Constraining new physics in charm quark associated Higgs boson production events using the Standard Model effective field theory approach

This paper presents a first-time investigation using the Standard Model effective field theory to demonstrate how measurements of charm quark-associated Higgs boson production decaying to four muons at the LHC can constrain dimension-six operators, deriving expected limits on Wilson coefficients through a proposed analysis strategy based on CMS-like detector simulations.

The Gist

Imagine the universe is a giant, incredibly complex machine built according to a specific instruction manual called the Standard Model. For decades, scientists have checked every gear and spring in this machine, and so far, it works exactly as the manual says. But physicists suspect there might be hidden, secret gears (New Physics) that we haven't found yet because they are too small or too heavy to see directly.

This paper is like a detective story where the authors are trying to find those hidden gears by looking at a very specific, rare, and tricky part of the machine: the Higgs boson hanging out with a "charm" quark.

Here is the breakdown of their investigation using simple analogies:

1. The Detective's Toolkit: The "EFT"

Since the scientists can't build a machine big enough to see the secret gears directly, they use a tool called Effective Field Theory (EFT).

• The Analogy: Imagine you are trying to figure out what's inside a sealed, heavy box by shaking it. You can't see inside, but you can feel how the weight shifts or how the box rattles.
• In the paper: The "box" is the collision of particles at the Large Hadron Collider (LHC). The "rattling" is the math they use to describe how the Higgs boson behaves. They add "extra terms" to their math (like adding a little extra weight to the box) to see if the real data matches the prediction. If the data wobbles differently than expected, it means there's a hidden gear (New Physics) inside.

2. The Rare Event: "Higgs + Charm"

The scientists are looking for a specific event: A Higgs boson being born right next to a charm quark (a type of particle).

• The Analogy: Imagine a crowded dance floor (the LHC). Most of the time, the Higgs boson dances with heavy partners (like top quarks) or light partners (like electrons). But sometimes, it dances with a "charm" partner. This is a very rare dance.
• Why look here? Because in the standard manual, this dance is very clumsy and rare. If there are hidden gears, they might make this specific dance move much more often or make the dancers spin much faster.

3. The Three Suspects (The Operators)

The paper focuses on three specific "suspects" (mathematical rules) that could be messing up the dance:

1. The Chromomagnetic Dipole (The "Spin-Doctor"): This suspect tries to twist the charm quark's spin in a weird way. It's like a dancer suddenly spinning uncontrollably fast.
2. The Yukawa Operator (The "Volume Knob"): This suspect just turns the volume up or down on how strongly the Higgs and charm quark talk to each other.
3. The Higgs-Gluon Operator (The "Background Noise"): This suspect changes how the Higgs interacts with the "glue" holding the particles together.

4. The Investigation Strategy

The authors ran a massive computer simulation (like a video game) of the LHC to see what happens if these suspects are real.

• The Clue: They looked at the speed of the particles.
  • If the "Spin-Doctor" is real, the charm quark (and the jet of particles it creates) would fly off with huge speed (high momentum).
  • If the "Volume Knob" is real, they would just see more of these events, but the speed wouldn't change as much.
• The Filter: They focused on a very clean signal: The Higgs boson decaying into four muons (four tiny, ghost-like particles). It's like looking for four specific colored balloons in a sea of confetti. It's hard to find, but if you find them, you know exactly what you have.

5. The Results: "Not Guilty... Yet"

After running the simulation and checking the math against what we know about the universe:

• The Verdict: They didn't find the hidden gears yet. The data still looks mostly like the Standard Model.
• The New Limits: However, they drew a new "fence" around the suspects. They can now say: "If the Spin-Doctor exists, its power must be weaker than X." And "If the Volume Knob exists, it can't be turned louder than Y."
• The Future: They also calculated what will happen when the LHC gets even more powerful (the High-Luminosity LHC). With more data, the fence will get tighter, making it much harder for these hidden gears to hide.

6. Why This Matters

This paper is important because it's the first time anyone has tried to use this specific "Higgs + Charm" dance to hunt for these specific types of new physics.

• The Takeaway: Even though they didn't find new physics today, they built a better map for the future. They showed that looking at this rare, specific dance is a powerful way to catch the universe's secrets, especially if the secrets involve how the Higgs talks to charm quarks.

In a nutshell: The authors built a super-accurate simulation to see if the Higgs boson behaves strangely when dancing with a charm quark. They didn't find the stranger, but they successfully tightened the rules on how strange the dance can be, paving the way for future discoveries.

Technical Summary

1. Problem Statement

The discovery of the Higgs boson has opened a new era for probing the scalar sector of the Standard Model (SM). While couplings to heavy particles (top, bottom, vector bosons) are well-measured, the Higgs-charm Yukawa coupling remains poorly constrained. Direct searches for $H \to c\bar{c}$ are challenging due to overwhelming QCD backgrounds.

• The Gap: The process of Higgs boson production in association with a charm quark ($pp \to H + c$, denoted as cH) offers an alternative probe. However, this is a rare SM process ($\sigma \sim O(10^{-1})$ pb) and has not been thoroughly exploited for Beyond the Standard Model (BSM) searches.
• The Goal: To investigate the sensitivity of the cH process to BSM physics using the Standard Model Effective Field Theory (SMEFT) framework, specifically focusing on dimension-six operators that modify charm-Higgs interactions.

2. Methodology

A. Theoretical Framework (SMEFT)

The authors extend the SM Lagrangian with dimension-six operators ($d=6$) in the Warsaw basis. They focus on three specific operators relevant to cH production at Leading Order (LO):

1. Chromomagnetic Dipole Operator ($\hat{O}_{cG}$): Generates a tree-level four-point interaction ($c_L c_R H G$). Crucially, unlike other processes, the interference between this operator and the SM is not suppressed by the small charm mass ($m_c$), making cH the ideal channel to constrain it.
2. Yukawa Operator ($\hat{O}_{cH}$): Rescales the SM charm Yukawa coupling ($y_c$).
3. Higgs-Gluon Operator ($\hat{O}_{HG}$): Generates contact interactions between the Higgs and gluons.

The cross-section is modeled as:
$$\sigma = \sigma_{SM} + \frac{c_i}{\Lambda^2} \delta_{int} + \frac{c_i^2}{\Lambda^4} \sigma_{EFT}$$
where $c_i$ are Wilson coefficients and $\Lambda$ is the new physics scale.

B. Validity and Perturbativity

To ensure the EFT interpretation is valid, the authors impose perturbativity bounds. They assume a UV-complete theory with a single new coupling $g_*$ and use Naive Dimensional Analysis (NDA) to relate the Wilson coefficients to a cutoff scale $M_{cut}$. Limits are only considered valid if they satisfy $| \tilde{c}_i | M_{cut}^2 \lesssim g_* g_{SM}$, ensuring the coupling does not become non-perturbative.

C. Simulation and Event Selection

• Signal: $pp \to H + c$ with $H \to ZZ^* \to 4\mu$.
  • Generated using MadGraph5_aMC@NLO with the SMEFTsim model.
  • Parton showering via Pythia8.
  • Detector simulation via Delphes (parametrized to mimic CMS Run-2 performance), including DeepJet c-tagging parameterization.
• Backgrounds:
  • Irreducible: $ZZ \to 4\mu$ (via $q\bar{q}$ and $gg$),$H \to ZZ$ (ggF, VBF, $VH$, $t\bar{t}H$).
  • Reducible: Drell-Yan ($Z/\gamma^* + jets$) and $t\bar{t} + jets$ with misidentified muons.
• Selection Strategy:
  • Four muons with $p_T > 5$ GeV (leading $>20$ GeV), $|\eta| < 2.4$.
  • Reconstructed $Z_1$ ($40 < m_{\mu\mu} < 120$ GeV) and $Z_2$ ($12 < m_{\mu\mu} < 120$ GeV).
  • Higgs candidate mass $m_{4\mu} > 70$ GeV.
  • Selection of the leading jet ($p_T > 20$ GeV) to complete the cH candidate.

D. Statistical Analysis

• Tool: Combine (profile likelihood ratio test statistic).
• Discriminators:
  • For $\hat{O}_{cG}$: Leading jet transverse momentum ($p_T^{jet}$), as this operator significantly enhances the high-$p_T$ tail.
  • For $\hat{O}_{cH}$: Higgs candidate mass ($m_{4\mu}$), as it primarily affects the production rate (normalization).
• Uncertainties: Systematic uncertainties (experimental: JES, muon ID, luminosity; theoretical: PDF, $\alpha_s$, scale variations, K-factors) are included as nuisance parameters.

3. Key Contributions

1. First-Time Investigation: This is the first study to systematically evaluate the cH process ($H+c$) as a probe for dimension-six SMEFT operators, specifically highlighting its unique sensitivity to the chromomagnetic dipole operator ($\hat{O}_{cG}$).
2. Chirality Argument: The paper theoretically demonstrates why cH is the only viable channel to constrain $\hat{O}_{cG}$ at tree level, as the interference term is not chirality-suppressed by $m_c$ (unlike in dijet or flavor-blind Higgs production).
3. Perturbativity Constraints: The authors derive rigorous validity bounds for the Wilson coefficients based on $M_{cut}$, ensuring that the derived limits do not violate the perturbative nature of the underlying UV theory.
4. Comprehensive Simulation: A full simulation chain from LO matrix elements to detector-level reconstruction for the $H \to 4\mu$ channel, including realistic background modeling and systematic uncertainty propagation.

4. Results

The study derives expected 95% Confidence Level (CL) upper limits on the Wilson coefficients ($\tilde{c} = c/\Lambda^2$) for two scenarios: LHC Run-2 (138 fb$^{-1}$) and High-Luminosity LHC (HL-LHC, 3000 fb$^{-1}$).

Operator	Wilson Coefficient	Limit (Run-2, 138 fb$^{-1}$) [TeV$^{-2}$]	Limit (HL-LHC, 3000 fb$^{-1}$) [TeV$^{-2}$]
Chromomagnetic ($\hat{O}_{cG}$)	$\tilde{c}_{cG}$	1.36	0.56
Yukawa ($\hat{O}_{cH}$)	$\tilde{c}_{cH}$	2.31	1.76

• Sensitivity Comparison: The analysis is roughly two orders of magnitude less sensitive to the Higgs-gluon operator ($\hat{O}_{HG}$) compared to inclusive Higgs production measurements, confirming that cH is not the optimal channel for constraining $\hat{O}_{HG}$.
• Simultaneous Fits: When fitting two operators simultaneously:
  • $\tilde{c}_{cG}$ and $\tilde{c}_{cH}$ are largely uncorrelated because they affect different observables (shape vs. normalization).
  • $\tilde{c}_{HG}$ introduces degeneracy with the other operators, as it affects the jet $p_T$ spectrum similarly to $\hat{O}_{cG}$.
• Validity Check: The derived limits for $\hat{O}_{cG}$ with $M_{cut} < 1$ TeV satisfy the perturbativity requirements ($\epsilon > 0.09$).

5. Significance and Outlook

• Unique Probe: The paper establishes cH production as a critical, unique channel for constraining the chromomagnetic dipole moment of the charm quark, a parameter inaccessible via other standard Higgs or jet analyses due to chirality suppression.
• Future Potential: While current limits are weaker than those on the Higgs-gluon operator, the cH channel provides complementary information essential for a complete SMEFT fit.
• Recommendations:
  • Future experimental analyses should utilize multivariate techniques to break degeneracies between operators (e.g., $\hat{O}_{cG}$ vs $\hat{O}_{HG}$).
  • Improvements in c-jet tagging (e.g., using ParticleTransformer algorithms) could significantly enhance sensitivity.
  • Extending the analysis to other Higgs decay modes (e.g., $H \to \gamma\gamma$, $H \to WW^*$) and including electron channels could further improve statistical power.

In conclusion, this work provides a foundational framework for using cH events to search for new physics, demonstrating that despite the rarity of the process, it offers unique constraints on specific BSM operators that are otherwise unconstrained.