Ultrarare Higgs Boson Decays

• Ultrarare Higgs boson decays are exclusive processes with branching fractions below 10⁻⁵, offering precise tests of the Standard Model and insights into potential new physics.
• They involve loop-induced and flavor-changing mechanisms that enable extraction of light Yukawa couplings and assessment of CP, QCD, and QED factorization methods.
• Advanced theoretical modeling and experimental strategies focus on channels like H→γρ⁰ and H→J/ψγ to constrain BSM scenarios and refine decay predictions.

Ultrarare Higgs boson decays are defined as exclusive rare decay modes of the Standard Model (SM) Higgs boson, typically involving two to four final-state particles, with branching fractions $\mathcal{B} \lesssim 10^{-5}$. These decays, predominantly loop-induced or mediated by highly suppressed couplings (such as those to light quarks or via flavor-changing currents), serve as uniquely sensitive probes of the SM structure and as potential windows to new physics. Precision measurements or even upper limits on these ultrarare processes provide constraints on Yukawa couplings, flavor violation, CP structure, possible invisible or dark-sector states, and validate QCD and electroweak factorization approaches. The exploration of such decays requires both sophisticated theoretical calculations and advanced experimental techniques, given their extremely low expected rates and the challenging experimental environments.

1. Definition, Classification, and Relevance

Ultrarare Higgs decays are those exclusive decays of the Higgs boson with branching fractions typically well below $10^{-5}$ (d'Enterria et al., 1 Aug 2025, d'Enterria et al., 2023). These include processes such as $H\to\gamma M$ (where $M$ is a meson or leptonium), $H\to VV$/few-body states with $V=\gamma, Z$, radiative flavor-changing decays, and multibody decays involving photons and/or neutrinos. Their defining characteristics are:

• Occur via suppressed tree-level or loop-induced amplitudes;
• Probe first- and second-generation fermion Yukawa couplings otherwise inaccessible in inclusive measurements because of overwhelming QCD backgrounds;
• Are often sensitive to BSM scenarios, including new sources of flavor violation, CP violation, axion-like particles (ALPs), hidden photons, or dark sector states (Biekötter et al., 2022, Huang et al., 2013, Falkowski et al., 2014, Liu et al., 2016);
• Serve as backgrounds for genuinely exotic Higgs decays in BSM analyses and as precision tests of effective field theory in electroweak and strong sectors;
• Provide clean tests of factorization approaches in QCD, quantum electrodynamics (QED), and the interplay of perturbative and nonperturbative effects.

Experimentally, these decays are challenging to observe due to the combination of tiny branching fractions (e.g., as low as $10^{-36}$ for $H\to\nu\bar\nu$) and the difficulty in reconstructing final states with soft or collimated decay products, or with significant backgrounds (d'Enterria et al., 1 Aug 2025, d'Enterria et al., 2023).

2. Theoretical Predictions, Branching Fractions, and Direct/Indirect Amplitudes

Theoretical predictions for ultrarare decays involve both "direct" (Yukawa-mediated) and "indirect" (loop-induced or gauge-mediated) amplitudes (Koenig et al., 2015, Gao, 2014, d'Enterria et al., 2023). For example, in exclusive radiative decays of the form $h\to V\gamma$, where $V$ is a neutral vector meson, the amplitude is:

$$i\mathcal{A}(h\to V\gamma) = -\frac{ef_V}{2} \{ [\epsilon_V^*\cdot\epsilon_\gamma^* - \frac{q\cdot\epsilon_V^* k\cdot\epsilon_\gamma^*}{k\cdot q}] F_1^V - i\epsilon_{\mu\nu\rho\sigma} \frac{k^\mu q^\nu \epsilon_V^{*\rho} \epsilon_\gamma^{*\sigma}}{k\cdot q} F_2^V \},$$

with branching fraction

$$\Gamma(h\to V\gamma) = \frac{\alpha f_V^2}{8 m_h} (|F_1^V|^2 + |F_2^V|^2),$$

where $F_{1,2}^V$ receive contributions from both quark-level (direct) and loop-induced (indirect) terms. In many channels, interference is highly destructive, as in $h\to\Upsilon(nS)\gamma$, leading to pronounced sensitivity to BSM modifications of the bottom Yukawa coupling (Koenig et al., 2015, Renstrom, 2023).

A representative summary of SM branching fractions for select channels is given below (d'Enterria et al., 1 Aug 2025, d'Enterria et al., 2023):

Channel	Predicted $\mathcal{B}$ (SM)	Experimental Limit (HL-LHC, current/proj.)
$H\to\gamma\gamma\gamma$	$1.0\times 10^{-40}$	–
$H\to\gamma\gamma\gamma\gamma$	$5.4\times 10^{-12}$	–
$H\to\nu\bar{\nu}$	$7.2\times 10^{-36}$	–
$H\to\gamma+\nu\bar{\nu}$	$3.4-3.7\times 10^{-4}$	–
$H\to\gamma + \rho^0$	$1.68\times 10^{-5}$	$<3.7\times 10^{-4}$ (current), $<5.7\times 10^{-5}$ (HL-LHC)
$H\to\gamma + J/\psi$	$2.95\times 10^{-6}$	$<2\times 10^{-4}$ (current), $<3.9\times 10^{-5}$ (HL-LHC)
$H\to\omega\gamma$	$1.5\times 10^{-6}$	$<5.5\times 10^{-4}$
$H\to K^{*0}\gamma$	$\sim 10^{-11}$	$<2.2\times 10^{-4}$
$H\to\gamma +$ ortho-leptonium	$3.5\times 10^{-12}$	–
$H\to Z +$ ortho-leptonium	$5.2\times 10^{-13}$	–

The SM rates for flavor-changing decays, such as $H\to D^*\gamma$, are orders of magnitude smaller: $\sim 10^{-27}$ (Das, 22 May 2024). Channels such as $H\to ZA$ (where $A$ is a light pseudoscalar) are possible in extended Higgs sectors but are forbidden or negligibly small within the SM (Chisholm et al., 2016, Liu et al., 2016). For multibody final states involving ALPs or dark sector states (e.g., $H\to 4\mu, 2\mu 2\gamma, 6\mu, 4\mu 2j$), branching ratios can be constrained down to $\sim 10^{-5}-10^{-9}$ at HL-LHC depending on the channel and kinematic regime (Biekötter et al., 2022).

3. Experimental Constraints, Methods, and Prospects

Experimental searches for ultrarare decays have provided upper limits for only a minority of the theoretically catalogued channels. The most stringent constraints currently arise from the ATLAS and CMS experiments, with analyses typically utilizing:

• Isolated photon and lepton or meson triggers and reconstruction (Collaboration, 2023, Reynolds, 2018);
• Kinematic fitting (often using mass-constrained fits and BDTs) in challenging final states like $h\to aa\to 2b2\mu$ or $h\to 4b$ (Morvaj, 2021, Das, 22 May 2024);
• Matrix-element and multidimensional likelihood fits to maximize statistical sensitivity, as demonstrated in $h\to 4\ell$ analyses to distinguish between SM and BSM decay hypotheses (Falkowski et al., 2014);
• Exploitation of the recoil mass technique in $e^+e^-$ colliders, where $e^+e^-\to ZH$ production with clean $Z\to\ell\ell$ tagging allows for sensitivity to $h+$invisible or hadronic final states down to branching ratios of $10^{-3}-10^{-5}$ (Liu et al., 2016).

A crucial limiting factor is the available statistics: the HL-LHC is expected to produce of order $3.5\times 10^8$ Higgs bosons per experiment, enabling sensitivity to branching fractions as low as $10^{-5}-10^{-6}$ in optimal channels provided backgrounds are well controlled (d'Enterria et al., 1 Aug 2025, d'Enterria et al., 2023).

Future electron-positron colliders (e.g., FCC-ee, CEPC) offer superior backgrounds and enhanced energy/mass resolution, particularly advantageous for modes involving jets or missing energy (Liu et al., 2016). However, many ultrarare decays with branching fractions at or below $10^{-8}$ will remain unobservable without orders-of-magnitude increases in event yields or major improvements in detector and analysis techniques (d'Enterria et al., 2023).

4. Novel and Recently Computed Channels

The systematic cataloguing of ultrarare decays has resulted in explicit predictions and first theoretical calculations for a broad class of processes (d'Enterria et al., 1 Aug 2025, d'Enterria et al., 2023):

• Multiphoton final states, e.g., $H\to 3\gamma, 4\gamma$, with $C$-symmetry severely suppressing the rates;
• Radiative decays into leptonium bound states, such as $H\to\gamma +$ ortho-dimuonium, $H\to Z +$ para-positronium, with formation probabilities proportional to $|\phi_n(0)|^2 = (m_\ell\alpha)^3 / (8\pi n^3)$ for principal quantum number $n$ (d'Enterria et al., 2023);
• Radiative flavor-changing decays (e.g., $H\to\gamma + D^{*0}$, $H\to\gamma + K^{*0}$), for which the SM rates are negligibly small yet provide stringent probes of BSM-induced FCNCs;
• Double meson final states ($H\to J/\psi J/\psi$, $H\to\omega\rho^0$, etc.) with rates typically $10^{-9}-10^{-11}$;
• Final states involving photons and neutrinos, e.g., $H\to\gamma\nu\bar{\nu}$, which is calculable at $\mathcal{O}(10^{-4})$ but challenging to isolate experimentally due to missing energy signatures.

Many of these channels are motivated as backgrounds for searches for ALPs, dark photons, or Higgs portal models, and their theoretical values serve as essential anchor points for exotic Higgs decay searches (Biekötter et al., 2022, Liu et al., 2016).

5. Applications: Yukawa Couplings, Flavor Violation, and Factorization

Ultrarare Higgs decays enable incisive studies in the following research domains:

• Extraction of Light Yukawa Couplings: Exclusive decays such as $H\to\gamma\rho^0$, $H\to\gamma J/\psi$, and $H\to\omega\gamma$ provide direct sensitivity to first- and second-generation Yukawa couplings, avoiding QCD multi-jet backgrounds present in inclusive $h\to q\bar{q}$ decays. The analysis exploits the interference between direct Yukawa and indirect loop contributions, and ratios such as $$\mathcal{B}(h\to V\gamma)/\mathcal{B}(h\to\gamma\gamma)$$ to minimize theoretical and experimental uncertainties (Koenig et al., 2015, Reynolds, 2018).
• Flavor-Changing Neutral Currents (FCNC): Channels such as $H\to D^*\gamma$ or $H\to K^{*}\gamma$ are highly suppressed in the SM ($\mathcal{B}\sim 10^{-27}$) but become significant tests of BSM FCNCs if any observable signal is found (Das, 22 May 2024, Collaboration, 2023).
• QCD and QED Factorization: The calculation of exclusive decays incorporates SCET, NRQCD, and light-cone factorization techniques, isolating perturbative and nonperturbative contributions. Matching measured rates to theory provides benchmarks for these factorization approaches and nonperturbative QCD parameters (Koenig et al., 2015, d'Enterria et al., 1 Aug 2025).
• Exotic and Invisible Higgs Decay Backgrounds: SM ultrarare processes such as $H\to 4\gamma$, $H\to\gamma\nu\bar\nu$, and $H\to\gamma$ + invisible serve as irreducible backgrounds in searches for ALPs, dark photons, and Higgs portal dark matter models (Biekötter et al., 2022, d'Enterria et al., 2023).

6. Prospects and Strategic Priorities for Future Searches

The maturation of both theoretical predictions and experimental capabilities at the HL-LHC and future colliders refines the strategic landscape for testing ultrarare Higgs decay channels (d'Enterria et al., 1 Aug 2025, Das, 22 May 2024, d'Enterria et al., 2023):

• At the HL-LHC, channels with SM branching ratios near $10^{-5}$ (e.g., $H\to\gamma\rho^0$, $H\to\gamma J/\psi$) are on the threshold of sensitivity. Enhanced event selection (BDTs, matrix-element approaches), better categorization (decay topology, production modes), and higher-resolution detectors could enable either the first observation or further tightening of bounds.
• FCC-ee or future high-energy $pp$ colliders promise progress in even more suppressed channels, leveraging both improved luminosity and reduced backgrounds (Liu et al., 2016).
• Dedicated experimental searches are warranted for the $\approx$ 20 newly computed channels (including leptonium and radiative FCNC decays), since even a modest enhancement over the SM could signify new physics.
• Advances in detector techniques (e.g., improved calorimetry for multiphoton final states, vertexing for displaced leptonium decays) and data analysis (background suppression, invariant mass fitting) will be essential in reducing the effective sensitivities by another order of magnitude.

Synergistic efforts between theory and experimental collaborations are needed to further refine calculations (higher-order corrections, hadronic uncertainties) and optimize search strategies, especially for multibody final states and those channels with strong destructive interference (d'Enterria et al., 1 Aug 2025, d'Enterria et al., 2023, Reynolds, 2018, Koenig et al., 2015). Careful estimation and background subtraction of the SM ultrarare decays will remain indispensable in the program for BSM exotic Higgs search pipelines.

7. Summary and Outlook

Ultrarare Higgs boson decays, with branching fractions $\lesssim 10^{-5}$, encompass a spectrum of theoretically clean, experimentally challenging, and phenomenologically rich channels. They provide key tests of Yukawa universality, flavor structure, QCD and EW factorization, and sensitivity to BSM scenarios. Current observed limits are within one to three orders of magnitude of the SM predictions for the most favorable channels, and future facilities (HL-LHC, FCC-ee/hh) are projected to shrink this gap further. Prioritizing searches for exclusive, radiative, flavor-changing, and multibody modes, including newly calculated channels, offers a strategic venue to sharpen both SM tests and new physics discovery potential as Higgs precision studies enter their next phase.