Rare few-body decays of the Standard Model Higgs boson

This paper surveys approximately 70 rare and exclusive few-body Standard Model Higgs boson decays with branching fractions below $10^{-5}$, providing theoretical predictions, current experimental limits, and HL-LHC projections—including 20 newly computed channels—to guide future research in constraining couplings, probing flavor-changing processes, and estimating backgrounds for exotic physics.

The Gist

Imagine the Higgs boson as a very shy, heavy celebrity who just showed up at a massive party (the Large Hadron Collider). Since its discovery in 2012, scientists have been watching this celebrity to see how they behave. We know the "standard" ways this celebrity usually leaves the party: they might drop a few heavy bags (common particles) or split into a few familiar groups. These are the "easy" exits that happen all the time.

But this paper is about the rare, weird, and almost impossible exits.

The authors, David d'Enterria and Van Dung Le, are essentially writing a "Lost & Found" guide for the Higgs boson's most obscure behaviors. They are looking for the times the Higgs decides to do something incredibly unusual, like:

• Vanishing into thin air (decaying into invisible neutrinos).
• Turning into a flash of light and a ghost (a photon and neutrinos).
• Splitting into four tiny flashes of light at once.
• Or, in a very specific dance, turning into a gauge boson (like a Z or W particle) and a tiny, tightly bound "knot" of matter called a meson or leptonium.

The "Why" Behind the Search

Why bother looking for these needle-in-a-haystack events? The authors give three main reasons, using some great metaphors:

1. The "Smoking Gun" for New Physics:
   Imagine you are watching a magician. You know the standard tricks. But if you see the magician pull a rabbit out of a hat that should be empty, you know something new is happening. These rare decays are the "empty hats." If the Higgs decays in a way the Standard Model says is impossible (or extremely unlikely), it's a sign that there are new, hidden forces or particles (Beyond Standard Model physics) helping it out.

2. The "Background Noise" Problem:
   Sometimes, scientists are looking for a specific exotic signal, like a new type of particle. But the Standard Model itself can produce "fake" signals that look exactly like the exotic ones. These rare decays are the "static on the radio." To hear the new music clearly, you first need to know exactly how loud the static is. This paper calculates that static so future experiments don't get confused.

3. Testing the "Glue" of the Universe:
   The Higgs interacts with other particles via "Yukawa couplings" (think of these as the strength of a handshake). For heavy particles like the top quark, the handshake is strong. For light particles like up or down quarks, the handshake is so weak it's almost a whisper. It's very hard to hear that whisper in the noisy crowd of the LHC. But if the Higgs decays into a specific, rare "knot" of matter (a meson), it amplifies that whisper, allowing scientists to finally measure how strongly the Higgs shakes hands with light particles.

The "Impossible" Math

The paper is a massive catalog of about 70 different rare decay channels. The authors did the math to predict how often these should happen. The numbers are mind-bogglingly small.

• The "Ultra-Rare" Category: Some decays happen once in every $10^{40}$ tries. That's like flipping a coin and getting heads every single time for the entire history of the universe, and then doing it again.
• The "Rare but Possible" Category: Others happen once in every $10^{-5}$ (one in 100,000) or $10^{-6}$ (one in a million) Higgs bosons.

The authors used powerful computer simulations (like a digital wind tunnel) to calculate these probabilities, including some they computed for the very first time, such as the Higgs turning into a photon and a "leptonium" (a bound state of an electron and a positron, like a tiny atom made of light).

The Future: The "High-Luminosity" Party

The paper looks ahead to the High-Luminosity LHC (HL-LHC), which is an upgrade to the current collider. Think of the current LHC as a party with 100 guests, and the HL-LHC as a stadium packed with 350 million guests.

With so many more Higgs bosons being produced, the odds of catching one of these rare events go up.

• The Goal: The authors estimate that with this massive amount of data, we might finally see evidence of decays like Higgs $\to$ Photon + $\rho$ meson or Higgs $\to$ Photon + J/$\psi$.
• The Reality Check: For the truly ultra-rare ones (like the 4-photon decay), even the HL-LHC might not be enough. We might need a future, even bigger machine (like the FCC) to see them.

The Bottom Line

This paper is a roadmap for the next decade of particle physics. It tells experimentalists: "Don't just look at the easy stuff. Here is a list of 70 weird things the Higgs might do. Here is how often we think they happen. Here is what our current limits are. And here is what we hope to see when we turn up the volume on the collider."

It's a mix of theoretical prediction and practical advice, urging scientists to keep their eyes open for the universe's most subtle and surprising tricks.

Technical Summary

1. Problem Statement

The discovery of the Higgs boson confirmed the Standard Model (SM), yet the SM remains incomplete regarding dark matter, neutrino masses, and the hierarchy problem. Precision tests of the Higgs sector are a primary goal for the High-Luminosity Large Hadron Collider (HL-LHC). However, most experimental efforts focus on dominant decay modes.

• The Gap: There is a lack of comprehensive surveys regarding rare and exclusive few-body decays (branching fractions $B \lesssim 10^{-5}$) involving 2 to 4 final-state particles.
• The Challenge: These decays are theoretically suppressed due to:
  • Small Yukawa couplings to light fermions (first and second generation).
  • Suppression by virtual loops (electroweak or QCD).
  • The low probability of forming exclusive bound states (mesons or leptonium) from primary decay products.
• The Necessity: Understanding these SM rates is crucial for:
  • Constraining Yukawa couplings and probing Flavor-Changing Neutral Currents (FCNC).
  • Estimating backgrounds for exotic Beyond-Standard-Model (BSM) searches (e.g., decays into Axion-Like Particles or Dark Photons).
  • Testing QCD factorization formalisms in a high-energy regime.

2. Methodology

The authors conducted a comprehensive survey combining theoretical calculations, literature review, and experimental extrapolation.

• Theoretical Calculations:

  • New Computations: Approximately 20 previously uncalculated channels were computed using MADGRAPH5_AMC@NLO (MG5_AMC). These include ultrarare decays into photons/neutrinos ($H \to 3\gamma, 4\gamma, \gamma\nu\nu$), $Z$ boson plus gluons/photons, and exclusive Flavor-Changing Neutral Current (FCNC) decays into neutral flavored mesons ($H \to \gamma/Z + K^*, D^*, B^*$).
  • Framework: Calculations utilized Next-to-Leading Order (NLO) accuracy in QCD and Electroweak (EW) couplings.
  • Factorization: For exclusive decays involving mesons ($H \to V + M$) and leptonium, the authors employed QCD factorization (SCET and NRQCD). This separates short-distance perturbative interactions from non-perturbative hadronization described by Light-Cone Distribution Amplitudes (LCDAs) or Long-Distance Matrix Elements (LDMEs).
  • Amplitude Interference: The total branching fraction was calculated as the coherent sum of direct amplitudes (Higgs coupling directly to quarks/leptons) and indirect amplitudes (Higgs decaying to gauge bosons which then form the meson), accounting for destructive interference.

• Experimental Extrapolation:

  • Data Sample: Based on the expected HL-LHC yield of $N_{H} \approx 3.5 \times 10^8$ Higgs bosons (from $2 \times 3 \text{ ab}^{-1}$ integrated luminosity).
  • Projection Methods:
    1. Directly quoted existing HL-LHC projections from ATLAS/CMS where available.
    2. For channels with only Run-2 limits, extrapolated bounds by scaling with the square root of the integrated luminosity ratio ($\sqrt{L_{HL-LHC}/L_{Run2}}$), assuming a factor of 2 improvement from combining ATLAS and CMS.

3. Key Contributions

The paper provides the first unified catalog of ~70 rare Higgs decay channels, including:

1. New Theoretical Estimates: First-time calculations for:
   • $H \to 3\gamma$ and $H \to 4\gamma$ (violating C-symmetry or requiring heavy loops).
   • $H \to \nu\nu$ (loop-induced) and $H \to \gamma\nu\nu$.
   • $H \to Z + gg$ and $H \to Z + \gamma\gamma$.
   • Exclusive FCNC decays: $H \to \gamma/Z + K^{*0}, D^{*0}, B^{*0}_{s,d}$.
   • Radiative decays into leptonium states (positronium, true muonium, true tauonium).
2. Comprehensive Tables: Systematic compilation of theoretical branching fractions, current experimental limits (95% CL), and projected HL-LHC sensitivity for all channels.
3. Background Analysis: Identification of these SM decays as irreducible backgrounds for exotic searches (e.g., $H \to a a \to 4\gamma$).

4. Key Results

A. Rare Multi-Boson Decays

• $H \to \nu\nu$: Purely loop-induced, $B \approx 2 \times 10^{-26}$ (negligible).
• $H \to \gamma\nu\nu$: $B \approx 3.7 \times 10^{-4}$ (the least rare in this survey).
• $H \to 3\gamma$: Extremely suppressed ($B \approx 10^{-40}$) due to C-symmetry violation; requires $W$-box diagrams.
• $H \to 4\gamma$: $B \approx 5.4 \times 10^{-12}$. While rare, it is a potential background for BSM $H \to a(\gamma\gamma)a(\gamma\gamma)$ searches.
• $H \to Zgg$ and $Z\gamma\gamma$: Rates of $10^{-7}$ and $10^{-9}$ respectively.

B. Exclusive Decays: $H \to V + M$ (Gauge Boson + Meson)

• Mechanism: Rates are dominated by indirect amplitudes (virtual gauge boson $\to$ meson) due to the smallness of light-quark Yukawa couplings. Direct contributions are often suppressed by destructive interference.
• Photon + Vector Meson ($H \to \gamma + V$):
  • $H \to \gamma + \rho^0$: $B \approx 1.7 \times 10^{-5}$.
  • $H \to \gamma + J/\psi$: $B \approx 3.0 \times 10^{-6}$.
  • $H \to \gamma + \Upsilon$: $B \approx 10^{-9}$ (heavily suppressed by cancellation).
  • Observability: $H \to \gamma + \rho$ and $H \to \gamma + J/\psi$ are potentially observable at HL-LHC.
• Z/W + Meson:
  • $H \to Z + \eta_c$ and $Z + \Upsilon$ have rates $\sim 10^{-5}$.
  • $H \to W^\pm + \rho^\mp$: $B \approx 1.3 \times 10^{-5}$ (most promising charged channel).
• Flavor-Changing (FCNC):
  • Decays like $H \to \gamma + K^{*0}$ are predicted at $B \sim 10^{-23}$ in the SM (via $W$-loops).
  • Current limits are $\sim 10^{-4}$, leaving a gap of $\sim 19$ orders of magnitude. These are pristine probes for BSM physics.

C. Radiative Leptonium Decays

• Decays into bound lepton-antilepton states ($H \to \gamma/Z + (\ell^+\ell^-)$) are suppressed by the small QED coupling and lepton masses compared to quarkonium.
• Rates are in the range $10^{-12}$ to $10^{-16}$.
• Signatures include displaced vertices (e.g., orthopositronium $\to 3\gamma$ with macroscopic decay length).

D. Exclusive Decays into Two Mesons ($H \to M + M$)

• Decays like $H \to J/\psi + J/\psi$ or $\Upsilon + \Upsilon$ have rates $\sim 10^{-10}$.
• Current limits are $\sim 10^{-3}$ to $10^{-4}$. Observation at HL-LHC is deemed unfeasible; FCC-hh would be required.

5. Significance and Outlook

• BSM Sensitivity: The survey highlights that while SM rates for many exclusive channels are too low for observation at the HL-LHC, they serve as critical "null tests." Any observation significantly above the predicted SM background (e.g., in FCNC channels) would be a definitive sign of New Physics.
• Yukawa Couplings: Exclusive decays offer a unique pathway to constrain Yukawa couplings for light quarks ($u, d, s, c$) which are otherwise swamped by QCD backgrounds in inclusive dijet searches.
• QCD Factorization: These processes provide a rigorous test of QCD factorization theorems in the high-energy limit, verifying the suppression of non-perturbative corrections ($O(\Lambda_{QCD}/m_H) \approx 10^{-3}$).
• Prioritization: The authors identify seven key channels (Table 8) that are within reach of the HL-LHC, specifically:
  1. $H \to \gamma + \rho^0$
  2. $H \to \gamma + J/\psi$
  3. $H \to Z + \rho^0$
  4. $H \to Z + \Upsilon(1S)$
  5. $H \to W^\pm + \rho^\mp$
  6. $H \to W^\pm + D_s^{*\mp}$
  7. $H \to 4\gamma$ (as a background constraint).

In conclusion, this report serves as a foundational guide for experimentalists at the HL-LHC to prioritize searches for rare Higgs decays, distinguishing between channels where SM observation is imminent and those that serve as high-sensitivity probes for BSM physics.