NMSSMScanner: Efficient Scans in the NMSSM Parameter Space Proof of Concept

This paper introduces NMSSMScanner, a new tool designed to efficiently scan the complex parameter space of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) under all relevant constraints, demonstrating its utility by identifying configurations that maximize resonant Higgs boson pair production.

The Gist

Imagine the Standard Model of particle physics as a very successful, but slightly incomplete, instruction manual for how the universe works. It explains how particles interact, but it leaves out some big mysteries, like what Dark Matter is or why there is more matter than antimatter.

Physicists have proposed a "Next-to-Minimal" version of this manual called the NMSSM (Next-to-Minimal Supersymmetric Standard Model). Think of the NMSSM as a massive, complex recipe book with thousands of ingredients and variables. You can tweak the amounts of sugar, flour, and eggs (the parameters) to see what kind of cake (the universe) you get. The problem is that there are so many ways to mix these ingredients that finding the perfect recipe that matches reality is like trying to find a specific grain of sand on a beach by looking at every single grain one by one. It's too slow and inefficient.

The New Tool: NMSSMScanner

This paper introduces a new digital tool called NMSSMScanner. You can think of this tool as a super-smart, high-speed drone that flies over that beach of sand. Instead of looking at every grain, it uses clever algorithms (like a smart search engine or a guided tour) to quickly zoom in on the specific grains that look promising.

The authors built this tool to efficiently scan the "recipe book" of the NMSSM. They wanted to see if they could find specific settings where the universe would produce a very rare and interesting event: two Higgs bosons appearing together (a "di-Higgs" event) in a specific way.

The Proof of Concept: Hunting for the "Golden Ticket"

To prove their tool works, the authors didn't just scan randomly; they set a specific goal. They wanted to find the "Golden Ticket" scenarios—settings where the production of these two Higgs bosons happens as often as possible.

They looked for two main ways this could happen:

1. The Scalar Route: A heavy particle (like a heavy drum) vibrates and splits into two lighter particles (a standard Higgs and a new, non-standard Higgs).
2. The Pseudoscalar Route: A similar process, but involving a different type of particle (like a spinning top instead of a drum).

They simulated these events at the Large Hadron Collider (LHC), the giant particle smasher in Europe. They asked: "If we mix the ingredients this way, how often do we get two Higgs bosons that then decay into things we can see, like pairs of bottom quarks (b-quarks), tau particles, or photons?"

The Results: What They Found

Using their new scanner, they found several "benchmark points." These are specific, valid recipes that the tool identified as the best candidates for producing these double Higgs events.

• The Best Candidates: They found scenarios where the production rate could be as high as 42 femtobarns (a tiny unit of probability) for certain combinations. To put this in perspective, in the world of particle physics, finding a needle in a haystack is hard; finding a needle that appears 42 times more often than usual is a huge win.
• The "Light" vs. "Heavy" Outcomes: They checked different ways the particles could break apart (decay).
  • Light endings: Some scenarios resulted in the Higgs bosons turning into pairs of bottom quarks, tau particles, or photons. The tool found that the "4-bottom-quark" ending was the most common and easiest to spot.
  • Heavy endings: They also looked for endings involving top quarks or W bosons. They found that while these happen less often, they are still possible and detectable.
• The "Grain of Salt" Warning: The authors were careful to note that for one specific scenario, the math gets a little tricky. It's like finding a recipe that works perfectly in the oven, but you aren't 100% sure if the fire alarm (experimental limits) will go off because of how the smoke mixes. They flagged this one case for future, more detailed checking.

Why This Matters (According to the Paper)

The paper doesn't claim to have discovered new particles yet. Instead, it claims to have built a better map and a better compass.

Before this, finding the best "recipes" in the NMSSM was slow and difficult. Now, with NMSSMScanner, physicists can quickly generate a list of the most promising scenarios to look for in real experiments. They have provided a "shopping list" of specific particle masses and decay patterns that experimentalists at the LHC should focus on to see if this version of the universe is real.

In short: The authors built a smart search engine for a complex physics model, used it to find the most exciting places to look for double Higgs bosons, and handed those coordinates to the experimentalists to check.

Technical Summary

1. Problem Statement

The Next-to-Minimal Supersymmetric Standard Model (NMSSM) extends the Standard Model (SM) by adding a complex singlet superfield to the two Higgs doublets of the MSSM. While this solves the $\mu$-problem of the MSSM, it introduces a significantly enlarged parameter space (over 20 independent parameters in the CP-violating case).

• Challenge: Scanning this high-dimensional space to find viable benchmark scenarios that satisfy all theoretical constraints (perturbativity, vacuum stability) and experimental constraints (Higgs mass, flavor physics, Dark Matter, LHC searches) is computationally expensive and notoriously difficult.
• Specific Goal: The authors aim to efficiently identify NMSSM parameter configurations that maximize the resonant production cross-section of a SM-like Higgs boson ($H$) and a non-SM-like Higgs boson ($Y$) in various final states, specifically looking for $gg \to X \to HY$ processes where $X$ is a heavy scalar or pseudoscalar resonance.

2. Methodology

The paper introduces NMSSMScanner, a new scanning framework designed to handle the complexity of the NMSSM parameter space.

A. Framework Architecture

The tool is built upon BSMArt (a Python-based scanning framework) which orchestrates a chain of specialized physics codes:

• BSMArt: Manages the scan strategy (Random scans, Markov-Chain-Monte-Carlo (MCMC), Active Learning) and data flow between codes.
• NMSSMCALC: Calculates the Higgs and SUSY particle spectra, including full one-loop and partial two-loop corrections to Higgs masses and trilinear couplings. It also computes decay widths and branching ratios.
• HiggsTools: Computes single-Higgs production cross-sections and checks compatibility with LHC/LEP/Tevatron single-Higgs data.
• SusHi: Calculates resonant heavy Higgs production cross-sections at NNLO QCD accuracy.
• SModelS: Checks constraints from SUSY particle searches (gluinos, squarks, electroweakinos) against LHC limits.
• RelExt: Computes Dark Matter relic density and direct detection cross-sections.
• HPAIR: Used for sanity checks on non-resonant di-Higgs production limits.

B. Scan Strategy

• Likelihood Functions: To maximize efficiency, the authors employed MCMC scans with custom likelihood functions ($L_{max}$) designed to maximize the target observable: $\sigma \times \text{BR}$.
  • For scalar resonances: $L \propto \exp(s_0 (\sigma \times \text{BR}) / \mu)$.
  • For pseudoscalar resonances (specifically for $A_1 \to \gamma\gamma$): An additional term was added to enhance the singlet admixture of the lighter pseudoscalar.
• Constraints: The scan enforces:
  • $m_H \in [124, 126]$ GeV (SM-like Higgs mass).
  • $m_{H^\pm} > 600$ GeV (to satisfy $b \to s\gamma$ constraints conservatively).
  • Perturbative unitarity: $\lambda^2 + \kappa^2 \leq 0.7$.
  • Electroweak precision observables (W-mass).
  • Dark Matter relic density ($\Omega h^2 \approx 0.12$) and direct detection limits.
• CP-Conservation: The initial proof-of-concept scan was restricted to the CP-conserving NMSSM (all parameters real) to simplify the mass spectrum into distinct CP-even and CP-odd states.

3. Key Contributions

1. Development of NMSSMScanner: A modular, efficient tool capable of performing complex scans in the NMSSM parameter space while integrating state-of-the-art higher-order corrections.
2. Optimization for Resonant Di-Higgs: The framework is specifically tuned to find "sweet spots" in the parameter space where resonant production of mixed Higgs pairs ($HY$) is maximized.
3. Comprehensive Benchmark Points: The authors provide a set of viable benchmark points (BPs) for various final states, including light states ($b\bar{b}, \tau\tau, \gamma\gamma$) and heavy states ($t\bar{t}, WW, HH$).
4. Validation of Limits: The study explicitly addresses the interference between resonant and non-resonant contributions, determining that for most found benchmarks, non-resonant search limits are sufficient, though specific cases (like BPp2b2gam) require further investigation.

4. Key Results

The scan was performed at $\sqrt{s} = 13$ TeV. The results are presented in terms of maximum cross-sections ($\sigma_{max}$) for the process $gg \to X \to HY$.

A. Light Final States

• 4b Final State ($H \to b\bar{b}, Y \to b\bar{b}$):
  • Scalar Resonance ($X=H_3$): Max $\sigma \approx 27$ fb.
  • Pseudoscalar Resonance ($X=A_2$): Max $\sigma \approx 42$ fb.
  • Observation: Pseudoscalar production yields higher cross-sections due to larger gluon fusion rates.
• Other Light Channels:
  • $(2b)(2\tau)$: $\sim 2.9$ fb (scalar), $\sim 4.5$ fb (pseudoscalar).
  • $(2b)(2\gamma)$: $\sim 0.12$ fb (scalar), $\sim 0.35$ fb (pseudoscalar).
  • $(2\tau)(2\gamma)$: $\sim 0.01$ fb.

B. Heavy Final States

• $(b\bar{b})(t\bar{t})$:
  • Scalar: $\sim 30$ fb.
  • Pseudoscalar: $\sim 37$ fb.
  • Note: The $Y$ boson decays to $t\bar{t}$ when kinematically allowed, dominating the branching ratio.
• 6b Final State ($X \to H(Y \to HH) \to 6b$):
  • Max $\sigma \approx 4.03$ fb. This scenario involves a cascade decay where a heavy scalar decays into a SM-like Higgs and a lighter scalar, which subsequently decays into two SM-like Higgses.
• $(\gamma\gamma)(WW)$:
  • Max $\sigma \approx 0.104$ fb.

C. Parameter Space Characteristics

• Masses: The resonant heavy Higgs ($X$) masses are typically near the lower scan boundary ($\sim 600$ GeV) to maximize production cross-sections.
• Couplings: $\lambda$ and $\kappa$ are around 0.5 (saturating unitarity bounds). $\tan\beta$ is generally small ($1-3$).
• SUSY Spectrum: Stop masses are large ($\sim 3-4$ TeV) to satisfy the 125 GeV Higgs mass constraint, but kept below 4 TeV to avoid EFT breakdown issues found in previous literature benchmarks.

5. Significance and Comparison

• Comparison with Literature: The authors compared their results with previous benchmarks (Refs. [91, 92]). They found good agreement for most channels but noted that previous benchmarks often relied on extremely heavy stop masses ($>100$ TeV), which require Effective Field Theory (EFT) treatments. The NMSSMScanner results are more reliable for fixed-order calculations as they restrict stop masses to $\leq 4$ TeV.
• Phenomenological Impact: The identified benchmark points offer concrete targets for LHC Run 3 and the High-Luminosity LHC (HL-LHC). The cross-sections for 4b and $b\bar{b}t\bar{t}$ final states are particularly promising for discovery.
• Future Work: The paper serves as a "Proof of Concept." The full package will be detailed in future publications, including CP-violating scenarios and further refinements to the scanning algorithms.

In summary, NMSSMScanner successfully demonstrates an efficient method to navigate the complex NMSSM landscape, providing a robust set of benchmark scenarios that maximize resonant di-Higgs production while strictly adhering to current experimental constraints.