Pseudoscalar contributions to Zh production at the LHC… — Plain-Language Explanation

Imagine the Standard Model of particle physics as a very successful, well-organized orchestra. For decades, it has played the music of the universe perfectly. In 2012, they finally found the last missing instrument: the Higgs boson (the "125 GeV" note). It sounded exactly as the sheet music predicted.

But, some musicians (physicists) suspect there might be a hidden section of the orchestra we haven't heard yet. They think there might be extra instruments playing in the background, specifically a "ghostly" instrument called a pseudoscalar.

This paper is like a detective story where the authors try to figure out if this ghostly instrument is playing a solo that we can hear, specifically by listening to a specific duet: the Higgs boson and the Z boson (let's call them the "Zh Duo").

The Mystery: The "Ghost" Instrument

In the Standard Model, the Zh Duo is produced when two protons smash together, and a quark and an antiquark (tiny particles inside the proton) annihilate to create them. It's like two people in a crowded room bumping into each other to create a spark. This happens, but it's rare because finding an "antiquark" inside a proton is like finding a specific needle in a haystack.

However, if a pseudoscalar exists, it can act as a shortcut. Instead of the needle-in-a-haystack method, the pseudoscalar can be created by gluon-gluon fusion. Think of gluons as the "glue" holding the proton together. There are lots of them. If the pseudoscalar can be made from this glue, it's like finding a whole pile of needles instead of just one. This makes the production of the Zh Duo much easier and louder.

The authors ask: If this ghost instrument is playing, can we hear it over the noise of the standard orchestra?

The Investigation: Two Scenarios

The authors looked at two different "mass ranges" for this ghost instrument to see if it leaves a trace.

Scenario 1: The Light Ghost (95 GeV)

There have been some strange, faint whispers in the data suggesting a particle exists at a mass of 95 GeV. Some scientists think this could explain a few odd signals (excesses) seen in photon and tau particle detectors.

The Analogy: Imagine trying to hear a whisper (the 95 GeV ghost) while it is trying to sing a duet with a heavy bass (the Z boson).
The Result: The authors found that for a 95 GeV particle, the "duet" is extremely quiet. Because the ghost is so light, it has to be "off-shell" (it's not quite a real particle, more like a fleeting shadow) to produce the heavy Zh Duo.
Conclusion: The signal is so weak that even our most sensitive microphones (the LHC detectors) can't distinguish it from the background noise. If this 95 GeV ghost exists, it's currently hiding perfectly well. It won't change the Zh measurements we see today.

Scenario 2: The Heavy Ghost (100 GeV to 1000 GeV)

What if the ghost is heavier? The authors looked at a wide range of heavier masses.

The Analogy: Now imagine the ghost is a heavy, resonant drum. If it's the right weight, it can really bang out a loud rhythm.
The Sweet Spot: They found a "Goldilocks zone" between roughly 216 GeV and 350 GeV.
- If the ghost is too light, it can't make the Zh Duo efficiently.
- If it's too heavy (heavier than two top quarks), it prefers to decay into top quarks instead of the Zh Duo, so the signal drops off.
The Result: In this "Goldilocks zone," the ghost instrument plays so loudly that it would drown out the standard orchestra.
The Catch: The LHC has already measured the Zh Duo very carefully, and it sounds exactly like the Standard Model predicts. There is no extra loudness.
Conclusion: This means we can now banish many versions of this ghost instrument. If the ghost existed in that heavy mass range, we would have heard it by now. The fact that we haven't means those specific "ghosts" don't exist, or at least they don't interact the way the models predicted.

The Shape of the Sound (Differential Distributions)

The authors also looked at how the sound is distributed.

Standard Sound: The normal Zh production creates a smooth, predictable curve of energy.
Ghost Sound: If the ghost is there, it creates a sharp "spike" (a Jacobian peak) in the energy distribution, like a sudden, sharp note in a melody.

They checked if the current experiments (ATLAS and CMS) could spot this spike. They found that even if the total volume (total cross-section) was only slightly higher than expected, looking at the shape of the energy (specifically the transverse momentum) could reveal the ghost.

The Final Verdict

For the 95 GeV ghost: It's too quiet to be heard right now. We need much more sensitive microphones (future upgrades to the LHC) to see if it's there.
For the heavy ghosts (100–1000 GeV): We have already ruled out a huge chunk of possibilities. The LHC data is so precise that if these heavy ghosts were playing, we would have noticed. This forces physicists to rewrite their sheet music for these models, narrowing down where the ghost could possibly be hiding.

In short: The paper uses the "Zh Duo" as a listening post. It tells us that while a light ghost might still be hiding in the shadows, any heavy ghost trying to play a solo has been caught and silenced by current data. As the LHC gets louder and more precise in the future, we might finally hear that light whisper, or confirm that the orchestra is complete after all.

1. Problem Statement

The Standard Model (SM) Higgs boson ( $h$ , $m_h \approx 125$ GeV) has been extensively studied, yet experimental anomalies suggest the existence of an extended scalar sector. Notably, CMS and ATLAS have reported local excesses in the diphoton ( $\gamma\gamma$ ) channel around 95.4 GeV, alongside hints in the $\tau\tau$ and $b\bar{b}$ channels. Many Beyond the Standard Model (BSM) theories, such as the Two Higgs Doublet Model (2HDM) and its extensions, predict the existence of a physical pseudoscalar boson ( $A$ ).

While direct searches for heavy Higgs bosons ( $A \to \tau\tau, b\bar{b}$ ) are standard, this paper investigates a specific, often overlooked production channel: associated production of the SM-like Higgs and the Z boson ($Zh$) mediated by a pseudoscalar.

SM Process: Dominated by quark-antiquark annihilation ( $q\bar{q} \to Z \to Zh$ ), which is suppressed by parton distribution functions (PDFs).
BSM Process: A pseudoscalar $A$ can be produced via gluon-gluon fusion ( $gg \to A$ ) and decay into $Zh $($ A \to Zh$).
Key Issue: Since the initial states differ ( $q\bar{q}$ vs. $gg$), there is no interference between the SM and BSM amplitudes at Leading Order (LO). The BSM contribution is purely additive. The authors aim to determine if current LHC measurements of the $Zh$ cross-section can constrain the parameter space of models containing a pseudoscalar, particularly those explaining the 95 GeV excesses or generic heavier pseudoscalars.

2. Methodology

The authors analyze two specific UV-complete models:

2HDM (Type I and Type II): The standard Two Higgs Doublet Model.
2HDMS (Type II): The 2HDM extended by a complex singlet scalar.

Calculation Framework:

Process: $pp \to gg \to A \to Zh$ .
Order of Calculation: Leading Order (LO) QCD calculations were performed using MadGraph5_aMC@NLO. These were normalized to Next-to-Leading Order (NLO) and Next-to-Next-to-Leading Order (NNLO) using a $K$ -factor (approx. 2) derived from the SusHi code, specifically for the gluon fusion production of a pseudoscalar.
Coupling Modifiers: The cross-sections were scaled using model-specific coupling modifiers ( $\xi$ $ξ$ ) for the $A$ $A$ -fermion and $A$ $A$ -$Zh$ vertices.
- For 2HDM Type I: All fermions couple to $\Phi_2$ .
- For 2HDM Type II: Up-type quarks couple to $\Phi_2$ , down-type quarks and leptons to $\Phi_1$ .
- For 2HDMS: Includes mixing angles ( $\alpha_4$ ) and singlet components.
Kinematic Analysis: The study compares differential distributions (transverse momentum $p_T$ of the Higgs/Z and invariant mass $m_{Zh}$ ) between the SM background ( $q\bar{q} \to Zh$ ) and the BSM signal ( $gg \to A \to Zh$ ) to validate the application of total cross-section limits.
Data Comparison: Results are compared against:
- Current ATLAS $Zh$ cross-section measurement: $\sigma = 0.80 \pm 0.14$ pb.
- Direct search limits from CMS for $gg \to A \to Zh$ .
- Future HL-LHC precision projections ( $\sim 7\%$ ).

3. Key Contributions

Systematic Calculation of $gg \to A \to Zh$ : The paper provides a comprehensive calculation of the pseudoscalar contribution to $Zh$ production, including top and bottom quark loop contributions and their interference terms.
Validation of "Naive" Limits: The authors rigorously test whether total cross-section limits derived from SM-like analyses can be applied to the BSM $gg \to A \to Zh$ signal. They demonstrate that while the shapes of differential distributions differ (signal peaks at lower $p_T$ for on-shell $A$ ), the integrated limits remain a robust constraint for the parameter space.
Differential Distribution Analysis: Using Simplified Template Cross Sections (STXS) bins, they show that the signal often dominates the background in low $p_T$ bins ( $p_T < 150$ GeV) when the cross-section is large, providing a distinct signature even if the total rate is marginal.
Model-Specific Constraints: They derive specific exclusion contours in the $(\tan\beta, \cos(\beta-\alpha))$ plane for both 2HDM Type I and Type II.

4. Results

A. The 95 GeV Pseudoscalar ( $A_{95}$ )

2HDM Type I: To explain the 95 GeV diphoton excess, the model requires specific $\tan\beta$ $tan β$ and $\cos(\beta-\alpha)$ $cos (β - α)$ values. However, for $m_A = 95$ $m_{A} = 95$ GeV, the $A \to Zh$ $A \to Z h$ process requires the pseudoscalar to be highly off-shell ( $m_A < m_Z + m_h \approx 216$ $m_{A} < m_{Z} + m_{h} \approx 216$ GeV).
- Result: The predicted cross-section is extremely small ( $\sim 0.008$ pb), well below the current experimental uncertainty ($0.14$ pb).
- Conclusion: Current $Zh$ measurements cannot constrain the 2HDM Type I interpretation of the 95 GeV excess. A precision of $\sim 1\%$ would be required, which is beyond HL-LHC capabilities.
2HDMS Type II: Similar to Type I, the presence of a singlet component further suppresses the $A-Zh$ coupling.
- Result: The contribution is even smaller than in the pure 2HDM case.
- Conclusion: No constraints can be set on the 95 GeV pseudoscalar via this channel.

B. Generic Heavier Pseudoscalars ( $100 \text{ GeV} \le m_A \le 1000 \text{ GeV}$ )

Kinematic Thresholds: Significant contributions to $\sigma(pp \to Zh)$ only occur when $m_A \ge m_Z + m_h$ (allowing on-shell production).
Branching Ratio Suppression:
- If $m_A > 2m_t$ (top threshold), the decay $A \to t\bar{t}$ opens, drastically reducing the branching ratio to $Zh$.
- If $m_A > m_Z + m_H$ or $m_A > m_W + m_{H^\pm}$ , decays to other heavy scalars dominate, suppressing $Zh$.
Exclusion Power:
- Optimal Region: The strongest constraints arise in the window $m_Z + m_h \le m_A \le 2m_t$ (approx. 216 GeV to 350 GeV) where $A \to Zh$ is kinematically allowed and dominant over $t\bar{t}$ .
- 2HDM Type I: Current $Zh$ cross-section measurements (at $2\sigma$ ) exclude regions of parameter space with $\tan\beta$ up to $\sim 35$ and specific $\cos(\beta-\alpha)$ values. These limits are more restrictive than direct search limits for $m_A \lesssim 450-500$ GeV.
- 2HDM Type II: Constraints are tighter on low $\tan\beta$ ( $\tan\beta \le 3$ ) due to the enhanced bottom-quark coupling ( $\xi_b^A \propto \tan\beta$ ) affecting the production loop and interference.
Future Prospects: HL-LHC precision (7%) will extend the exclusion reach up to $m_A \approx 600-700$ GeV, surpassing current direct search sensitivities.

5. Significance

Complementary Probe: This work establishes $Zh$ production as a powerful, complementary probe for pseudoscalars, independent of direct resonance searches. It is particularly effective in mass regions where direct searches are less sensitive or where the pseudoscalar decays dominantly to $Zh$.
Model Discrimination: The analysis highlights how different 2HDM types (I vs. II) respond differently to $Zh$ constraints due to their distinct Yukawa coupling structures.
Experimental Guidance: By analyzing differential distributions ( $p_T$ and $m_{Zh}$ ), the authors provide experimentalists with specific kinematic regions (low $p_T$ bins) where BSM signals might be most visible, even if the total cross-section deviation is small.
Tool Integration: The results are intended for integration into HiggsBounds, allowing global fits to automatically include constraints from $Zh$ production when testing BSM scenarios.

In summary, while the $Zh$ channel cannot currently constrain a 95 GeV pseudoscalar explaining the diphoton excess, it provides stringent, model-dependent constraints on heavier pseudoscalars (up to $\sim 500$ GeV), often outperforming direct search limits in specific regions of the parameter space.

Pseudoscalar contributions to Zh production at the LHC at 95 GeV and above