Loop-Induced Higgs Boson Decays into Gauge Bosons in Radiative Natural Supersymmetry

This paper investigates loop-induced Higgs decays into gauge bosons within the Radiative Natural Supersymmetry framework, demonstrating that a specific parameter space can enhance the $h \to Z\gamma$ decay width while remaining consistent with current experimental constraints on the $h \to \gamma\gamma$ and $h \to gg$ channels.

The Gist

The Cosmic Tuning Fork: A Story of Hidden Vibrations

Imagine you are a master musician, and you have just discovered a legendary, ancient instrument: The Higgs Boson. This instrument is the reason everything in the universe has "weight" (mass). Without it, particles would zip around like light, never clumping together to form atoms, stars, or people.

Scientists at the Large Hadron Collider (LHC) have found this instrument, and they’ve been playing it to see how it sounds. But there is a mystery: we suspect there might be "hidden strings" or "ghost notes" playing along with it—particles we haven't seen yet, belonging to a theory called Supersymmetry (SUSY).

This paper, written by Edilson A. Reyes R., is like a high-tech acoustic analysis of that instrument to see if those ghost notes are actually there.

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1. The "Ghost Notes" (Radiative Natural Supersymmetry)

In physics, we often look for new particles by seeing how they affect the ones we already know. The author focuses on a specific version of this theory called Radiative Natural Supersymmetry (RNS).

The Analogy: Imagine you are listening to a piano. You can’t see the pianist, but you notice that every time a certain low note is played, a faint, shimmering echo appears. You can’t see the source of the echo, but you know something must be in the room causing it.

In this paper, the "echoes" are the loop-induced decays. The Higgs boson doesn't just vanish; it occasionally transforms into pairs of light particles (like photons or gluons) through a "loop" of other particles. If there are "ghost" particles (Supersymmetric particles) hiding in those loops, they will change the volume and pitch of the Higgs' "song."

2. The Three Main Songs (The Decay Channels)

The researcher looked at three specific ways the Higgs "sings" (decays):

• The Diphoton Song ($h \to \gamma\gamma$): The Higgs turns into two flashes of light. This is a very clean, clear note that scientists have measured very accurately.
• The $Z\gamma$ Song ($h \to Z\gamma$): A rarer, more subtle melody where the Higgs turns into a $Z$ boson (a heavy particle) and a photon (light). This is the "hidden treasure" of the paper.
• The Gluon Song ($h \to gg$): The Higgs turns into gluons (the "glue" that holds atoms together). This is a much louder, messier sound.

3. The Big Discovery: The "Loud" $Z\gamma$ Note

The author searched through millions of mathematical possibilities to find a specific "tuning" (a set of parameters) where the $Z\gamma$ song gets much louder.

He found that in the RNS theory, the $Z\gamma$ decay can be boosted by about 20% compared to what the Standard Model (our current rulebook) predicts.

The Analogy: It’s like finding a setting on a guitar that makes the $Z\gamma$ string ring out much more vibrantly than usual. The best part? This "loudness" doesn't break the other songs. The "Diphoton Song" stays almost exactly the same, which is good, because if it had changed too much, it would have contradicted what we’ve already heard from our current experiments.

4. The Trade-off (The Gluon Suppression)

However, there is a catch. In physics, you rarely get something for nothing. To make the $Z\gamma$ note louder, the Gluon Song ($h \to gg$) actually gets quieter—it drops by about 12%.

The Analogy: It’s like a sound engineer adjusting the equalizer on a stereo. If you crank up the treble to make the high notes ($Z\gamma$) pop, you might accidentally muffle the bass ($gg$).

5. Why does this matter?

Right now, our "microphones" (the LHC detectors) aren't quite sensitive enough to tell for sure if the $Z\gamma$ note is actually 20% louder or if it's just a bit of background noise.

But the author is providing the musical score for future scientists. He is saying: "If you build a better microphone (like the proposed future colliders), look specifically for this pattern: a louder $Z\gamma$ note and a slightly quieter gluon note. If you see that specific combination, you've found the ghost notes of Supersymmetry!"

Summary in a Nutshell

The paper proves that a specific theory of "hidden particles" can explain a potential boost in a rare Higgs decay without breaking the rules we already know. It gives future experiments a "treasure map" of exactly what kind of sounds to listen for to prove that the universe is even more complex than we currently think.

Technical Summary

Technical Summary: Loop-Induced Higgs Boson Decays in Radiative Natural Supersymmetry

1. Problem Statement

The discovery of the Higgs boson at the LHC has established the Standard Model (SM) but left open the question of whether its properties are exactly as predicted or influenced by Beyond the Standard Model (BSM) physics. While the Higgs mass and tree-level couplings are well-studied, loop-induced decays—specifically $h \to \gamma\gamma$, $h \to Z\gamma$, and $h \to gg$—are highly sensitive to new, heavy particles circulating in the loops.

The specific challenge addressed in this paper is to determine if the Radiative Natural Supersymmetry (RNS) framework can explain potential enhancements in the rare $h \to Z\gamma$ decay channel without violating the stringent experimental constraints already established for the $h \to \gamma\gamma$ and $h \to gg$ channels.

2. Methodology

The author employs a theoretical and numerical approach within the Minimal Supersymmetric Standard Model (MSSM), specifically focusing on the RNS regime.

• Theoretical Framework: The study utilizes one-loop calculations for the scattering amplitudes of $h \to V_1V_2$ (where $V$ are gauge bosons). The author reproduces the MSSM analytical expressions for the form factors, accounting for contributions from SM particles (W-bosons, top quarks) and SUSY particles (charginos, stops, and sfermions).
• Computational Tools:
  • FeynArts/FeynCalc/Package-X: Used for generating Feynman diagrams and performing algebraic manipulations and loop integral evaluations.
  • LoopTools: Used for numerical evaluation of Passarino–Veltman functions.
  • ISAJET/ISASUGRA: Used to evolve MSSM parameters from the Grand Unification Scale ($\Lambda_{GUT}$) to the SUSY scale via Renormalization Group Equations (RGEs).
  • FeynHiggs: Used to calculate the total Higgs decay width ($\Gamma_h$).
• Parameter Scan: A targeted scan was performed to maximize the $h \to Z\gamma$ width. The scan parameters included $\mu = 100$ GeV (to satisfy electroweak naturalness), varying $m_0$ (scalar mass), $\tan \beta$, and $A_0$ (trilinear coupling), while maintaining the Higgs mass within $125 \pm 2$ GeV.

3. Key Contributions

• Analytical Reproduction: The paper provides a rigorous reproduction of the one-loop MSSM calculations for the three primary loop-induced gauge boson decay channels.
• RNS Correlation Analysis: Unlike studies that look at channels in isolation, this work provides a correlated prediction. It maps how an enhancement in one channel (like $Z\gamma$) necessitates specific, predictable shifts in others ($\gamma\gamma$ and $gg$).
• Decoupling Limit Validation: The study demonstrates how RNS maintains a "SM-like" Higgs sector in the decoupling limit while allowing for measurable loop-level deviations.

4. Results

The numerical analysis yields three distinct behaviors for the Higgs decay channels in the optimized RNS region:

• $h \to Z\gamma$ (The Target): The decay width is significantly enhanced, reaching a maximum of $\simeq 7.5$ keV (a $\sim 20\%$ increase over the SM prediction of $6.19$ keV). This remains compatible with current ATLAS/CMS measurements, which currently have large uncertainties.
• $h \to \gamma\gamma$ (The Constraint): The diphoton channel remains very close to SM expectations. The signal strength ($\mu_{\gamma\gamma}$) shows only a mild suppression ($\simeq 0.95–0.97$), meaning the RNS enhancement of $Z\gamma$ does not "spoil" the successful SM-like predictions for the diphoton mode.
• $h \to gg$ (The Sensitive Probe): This channel shows the strongest sensitivity to SUSY effects. The partial width is suppressed by approximately $12\%$, and the signal strength ($\mu_{gg}$) can drop to $\sim 0.8$. This suggests that the gluon channel is a powerful indirect probe of the stop sector in RNS.

5. Significance

This research is significant for the future of collider physics (HL-LHC, ILC, FCC). It establishes that:

1. RNS is a viable BSM candidate: It can explain potential future deviations in the $h \to Z\gamma$ rate without contradicting current LHC data.
2. Complementarity of Observables: It highlights that a "discovery" in the $Z\gamma$ channel must be accompanied by specific, detectable patterns in the $gg$ and $\gamma\gamma$ channels to be consistent with RNS.
3. Precision Requirements: The paper quantifies the level of experimental precision (roughly $8\%–12\%$) required by future colliders to definitively distinguish RNS from the Standard Model.