Higgs-Boson Decays: Updates

This paper summarizes recent updates to Standard Model Higgs-boson decay calculations, including NLO mass effects for $H\to gg$, precise branching fractions for the strange-Yukawa induced $H\to s\bar s$ channel, and new results on Dalitz decays that are crucial for determining the strange-Yukawa coupling at future $e^+e^-$ colliders and the LHC.

The Gist

Imagine the Higgs boson as a celebrity chef in the universe's most exclusive kitchen. This chef is famous for creating a specific dish (the Higgs boson itself), but the real mystery isn't just that they exist; it's what ingredients they use and how they cook.

For years, scientists have been trying to figure out the chef's "recipe" by watching what happens when the chef breaks down (decays) after being created in particle collisions. This new paper is like a culinary update from a team of expert food critics (physicists) who have refined the measurements of these recipes.

Here is the breakdown of their new findings, explained with everyday analogies:

1. The "Heavy" Glue (H → gg)

The Science: The Higgs boson often decays into two gluons (particles that hold atomic nuclei together). This happens mostly through a "loop" involving heavy top quarks.
The Analogy: Think of the Higgs boson as a giant boulder rolling down a hill. Usually, it rolls over a smooth path (the "heavy quark limit"). But sometimes, the path has bumps and potholes (finite mass effects) that change how fast it rolls.
The Update: Previously, the scientists' map (a computer grid used for calculations) only showed the smooth path up to a certain size. They have now extended the map to cover much larger, more extreme boulders (Higgs masses up to 3 TeV). This ensures that if we ever find a "super-Higgs" in the future, we won't get lost because our map stopped at the edge of the cliff.

2. The "Rare Spice" (H → s¯s)

The Science: The Higgs boson can decay into a pair of strange quarks. This is very rare and hard to see because the "signal" is tiny.
The Analogy: Imagine the chef is making a soup. The main ingredients are beef and potatoes (top and bottom quarks). But the chef also adds a tiny pinch of saffron (the strange quark). The saffron gives the soup a unique flavor, but because there's so little of it, it's hard to taste against the strong beef flavor.
The Update: The team has finally calculated the exact amount of saffron needed and how much it varies (uncertainties). They've provided a precise "tasting note" for this rare decay. This is crucial because if we can measure this tiny flavor, we can prove the chef actually likes saffron (confirming the "strange-Yukawa coupling").

3. The "Background Noise" Problem (Dalitz Decays)

The Science: The problem with measuring the "saffron" (strange quarks) is that there are other processes that also produce strange quarks, but not because the chef added them. These are called "Dalitz decays" (H → s¯s + g or γ).
The Analogy: Imagine you are trying to hear the chef whisper a secret recipe (the strange-Yukawa coupling). But, there are other people in the kitchen shouting and clanging pots (the "Dalitz decays" or background noise).

• The Strong Dalitz: Like someone dropping a heavy pot (gluon) that makes a loud crash.
• The Weak Dalitz: Like someone ringing a bell (photon) that sounds similar to the chef's voice.

These background noises are 10 times louder than the chef's whisper. If you just listen to the whole kitchen, you can't tell if the sound came from the chef or the noise.

The Update: The paper provides a new soundproofing strategy. They calculated exactly how the "noise" behaves at different frequencies (energies). They found that if you listen to the high-pitched frequencies (high energy of the strange quark pair), the noise fades away, and the chef's whisper becomes clear. This gives future experiments (like at the LHC or future electron-positron colliders) a specific "ear" to tune into so they can finally isolate the strange quark signal.

4. Why Does This Matter?

The Big Picture:

• Standard Model Check: The Standard Model is the "rulebook" of physics. If the chef's recipe for saffron doesn't match the rulebook, it means there's a secret ingredient (New Physics) we haven't discovered yet.
• Future Tools: By refining these calculations now, scientists are building better "microscopes" for the future. When the next big particle collider comes online, they will know exactly where to look and how to filter out the noise to find these tiny, rare signals.

Summary

This paper is a refinement of the instruction manual for the Higgs boson.

1. They updated the map for heavy scenarios.
2. They gave a precise recipe for a very rare ingredient (strange quarks).
3. They figured out how to filter out the loud kitchen noise so we can finally hear the chef's secret recipe.

It's a vital step toward proving whether the universe's "chef" is cooking exactly according to the standard recipe, or if they are secretly experimenting with new, unknown ingredients.

Technical Summary

1. Problem Statement

The discovery of the Higgs boson at the LHC confirmed the Standard Model (SM) mechanism for electroweak symmetry breaking. However, a rigorous test of the SM requires precise measurements of Higgs couplings to all fermions and bosons. Current challenges include:

• Theoretical Precision: Extracting SM parameters from observables is limited by theoretical and parametric uncertainties. Higher-order corrections (NLO, NNLO, etc.) and finite mass effects must be consistently included.
• Strange-Yukawa Coupling ($y_s$): The coupling of the Higgs to strange quarks is extremely small ($\sim 0.02\%$ branching ratio) and difficult to isolate. It is obscured by "continuum" processes (Dalitz decays) where strange quarks are produced via loop-induced gluon or photon emissions rather than direct Yukawa coupling.
• BSM Extensions: Existing computational tools (specifically the Hdecay grid) lacked coverage for Higgs masses significantly above 1 TeV, limiting Beyond Standard Model (BSM) studies.
• Dalitz Decays: The separation between the Yukawa-induced signal ($H \to s\bar{s}$) and the loop-induced continuum ($H \to s\bar{s} + g/\gamma$) is not well-defined in current literature, hindering the extraction of $y_s$ at future $e^+e^-$ colliders and the LHC.

2. Methodology

The authors utilized and updated the public tool Hdecay, incorporating state-of-the-art perturbative QCD and electroweak calculations. Key methodological steps included:

• Extension of NLO Mass Grids: The grids used for finite quark-mass effects in the $H \to gg$ decay were extended from $M_H = 1$ TeV to $M_H = 3$ TeV. This allows for accurate interpolation in BSM scenarios with heavy Higgs bosons.
• Strange-Yukawa Calculations:
  • Calculated the Yukawa-induced branching ratio for $H \to s\bar{s}$ using the $\overline{\text{MS}}$ strange quark mass $m_s(2 \text{ GeV}) = 93.5 \pm 3.2$ MeV.
  • Evaluated theoretical uncertainties (scale dependence) and parametric uncertainties (variations in $m_s$, $m_b$, $m_c$, $m_t$, and $\alpha_s$).
• Dalitz Decay Analysis:
  • Computed the differential decay widths for strong ($H \to s\bar{s}g$) and weak ($H \to s\bar{s}\gamma$) Dalitz decays.
  • Included interference terms between the tree-level Yukawa amplitude and the loop-induced amplitudes.
  • Analyzed the invariant mass distribution ($Q = M_{s\bar{s}}$) to identify kinematic regions where the Yukawa contribution dominates over the continuum.

3. Key Contributions

A. $H \to gg$ Updates

• Extended Grids: The NLO QCD correction grids for finite quark-mass effects ($\Delta E$) are now valid up to 3 TeV.
• Impact: While the charm quark contribution remains negligible beyond the heavy quark limit (HQL), the extension is crucial for BSM studies involving heavy Higgs bosons where the top-quark mass expansion limit may no longer be sufficient.

B. Strange-Yukawa Induced $H \to s\bar{s}$

• Reference Values: Provided precise branching ratios and uncertainties for $H \to s\bar{s}$ across the mass range $120 \text{--} 130$ GeV.
  • At $M_H = 125$ GeV, $BR(H \to s\bar{s}) \approx 2.12 \times 10^{-4}$.
  • Uncertainties: Theoretical uncertainty is $\sim 0.7\%$, while parametric uncertainty is dominated by the strange quark mass ($\sim 7\%$) and $\alpha_s$ ($\sim 2\%$).
• These values serve as the baseline for extracting $y_s$ in future experiments.

C. Dalitz Decays ($H \to s\bar{s} + g/\gamma$)

• First Comprehensive Results: Presented the first detailed results for strong and weak Dalitz decays involving strange quarks.
• Magnitude: The inclusive branching ratios for these continuum processes are at the percent level, roughly two orders of magnitude larger than the direct Yukawa-induced $H \to s\bar{s}$ decay.
• Kinematic Separation: The analysis of differential decay widths ($d\Gamma/dQ^2$) reveals that:
  • The loop-induced (continuum) contribution dominates at low invariant masses ($Q$).
  • The Yukawa-induced contribution dominates at high invariant masses ($Q$).
  • This kinematic separation is the key to isolating the strange-Yukawa coupling.

4. Results

• $H \to gg$ Corrections: The NLO QCD corrections enhance the partial width by $\sim 70\%$. The inclusion of finite mass effects is negligible for $M_H < 1$ TeV but becomes relevant for BSM masses. The perturbative series shows good convergence, with corrections beyond NLO contributing $<20\%$ of the NLO result.
• Strange Quark Branching Ratio:
  • $BR(H \to s\bar{s})$ at 125 GeV is $2.119 \times 10^{-4}$.
  • The total parametric uncertainty is driven by the strange mass ($m_s$), contributing a $\sim 7\%$ error.
• Dalitz Decay Spectra:
  • Strong Dalitz ($H \to s\bar{s}g$): The distribution peaks at low $Q$ but falls off, allowing the Yukawa signal to emerge at high $Q$.
  • Weak Dalitz ($H \to s\bar{s}\gamma$): Similar in magnitude to the strong decay due to the $Z$-boson resonance contribution.
  • Interference: The interference between the Yukawa and loop amplitudes is significant and must be included in signal simulations.
• Sensitivity: The ability to measure $y_s$ depends critically on the experimental resolution of the $s\bar{s}$ invariant mass. A high-resolution cut on large $Q$ can suppress the continuum background, making the Yukawa signal accessible.

5. Significance

• Future Colliders: This work provides the theoretical foundation required for the measurement of the strange-Yukawa coupling at future $e^+e^-$ Higgs factories (e.g., FCC-ee, ILC, CLIC). Without the precise definition of the Dalitz continuum, the extraction of $y_s$ would be impossible due to overwhelming background.
• LHC Constraints: The results offer a pathway to set solid bounds on $y_s$ at the High-Luminosity LHC (HL-LHC) by utilizing kinematic cuts on the strange-jet pair invariant mass.
• BSM Physics: The extension of the Hdecay grids to 3 TeV enables more robust searches for heavy Higgs bosons in BSM scenarios, ensuring that theoretical uncertainties do not obscure potential new physics signals.
• Standard Model Precision: By quantifying the uncertainties in the strange sector and refining the $H \to gg$ predictions, this report reduces the theoretical error budget in global Higgs coupling fits, allowing for more stringent tests of the SM.

In conclusion, this paper bridges a critical gap in Higgs phenomenology by defining the "signal vs. background" landscape for the elusive strange-Yukawa coupling and updating the theoretical infrastructure for high-mass Higgs studies.