Theory uncertainties of the irreducible background to VBF Higgs production

This paper demonstrates that NLO calculations are essential for achieving reliable predictions of the irreducible gluon-fusion background to vector boson fusion Higgs production, while providing consistent simulation setups to resolve discrepancies among existing event generators.

The Gist

Imagine you are a detective trying to find a very rare, shy ghost (the Higgs boson) hiding in a crowded, noisy party (the Large Hadron Collider).

The ghost likes to show up in a specific way: it arrives with two bodyguards (jets) that stand far apart from each other. This specific arrival pattern is called Vector Boson Fusion (VBF). Detecting this pattern helps scientists understand the ghost's personality (its properties).

The Problem:
Unfortunately, there is a "lookalike" impostor. Sometimes, the ghost arrives via a different, much more common route called Gluon Fusion (ggF). In this route, the ghost also brings two bodyguards that look exactly like the VBF ones.

This impostor is the irreducible background. You can't just filter it out because it looks identical to the real thing. To find the real ghost, scientists have to subtract the impostor from the total crowd. But to do that subtraction accurately, they need to know exactly how many impostors are there and what they look like.

The Paper's Mission:
This paper is like a massive quality control check on the "impostor simulation software."

Scientists use complex computer programs (called Event Generators like Pythia, Herwig, and Sherpa) to simulate these impostors. Think of these programs as different chefs trying to bake the same cake (the impostor event).

• The Old Way: Previously, the chefs were using recipes that were a bit vague. They were baking the cake at a "Low Resolution" (Leading Order). Sometimes, Chef Pythia would make a cake that looked slightly different from Chef Herwig's cake. Because the recipes weren't precise, the scientists had to guess the uncertainty, often assuming the difference between the cakes was huge (up to 20%). This made the "background noise" seem much scarier than it might actually be.

What This Study Did:
The authors decided to upgrade the recipes. They told all the chefs: "Stop guessing. Let's bake this cake using the most precise, high-resolution recipe available (Next-to-Leading Order, or NLO)."

They set up a "baking competition" where:

1. Standardized Ingredients: Everyone used the exact same flour and sugar (the same physics parameters and settings).
2. High-End Ovens: They forced the programs to use the most advanced calculation methods available.
3. The Taste Test: They compared the cakes side-by-side.

The Surprising Results:

1. The Chefs Agree: When they all used the high-precision recipe, the cakes turned out almost identical! The differences between Chef Pythia, Chef Herwig, and Chef Sherpa dropped from a scary 20% down to a manageable 10% or less.
2. The "Out of the Box" Mistake: The study found that the big differences seen in the past weren't because the physics was different; it was because the scientists were using the software with "default settings" that weren't perfectly tuned to each other. It was like comparing a cake baked with a gas oven to one baked in a microwave, rather than comparing two cakes baked in the same type of high-end oven.
3. One Chef Stumbled: They found that one specific method (called MiNNLOPS), which is currently used by the big experiments (ATLAS and CMS), had a glitch when predicting the angle between the two bodyguards. It was like one chef consistently putting the frosting on the wrong side of the cake. The other, more precise methods got this right.

Why This Matters:

• Less Fear, More Precision: Because the simulations now agree much better, scientists can be more confident in their background estimates. They don't need to assume the "noise" is as huge as they thought. This makes it easier to spot the real Higgs ghost.
• Better Recipes: The paper provides a "Master Recipe Book" for the experiments. It tells them exactly how to configure their software so that everyone is baking the same cake, ensuring that when they claim to have discovered something new, it's not just a difference in how they baked the background.
• CP Properties: The study specifically looked at the angle between the jets. This angle is crucial for determining if the Higgs boson behaves like a mirror image of itself (a property called CP symmetry). The fact that the high-precision simulations agree on this angle is a huge win for understanding the fundamental nature of the universe.

In a Nutshell:
This paper is a "tune-up" for the computer simulations that act as the background noise for Higgs boson research. By forcing the simulations to use higher-precision math and consistent settings, the authors showed that the "noise" is much more predictable and consistent than we thought. This means the signal of the Higgs boson is clearer, and our understanding of the universe is a little less blurry.

Technical Summary

1. Problem Statement

The Vector Boson Fusion (VBF) channel is a critical process for studying Higgs boson properties, particularly its couplings to $W$ and $Z$ bosons and its CP nature. However, the dominant background to VBF is the irreducible gluon-gluon fusion (ggF) process producing a Higgs boson in association with two jets ($ggF \to Hjj$).

• The Challenge: Precise theoretical predictions for this background are notoriously difficult. Current experimental analyses (ATLAS and CMS) rely on Monte Carlo (MC) event generators that often exhibit discrepancies of up to 20% or more when comparing different generator setups (e.g., Pythia vs. Herwig).
• The Root Cause: These discrepancies often stem from "out-of-the-box" configurations where perturbative calculations (matrix elements) and non-perturbative models (parton showers, hadronization) are mismatched. For instance, the current standard for ggF background (MiNNLOPS) provides Next-to-Leading Order (NLO) accuracy for inclusive Higgs production but only Leading Order (LO) accuracy for the specific $H+2j$ final state, which is crucial for VBF selection.
• Goal: To determine if the large theory uncertainties currently assigned by experiments are due to fundamental physics differences or inconsistent simulation setups, and to provide a consistent, high-precision baseline for future analyses.

2. Methodology

The authors performed a comprehensive comparison of various state-of-the-art event generators and calculation tools under a consistent, unified setup to isolate theoretical uncertainties.

• Simulation Tools:

  • NNLOJet: Used as a fixed-order reference (NNLO for $H+1j$, NLO for $H+2j$).
  • Sherpa: Used for Multi-jet Merging at NLO (MEPS@NLO) and NLO matching (MC@NLO).
  • Powheg Box: Used for NLO matching to parton showers (Hjj process).
  • Parton Showers: Pythia 8.3 (Simple and Dipole-recoil showers) and Herwig 7.3 (Angular-ordered and Dipole showers).
  • MiNNLOPS: The current standard used by ATLAS/CMS (NNLO for $H$, NLO for $H+1j$, LO for $H+2j$).

• Setup Consistency:

  • Kinematics: $\sqrt{s} = 13.6$ TeV, $m_H = 125$ GeV.
  • Scales: Renormalization ($\mu_R$) and factorization ($\mu_F$) scales varied around $H_T/2$.
  • PDFs: PDF4LHC21 NNLO set.
  • Jet Definition: Anti-$k_T$ algorithm with $R=0.4$ (central), $p_T > 30$ GeV.
  • Matching: The study specifically constructed setups where the $H+2j$ final state is calculated at NLO precision for all generators (Sherpa MC@NLO, Powheg Box + Pythia/Herwig) to ensure a fair comparison.

• Observables:

  • Higgs transverse momentum ($p_{T,H}$).
  • Dijet invariant mass ($m_{jj}$).
  • Dijet rapidity separation ($\Delta y_{jj}$).
  • Dijet azimuthal separation ($\Delta \phi_{jj}$) – crucial for CP studies.

3. Key Contributions

1. Identification of Setup-Induced Discrepancies: The paper demonstrates that the large differences (up to 20-30%) previously observed between generators (e.g., MiNNLOPS+Pythia vs. MiNNLOPS+Herwig) are largely due to the LO accuracy of the $H+2j$ calculation in the MiNNLOPS framework and inconsistent matching schemes, rather than fundamental differences in QCD physics.
2. Establishment of a Consistent NLO Baseline: The authors provide a set of "consistent setups" where the $H+2j$ process is calculated at NLO accuracy across different generators (Sherpa MC@NLO, Powheg Box + Pythia, Powheg Box + Herwig).
3. Decoupling Uncertainty Sources: The study disentangles uncertainties arising from:
   • Fixed-order accuracy (LO vs. NLO).
   • Matching schemes (Born suppression vs. generation cuts).
   • Parton shower algorithms (Angular-ordered vs. Dipole).
   • Hadronization models (Cluster vs. String) and underlying event tunes.
4. Rivet Routine: A Rivet analysis routine is provided to allow experiments to directly validate the correct usage of these generators.

4. Key Results

• NLO Precision is Essential: When comparing generators where the $H+2j$ state is calculated at NLO (Sherpa MC@NLO, Powheg Box + Pythia/Herwig), the predictions agree within 10% (and often better) across all observables. This is a significant improvement over the 20-30% discrepancies seen with the standard MiNNLOPS (LO for $H+2j$) setup.
• MiNNLOPS Limitations: The MiNNLOPS framework, while excellent for inclusive Higgs production, shows deficiencies in the $H+2j$ sector:
  • It predicts a different shape for the dijet azimuthal separation ($\Delta \phi_{jj}$) compared to NLO-matched generators, particularly around $\Delta \phi_{jj} \approx \pi$.
  • It shows larger deviations in the Higgs $p_T$ spectrum compared to fixed-order NLO references.
• Parton Shower & Matching Variations:
  • Once the hard process is NLO-accurate, variations in the parton shower (Pythia vs. Herwig) and matching parameters (e.g., hdamp, btlscale in Powheg) result in differences of < 5% for most observables.
  • The choice of hadronization model (Cluster vs. String) and underlying event tunes (Monash, AZNLO, CP5) introduces differences of < 5%.
• Jet Radius Dependence: The study confirms that while jet radius ($R$) affects absolute cross-sections, the relative agreement between NLO-matched generators remains robust across different $R$ values (0.3 to 0.8).
• Cutflow Analysis: In VBF-enriched regions (tight cuts on $m_{jj}$ and $\Delta y_{jj}$), the NLO-matched generators agree within 10%, whereas the MiNNLOPS prediction deviates more significantly, particularly in the high $p_{T,H}$ tail.

5. Significance and Recommendations

• Reduced Theory Uncertainties: The paper argues that the theory uncertainties currently quoted by ATLAS and CMS for the ggF background (often derived from the envelope of different "out-of-the-box" generators) are overestimated. By using consistent NLO-matched setups, the uncertainty can be reduced to the ~10% level (independent of scale and PDF uncertainties).
• Impact on CP Measurements: The accurate modeling of the $\Delta \phi_{jj}$ distribution is vital for measuring the CP properties of the Higgs boson. The study shows that NLO-matched generators provide consistent predictions for this observable, whereas the standard MiNNLOPS setup does not.
• Recommendation: The authors recommend that experimental collaborations default to any of the NLO-accurate $H+2j$ setups (Sherpa MC@NLO, Powheg Box + Pythia, or Powheg Box + Herwig) for background modeling. The uncertainty should be estimated by varying among these consistent NLO setups rather than relying on the spread of LO-accurate or mismatched generators.

Conclusion: The paper establishes that the irreducible ggF background to VBF Higgs production can be predicted with high reliability (within 10%) if the simulation is performed with NLO-accurate matrix elements for the $H+2j$ final state. This finding suggests that current experimental systematic uncertainties may be overly conservative and that a shift to consistent NLO-matched simulations will significantly improve the precision of Higgs property measurements at the LHC.