signal much clearer.
  • The paper used a machine learning tool called CATHODE (which acts like a smart detective) to learn this rhythm directly from the data, even without knowing the exact speed of the pulse beforehand.

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Why This Matters

The paper claims that by adding time as a new piece of information, physicists can:

• Boost sensitivity: Find signals that are too weak to see with current methods.
• Reduce uncertainty: Better understand the background noise by using "quiet times" to study it.
• Discover new physics: Specifically, interactions involving ultralight dark matter that are too heavy to be found at low-energy experiments but might show up at the LHC if we know when to look.

The Catch (The "Systematic" Noise)

The authors are careful to note that the LHC itself isn't perfectly quiet. The machine has its own rhythms:

• The beam intensity fades over the day.
• Dust particles hitting the beam create tiny blips.
• The ground moves slightly.

These are like the refrigerator humming changing pitch or the lights flickering due to a power surge. The paper admits that scientists will need to be very careful to make sure they aren't mistaking these machine glitches for the "dark matter song." However, they argue that because the dark matter signal has a very specific, long-period rhythm, it should be possible to distinguish it from the machine's own short-term glitches.

Summary

This paper is a proposal to stop treating the LHC like a camera that just takes a snapshot of energy. Instead, it suggests treating the LHC like a video camera that records how events change over time. If new physics has a "heartbeat," looking at the video allows us to hear that heartbeat much louder than just looking at a single photo.

Technical Summary

Technical Summary: Time-dependent signals of new physics at the LHC

Problem Statement
The Large Hadron Collider (LHC) currently searches for Beyond the Standard Model (BSM) physics primarily through kinematic distributions, such as invariant mass resonances or missing transverse momentum ($\not{p}_T$). These searches typically assume that both the Standard Model (SM) background and the hypothetical new physics signal are invariant in time, with variations attributed only to experimental systematic effects. However, specific BSM scenarios involving ultralight dark matter (DM) coupled to the SM predict intrinsic time-dependent signals. If the SM background remains time-invariant while the signal oscillates due to a coherent DM background field, the temporal behavior offers an orthogonal discriminator to kinematic variables. This paper investigates the potential for leveraging this time-dependence to enhance the sensitivity of LHC searches, specifically for models where ultralight DM interacts with a heavy TeV-scale particle.

Methodology
The authors propose a framework where the production rate of new physics varies with time, driven by the classical oscillation of an ultralight bosonic DM field ($\chi$). The study focuses on a specific interaction Lagrangian involving a quadratic coupling between the DM field, a heavy scalar ($\phi$), and a quark current: $\mathcal{L} \supset \frac{1}{\Lambda^2} \chi \partial_\mu \phi \, \bar{q}\gamma^\mu q$. This interaction leads to time-dependent signatures where the cross-section scales as $\chi^2(t)$ or $\chi^4(t)$, depending on the process (missing energy or resonance production).

The analysis proceeds through three distinct methodological approaches:

1. Reinterpretation of Existing Data (Missing Momentum): The authors reinterpret a model-independent and model-dependent ATLAS search for monojet + $\not{p}_T$ events [15]. They apply an unbinned time-dependent likelihood analysis to the observed events, assuming the background is uniform in time while the signal follows a probability density function (PDF) proportional to $\chi^2(t)$. They sample over DM velocity dispersion parameters ($\alpha_j, \delta_j$) and oscillation periods ($T_{Period}$) ranging from $10^{-9}$ to $10^3$ months.
2. Resonance Searches with Known Oscillation: Using simulated QCD dijet background and signal events (scalar $\phi \to jj$), the authors construct a likelihood ratio (LR) that includes a time-dependent term. They apply event weighting based on the known temporal form (e.g., $\sin^4(2\pi t/T_{Period} + \delta)$) to enhance the signal-to-background ratio.
3. Resonance Searches with Learned Oscillation (CATHODE): To address scenarios where the oscillation period and phase are unknown, the authors employ the CATHODE anomaly detection technique. This method uses a weakly-supervised classifier trained on mass sidebands to learn a score function that distinguishes signal from background using auxiliary features, specifically including Fourier features of the event timestamps. This allows the classifier to learn the time-dependence directly from the data without pre-specifying the period.
4. Sideband Analysis in Time: The authors extend the standard invariant mass sideband technique to include time sidebands. By analyzing time intervals with low signal-to-background ratios, they aim to constrain the shape and uncertainty of the background model within the signal mass window, particularly in cases where the background exhibits non-trivial features (e.g., efficiency turn-ons).

Key Contributions and Results

• Enhanced Sensitivity in Missing Energy Searches: Reinterpreting the ATLAS monojet analysis, the authors find that incorporating time information significantly tightens limits on the number of signal events ($N_s$). For oscillation periods where the coherence time is shorter than the experimental exposure but longer than the bunch spacing, the limits on $N_s$ improve by a factor of approximately 1.6 to 2 compared to time-independent analyses. In the limiting case of a completely unconstrained background uncertainty, this improvement factor can reach $\approx 7$.
• Resonance Search Improvements: For resonance searches with known oscillation parameters, time-dependent weighting yields limits approximately 50% stronger than those without time information for periods between $10^{-2}$ and 1 month.
• Data-Driven Background Learning: The application of the CATHODE classifier with learned time-dependence demonstrates that neural networks can effectively capture periodic timing information without prior knowledge of the period, though performance degrades for very rapid oscillations (high frequencies) or very long periods (weak modulation within the exposure window).
• Background Uncertainty Mitigation: The study demonstrates that utilizing time sidebands allows for a direct measurement of the background rate within the signal region. This is particularly effective in reducing sensitivity to systematic uncertainties in the background shape (e.g., trigger turn-on uncertainties), maintaining robust sensitivity even when mass-sideband-only analyses suffer from degraded statistical power.

Significance and Claims
The paper claims that time-dependent analysis provides a powerful, orthogonal handle to separate signal from background in LHC searches, specifically for models involving ultralight dark matter coupled to heavy particles. The primary significance lies in the statistical gain: by exploiting the temporal modulation of the signal against a static background, experiments can achieve tighter constraints on new physics rates without requiring additional kinematic cuts that might dilute the signal.

The authors emphasize that this approach is particularly valuable for scenarios where the background is not well-understood or has large systematic uncertainties; in such cases, the ability to probe the background distribution directly via time sidebands offers substantial improvements in discovery potential. While the paper acknowledges that systematic effects (e.g., luminosity degradation, beam dynamics) can introduce time-dependence, it argues that these can likely be distinguished from the specific oscillatory signatures of ultralight DM through Fourier analysis or by examining the coherence properties of the signal. The work suggests that future LHC analyses should explicitly consider time-dependence to fully harness the discovery potential of the collider, particularly for ultralight DM models that are difficult to probe at low-energy experiments due to energy thresholds.