Higgs-Mediated Repulsion in Particle Physics

• Higgs-mediated repulsion is a phenomenon where the Higgs field induces nontraditional repulsive forces that stabilize topological solitons like monopole-antimonopole pairs.
• It exhibits non-monotonic, mass- and topology-dependent behavior that extends beyond simple Yukawa suppression, crucial for maintaining soliton configurations.
• This mechanism also influences lepton flavor-violating processes and interference effects in diphoton production, underscoring its importance in both theoretical and experimental studies.

Higgs-mediated repulsion refers to physical mechanisms by which the Higgs field induces or modulates repulsive interactions between particles, topological entities, or quantum excitations. Such repulsive effects manifest across diverse contexts, including the stabilization of electroweak monopole-antimonopole pairs, competition in lepton flavor-violating transitions in supersymmetry, and interference phenomena in diphoton production. The underlying physics is governed not solely by the conventional Yukawa potential but also by non-monotonic behavior, topological charge, field-theoretic symmetry, and the interplay between Higgs and gauge bosons. Higgs-mediated repulsion is a distinctly non-trivial phenomenon that exhibits mass- and topology-dependent transitions, with implications for the stability of solitonic configurations, rare decay rates, and experimental observables.

1. Higgs-Mediated Repulsion in Topological Soliton Stabilization

Higgs-mediated repulsion plays a central role in the stabilization of Cho-Maison monopole-antimonopole pairs (MAPs) in the standard electroweak theory (Zhu et al., 22 Aug 2025). The mechanism is revealed through a detailed stress-energy tensor decomposition that isolates the Higgs contribution: $$T_{33} = T_{33}^{\text{Higgs}} + T_{33}^{SU(2)} + T_{33}^{U(1)}$$ where

$$T_{33}^{\text{Higgs}} \propto (D_3\phi)^2 + (A_3\phi)^2 + \cdots$$

The Higgs-mediated component provides a spatially extended repulsive force that counteracts the long-range magnetic attraction between the monopole and antimonopole. Notably, this repulsion is highly sensitive to the topological charge $n$ and Higgs self-coupling parameter $\beta$. The separation between the monopole poles ($dz$) as a function of $\beta$ and $n$ displays pronounced non-monotonic dependence; $dz$ can grow or shrink as $\beta$ increases, exhibiting a "recovery phase" beyond the region expected for Yukawa suppression. In particular, the pole separation peaks at intermediate $n$ and then decreases, a feature not predicted by a simple exponential decay with Higgs mass ($\sim e^{-m_H r}$).

2. Mass-Controlled Range Transitions and Deviations from Yukawa Suppression

While massive scalar fields typically mediate short-range forces described by an exponentially damped Yukawa potential,

$V(r) \sim g^2 \frac{e^{-m r}}{r}$

the Higgs-mediated repulsion observed in MAP stabilization extends beyond this canonical form. Numerical and analytical results (Zhu et al., 22 Aug 2025) reveal that for finite $\beta$ (or equivalently for a nonzero Higgs mass $m_H$), the repulsive force remains significant far beyond the Yukawa radius and undergoes a slow transition to short-range behavior. In practice,

$$V_{\text{Higgs}}(r) \sim g_H^2 (D_3\phi)^2 F(\beta, r)$$

where $F(\beta, r)$ encodes the non-exponential decay and resurgence of repulsive strength at large $r$. This prolonged interaction range is controlled jointly by the Higgs mass and the topological charge, leading to stabilization over a regime larger than simple dimensional analysis would suggest.

3. Interplay of Higgs-Mediated and Gauge Boson (Z) Repulsions

The stabilization of MAPs is orchestrated through the combined action of Higgs- and Z-boson–mediated repulsions. The Higgs field acts on topological scales, providing long-range balance against magnetic collapse. Simultaneously, the $Z$ field, arising from the $SU(2)$ sector and related via

$B_i = \cos\theta_W A_i^{em} - \sin\theta_W Z_i$

generates local repulsive cores at the pole positions, possessing a characteristic radius

$R_c \approx 0.8\, m_W^{-1}$

This dual mechanism divides the stabilization into long-range (Higgs/topological) and short-range ($Z$/electroweak) domains. The stress-energy tensor analysis demonstrates that the Higgs component manages global separation, while $Z$ boson exchange establishes localized repulsion preventing annihilation of the poles.

4. Higgs-Mediated Repulsion in Lepton Flavor Violation and Competition of Amplitudes

In the MSSM, Higgs-mediated repulsion can be interpreted as the dominance or suppression of certain flavor-changing transitions (Hisano et al., 2010, Yang, 2011). Non-holomorphic Yukawa interactions induce effective flavor-violating Higgs couplings that compete with gaugino/slepton exchange. The relevant terms are

$$-\mathcal{L}_{\text{eff}}^{(\mu-e)} = \frac{m_\mu\, \Delta^{(L)}_{\mu e}}{v\, \cos^2\beta} (\bar{\mu} P_L e)\, [\cos(\alpha-\beta) h^0 + \sin(\alpha-\beta) H^0 - iA^0] + \text{h.c.}$$

While barr-Zee diagrams driven by the Higgs can enhance rates like $\mu\to e\gamma$, they can also suppress (i.e., repel) gaugino-mediated channels through destructive interference or parameter-space–dependent amplitude competition. The relative strengths hinge on $M_{\text{SUSY}}/m_{A^0}$, $\tan\beta$, and the chirality of the flavor violation, with the Higgs-mediated effects sometimes overwhelming the gaugino contributions.

5. Higgs-Mediated Repulsion and Signal-Background Interference Phenomena

A distinct manifestation occurs in Higgs-mediated diphoton production interference at the LHC (Bargiela et al., 2022). Here, the "repulsion" is metaphorical—interference between the Higgs signal and continuum background shifts the invariant mass peak away from the true Higgs mass, an effect captured via

$I_{\text{Re}} \propto (m_{\gamma\gamma}^2 - m_H^2)$

This antisymmetric interference pushes the peak, and its magnitude is proportional to $\sqrt{\Gamma_H}$, with NNLO QCD corrections further modulating the mass shift. The result is an effective "repulsion" of the signal from its nominal position, used to extract bounds on the Higgs total width.

6. Broader Extensions and Universality in Field Theory

Analysis of Higgs-mediated repulsion in MAP stabilization (Zhu et al., 22 Aug 2025) suggests a universal mechanism extending to other topological solitons (such as electroweak vortex rings and sphaleron chains) in the Standard Model. The non-monotonic, mass- and charge-controlled regime transition mediated by the Higgs field is posited as a key ingredient in preventing collapse or destabilization, balancing attractive interactions intrinsic to soliton formation.

7. Summary Table: Dual Repulsion Mechanisms in MAPs

Mechanism	Effective Range	Controlling Parameters
Higgs-mediated	Topological / long	Topological charge $n$, $\beta$, $m_H$
Z-boson-mediated	Electroweak / short	$m_W$, neutral charge distribution

The coexistence of these repulsion mechanisms enables stable solitonic configurations, with the Higgs field providing an extended, non-Yukawa repulsion sensitive to topological and field-theoretic parameters, and the $Z$-boson establishing short-range reinforcement aligned with weak-scale physics.

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In conclusion, Higgs-mediated repulsion is a multifaceted phenomenon manifesting as a stabilizing force in topological soliton systems, as an amplitude suppressor in flavor-violating transitions, and as a shifting mechanism in interference-based measurements. Its topological origin, non-monotonic charge and coupling dependence, and mass-controlled range adjustments distinguish it conceptually from conventional Yukawa forces and underline its significance in both theoretical and experimental high-energy physics research.