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Simulations and flavour-scheme studies for Higgs-boson production in association with charm quarks

This paper presents a comprehensive NLO+PS study of Higgs-boson production with charm and bottom quarks, comparing massive and massless flavour schemes to quantify uncertainties and provide the first practical simulation recommendations for $c\bar{c}H$ production at the LHC.

Original authors: Tiziano Bevilacqua, Christian Biello, Lea Michela Caminada, Clemens Lange, Marino Missiroli, Davide Pagani, Michele Selvaggi, Marco Zaro

Published 2026-08-28

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CC BY 4.0

Original authors: Tiziano Bevilacqua, Christian Biello, Lea Michela Caminada, Clemens Lange, Marino Missiroli, Davide Pagani, Michele Selvaggi, Marco Zaro

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Large Hadron Collider is a machine built to smash protons together at speeds close to the speed of light, recreating the conditions that existed just moments after the birth of the universe. Among the many particles produced in these violent collisions is the Higgs boson, a fundamental particle that acts as a sort of cosmic glue, giving mass to other elementary particles. Since its discovery, physicists have been meticulously measuring how the Higgs boson interacts with other particles to see if the Standard Model of physics holds up under scrutiny. While the Higgs boson is known to interact strongly with the heaviest particles, such as the top quark, its relationship with lighter particles remains a mystery. Specifically, scientists are eager to understand how strongly the Higgs boson couples to the charm quark, a particle that is much lighter than the bottom quark but still heavy enough to be significant. Measuring this interaction is difficult because the signals are faint and easily drowned out by background noise, requiring extremely precise computer simulations to distinguish the true signal from the clutter of other particle collisions.

A team of researchers has now tackled the challenge of simulating the production of a Higgs boson alongside a charm quark. In the real world, when protons collide, they can produce a Higgs boson that travels away with a charm quark in tow. To study this, physicists rely on complex computer programs that calculate the probability of these events occurring. However, these calculations face a fundamental dilemma: how to treat the mass of the charm quark. In some calculations, the charm quark is treated as a heavy, distinct object with a specific weight, which is accurate when the collision energy is low. In other calculations, the charm quark is treated as a massless particle, similar to a photon, which is a useful simplification when the collision energy is very high. For a long time, these two approaches have produced different results, leaving experimentalists unsure which simulation to trust when analyzing data from the collider.

The authors of this study set out to resolve this confusion by running a series of high-precision simulations at the energy levels expected for the Large Hadron Collider. They compared the "heavy" approach, where the charm quark's mass is fully accounted for, against the "massless" approach, where the mass is ignored to simplify the math. Their work revealed that while the two methods agree well when the particles are moving very fast, they diverge significantly when the particles move more slowly. In the slow-moving region, the mass of the charm quark matters, and ignoring it leads to incorrect predictions about how often these events happen. The researchers also investigated whether the Higgs boson could be produced through more subtle, indirect pathways involving loops of particles or interference between different forces. They found that these exotic contributions are so small that they can be safely ignored for current experimental purposes, allowing scientists to focus on the main production mechanisms.

To create the most reliable guide for future experiments, the team developed a new method called "stitching." Instead of choosing one simulation method over the other, they combined them. They used the massless simulation for high-energy events where it is most accurate and switched to the heavy-mass simulation for low-energy events where the charm quark's weight is crucial. This hybrid approach was then tested against an even more advanced calculation that includes higher-order corrections, which are essentially more detailed layers of physics that account for rare, complex interactions. The stitched simulation matched this gold-standard calculation remarkably well, particularly in the difficult low-energy regions where previous methods struggled. The researchers also determined the best settings for the computer programs, such as how to handle the energy scales of the collision, to ensure the results are stable and reliable.

The findings provide a clear roadmap for experimentalists who are hunting for the Higgs boson produced with charm quarks. By using the stitched simulation, scientists can now model these events with greater confidence, reducing the uncertainty that has plagued previous analyses. The study confirms that while the charm quark is light, its mass cannot be ignored when the particles are moving slowly, and that a single, unified simulation strategy is necessary to capture the full picture. This work does not claim to have solved the mystery of the charm quark's interaction with the Higgs boson, but it has provided the essential tools needed to measure it accurately. With these improved simulations, the next generation of experiments will be better equipped to test whether the Higgs boson behaves exactly as the Standard Model predicts or if it hints at new, undiscovered physics.

Technical Summary: Simulations and Flavour-Scheme Studies for Higgs-boson Production in Association with Charm Quarks

Problem Statement
The paper addresses the theoretical and phenomenological challenges associated with simulating Higgs boson production in association with heavy-flavour (HF) quarks, specifically focusing on the charm sector ( $H+c$ ). While the bottom-quark Yukawa coupling ( $y_b$ ) has been extensively studied, the charm-quark Yukawa coupling ( $y_c$ ) remains poorly constrained, with current measurements allowing for significant deviations from Standard Model (SM) predictions. Accurate simulation of $H+c$ and $c\bar{c}H$ production is critical for probing $y_c$ at the Large Hadron Collider (LHC). However, existing simulation strategies face difficulties in reconciling two competing theoretical frameworks: the massive flavour scheme (3FS), which retains the charm mass and is accurate at low transverse momentum ( $p_T$ ), and the massless flavour scheme (4FS), which treats the charm quark as a massless parton to resum large logarithms at high $p_T$ . The paper aims to quantify the discrepancies between these schemes, assess the impact of interference and loop-induced effects, and provide practical recommendations for Next-to-Leading Order plus Parton Shower (NLO+PS) simulations.

Methodology
The authors employ a comprehensive simulation strategy using the MADGRAPH5_AMC@NLO (MG5_AMC) and POWHEG frameworks, interfaced with PYTHIA8 for parton showering and hadronization.

Theoretical Frameworks and Schemes:
- Massive Scheme (3FS): Retains the charm mass ( $m_c \approx 1.5$ GeV). Leading order (LO) processes are $gg \to c\bar{c}H$ and $q\bar{q} \to c\bar{c}H$ .
- Massless Scheme (4FS): Treats charm as massless, introducing a charm Parton Distribution Function (PDF). LO process is $c\bar{c} \to H$ .
- Renormalization: The charm Yukawa coupling is renormalized in the $\overline{\text{MS}}$ scheme with a running mass starting at $Q=3$ GeV, rather than the on-shell scheme, to handle the small charm mass more reliably.
Treatment of Subleading Effects:
- Interference: The interference between the top-quark induced loop ( $y_t$ ) and the charm-Yukawa dependent terms ( $y_c$ ) is studied at LO. The authors find this contribution is subleading ( $\sim 1\%$ ) and vanishes in the massless limit due to chirality conservation. Consequently, they neglect this interference in their primary simulations.
- Loop-induced Contributions: Genuine charm-loop contributions to gluon-fusion ( $gg \to H$ via charm loops) are studied. These are found to be negligible ( $\mathcal{O}(5)$ fb inclusive, further suppressed by tagging requirements) and are excluded from the main signal modeling.
Simulation Setups:
- NLO+PS: Performed in both 3FS and 4FS using MG5_AMC.
- FxFx Merging: Applied to the 4FS to include NLO corrections for $H+c$ and $H+c+jet$ processes, improving the description of high-multiplicity final states.
- NNLO+PS: Performed in the 4FS using the MINNLOPS method, providing a high-precision benchmark for $c\bar{c} \to H$ .
- Stitching Procedure: To combine the strengths of both schemes, a "stitched" sample is constructed. Events with zero charm jets ( $N_{c\text{-jet}}=0$ ) are taken from the 4FS-FxFx sample, while events with one or more charm jets ( $N_{c\text{-jet}} \ge 1$ ) are taken from the 3FS sample. The combined sample is normalized using K-factors derived from the ratio of NNLO/NLO cross sections (extrapolated from $b\bar{b}H$ results where $c\bar{c}H$ NNLO is unavailable).
Scale Choices: The study systematically evaluates renormalization ( $\mu_R$ ), factorization ( $\mu_F$ ), and parton-shower scales. The optimal configuration is identified as dynamic scales $\mu_R = \mu_F = H_T/4$ and a shower scale factor of 0.5, which minimizes discrepancies between the massive and massless schemes in fiducial regions.

Key Contributions and Results

Flavour Scheme Comparison: At 13.0 TeV, the inclusive cross sections between 3FS and 4FS differ significantly (up to a factor of two). In the fiducial region at 13.6 TeV, the discrepancy is reduced but remains sizeable, reflecting a large flavour-scheme uncertainty.
Differential Observables:
- Low $p_T$ : The 4FS (massless) fails to reproduce the shape of the $p_T$ spectrum for the Higgs and leading charm jet at low transverse momentum ( $p_T \lesssim 20$ GeV) due to the absence of mass effects. The 3FS provides a better description here.
- High $p_T$ : In the high momentum region, where mass effects are negligible, the 3FS and 4FS FxFx predictions yield comparable spectra in terms of shape, though normalization differences persist.
- NNLO Benchmark: The MINNLOPS (NNLO+PS) simulation in the 4FS serves as a benchmark. It shows excellent agreement with the FxFx prediction in the high- $p_T$ tail but includes higher-order logarithmic resummation that improves the low- $p_T$ description.
The Stitched Solution: The proposed stitching procedure successfully interpolates between the schemes. It yields a description of observables that is closer to the NNLO+PS prediction in the low- $p_T$ region (where mass effects dominate) while remaining consistent with the massless predictions at high $p_T$ . The scale uncertainty of the stitched sample is reduced compared to standalone NLO samples.
Interference and Loops: The study confirms that interference terms and pure loop-induced charm contributions are negligible for current experimental sensitivities, justifying their omission in standard $H+c$ signal modeling.

Significance and Claims
The paper claims to provide the first practical recommendations for simulating $c\bar{c}H$ production in LHC analyses. Its primary significance lies in establishing a coherent simulation framework that mitigates the large theoretical uncertainties arising from the choice of flavour scheme.

Specifically, the authors recommend:

Using NNLO+PS simulations (via MINNLOPS) whenever possible for $H+c$ production.
In the absence of full NNLO predictions at the analysis level, adopting the stitching procedure (combining 3FS and 4FS based on jet multiplicity). This approach mitigates the need for the flavour-scheme uncertainty obtained from a plain yield comparison of the massive and massless samples, which results in an $\mathcal{O}(30\%)$ discrepancy after fiducial cuts, as the residual discrepancy with respect to the MINNLOPS shapes is covered by the scale uncertainty of the stitched sample.
Utilizing the $\overline{\text{MS}}$ scheme with a running charm mass for Yukawa coupling renormalization.

The work concludes that this validated framework supports ongoing and future experimental efforts to probe the charm-Yukawa coupling, offering a robust method to handle the theoretical complexities of heavy-flavour associated Higgs production.

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