Hadrosymmetric Twin Higgs (HTH)

• Hadrosymmetric Twin Higgs (HTH) is defined as a Twin Higgs framework that retains a hadronic twin sector while omitting light twin leptons and radiation.
• The model stabilizes the Higgs mass by preserving pseudo-Nambu-Goldstone symmetry and enforcing near-identical twin top Yukawa and gauge couplings.
• Cosmological implementations of HTH demonstrate reduced ΔNₑff and alleviation of H₀ and σ₈ tensions, with implications for dark-matter phenomenology and testable portal signatures.

Searching arXiv for recent and foundational papers on the Hadrosymmetric Twin Higgs. I’ll look up arXiv entries relevant to HTH, including the 2025 cosmology paper and earlier model-building work. Hadrosymmetric Twin Higgs (HTH) denotes a class of Twin Higgs constructions in which the twin sector retains a hadronic copy of the Standard Model quark sector but removes the light states that dominate the dark-radiation phenomenology of fully mirrored realizations. In the formulation emphasized by recent cosmological work, HTH keeps all three generations of twin quarks and the twin $SU(3)_C' \times SU(2)_L'$ gauge sector, omits light twin leptons, and does not gauge twin hypercharge, so the low-energy twin spectrum is dominated by twin hadrons rather than twin photons or neutrinos. This structure is intended to preserve the pseudo-Nambu-Goldstone protection of the Higgs mass while driving $\Delta N_{\rm eff}$ to approximately zero, and it has also been studied as a cosmological sector that can reduce the $H_0$ tension from more than $4\sigma$ to about $2.5\sigma$ while alleviating the $\sigma_8$ discrepancy (Sotudeh et al., 1 Oct 2025).

1. Twin-Higgs setting and model motivation

The HTH framework is embedded in the broader Twin Higgs mechanism, a symmetry-based approach to the little hierarchy problem in which the Higgs is stabilized as a pseudo-Nambu-Goldstone boson of a spontaneously broken global symmetry, typically $SU(4)\rightarrow SU(3)$. In the archetypal Mirror Twin Higgs (MTH), the entire Standard Model is doubled. That structure preserves the neutral-naturalness logic, but it also introduces light twin photons and neutrinos, which contribute to the effective number of relativistic species,

$$\Delta N_{\rm eff} \equiv N_{\rm eff} - N_{{\rm eff},\,{\rm SM}}, \qquad N_{{\rm eff},\,{\rm SM}} \simeq 3.045.$$

The data summary states that existing Planck CMB and other data require $\Delta N_{\rm eff}\lesssim 0.3$ at high significance, so fully mirrored twin sectors are cosmologically problematic unless an engineered thermal history is added (Sotudeh et al., 1 Oct 2025).

HTH is motivated as a minimal cosmologically viable realization of Twin Higgs in which the hadronic twin sector is retained but the light twin radiation is removed. The hadrosymmetric scenario was identified in the literature as a model with symmetric twin QCD and generalized flavor structure, and later work connected it explicitly to dark-shower phenomenology and to cosmological tests (Jovančević et al., 2018). In this sense, HTH occupies an intermediate position between the fully mirrored MTH limit and more aggressively truncated fraternal constructions: it preserves a rich twin hadron spectrum while attempting to evade the dominant $\Delta N_{\rm eff}$ constraint (Freytsis et al., 2016).

2. Particle content and low-energy spectrum

The defining structural distinction of HTH is that it keeps the twin quark sector while removing the light twin electroweak matter responsible for late radiation. In the formulation summarized in the 2025 cosmology study, the twin sector contains all three generations of twin quarks, twin gluons, and massive twin weak bosons, but no gauged twin hypercharge and no light twin leptons. Consequently there is no twin photon, no light twin neutrinos, and no twin electrons. The low-energy degrees of freedom are therefore hadronic composites such as twin pions, twin protons, twin neutrons, and heavier hadrons (Sotudeh et al., 1 Oct 2025).

Feature	Mirror Twin Higgs	Hadrosymmetric Twin Higgs
Twin fermions	Full SM copy	All three generations of twin quarks; no light twin leptons
Hypercharge sector	Twin hypercharge gauged; twin photon present	Twin hypercharge global; no twin photon
Late relativistic states	Twin photons and neutrinos present	No light twin photons or neutrinos

The mass scales in the twin hadron sector are described as resembling those of the Standard Model up to rescalings set by the ratio $\Delta N_{\rm eff}$0, with $\Delta N_{\rm eff}$1 to avoid Higgs coupling deviations, and with similar QCD confinement scales up to small coupling differences. In the dark-shower formulation, the quark masses scale as

$\Delta N_{\rm eff}$2

and the twin pion mass is summarized as

$\Delta N_{\rm eff}$3

with $\Delta N_{\rm eff}$4 (Freytsis et al., 2016).

3. Naturalness requirements and symmetry structure

The naturalness logic of HTH follows the standard Twin Higgs requirement that the twin top Yukawa and the twin strong and weak gauge couplings remain close to their Standard Model values so that the leading quadratic divergences in the Higgs potential cancel. The summary of the cosmology paper gives the matching conditions

$\Delta N_{\rm eff}$5

and states that the cutoff for Higgs naturalness is pushed up to $\Delta N_{\rm eff}$6 TeV (Sotudeh et al., 1 Oct 2025).

Although HTH is often presented as a low-energy spectrum choice, later model-building work also described dynamical routes to hadrosymmetric or fraternal-like spectra. In the construction based on spontaneous twin hypercharge and $\Delta N_{\rm eff}$7 breaking, a scalar $\Delta N_{\rm eff}$8 charged under twin hypercharge acquires a vacuum expectation value through a potential of the form

$\Delta N_{\rm eff}$9

with negative $H_0$0 selecting $H_0$1. The resulting couplings can generate twin fermion masses independent of electroweak symmetry breaking, lift selected generations, and thereby dynamically realize hadrosymmetric or fraternal spectra rather than imposing them by hand. The same construction states that the twin confinement scale can be a factor of a few to ten larger than $H_0$2, depending on the spectrum and matching (Batell et al., 2019).

4. Twin hadrons, decay portals, and early-universe consistency

The cosmological viability of HTH depends not only on eliminating light twin radiation but also on ensuring that the lightest twin hadrons do not survive long enough to disrupt nucleosynthesis. In the minimal cosmology treatment, even the lightest twin hadrons, especially the neutral twin pion, must decay before BBN: $H_0$3 The summary explicitly states that this requires a portal, for example through twin-pion mixing with the Standard Model pion followed by decay to diphotons, and that there should be no stable relics in that specific twin sector implementation that overclose the Universe or contribute to late-time dark radiation or dark matter (Sotudeh et al., 1 Oct 2025).

The dark-shower realization sharpened this point. There, the neutral twin pion is the lightest twin hadron and cannot decay efficiently through the Higgs portal because it is a pseudoscalar while the Higgs portal is CP-even, with isospin breaking highly suppressed. To force $H_0$4 decay before BBN, the analysis introduced current-current dimension-6 operators between twin and Standard Model quarks and presented a simple UV completion based on a broken $H_0$5 gauge boson coupled to right-handed quarks. For $H_0$6, the requirement $H_0$7 implies $H_0$8, placing the mediator scale in a range relevant to collider, flavor, and intensity-frontier searches (Freytsis et al., 2016).

5. Cosmological implementation and the $H_0$9–$4\sigma$0 tensions

A central development in the recent HTH literature is the explicit implementation of the twin hadron sector in Boltzmann evolution. The 2025 study incorporated the HTH sector into CLASS by treating the twin hadron population, chiefly $4\sigma$1, as an effective decaying dark matter component. The analysis introduced two additional cosmological parameters, $4\sigma$2 and $4\sigma$3, modified the perturbation equations with new source terms in the CMB photon Boltzmann hierarchy, and performed MCMC scans with MONTEPYTHON using Planck 2018 CMB data together with local $4\sigma$4 measurements (Sotudeh et al., 1 Oct 2025).

The reported outcome is that HTH, while maintaining $4\sigma$5, softens both major late-time tensions. The Hubble tension is reduced from more than $4\sigma$6 in $4\sigma$7CDM to about $4\sigma$8, with the quoted values

$4\sigma$9

$2.5\sigma$0

and, with a local $2.5\sigma$1 prior,

$2.5\sigma$2

The same study states that the $2.5\sigma$3 values are reduced, bringing them closer to weak-lensing best fits. The mechanism identified in the summary is that the decaying twin hadron component modifies both the expansion history and the growth of structure without introducing the extra radiation that would violate $2.5\sigma$4 bounds. By contrast, the MTH can fully resolve the $2.5\sigma$5 tension only at the cost of a large $2.5\sigma$6, while an HTH extension with light twin leptons can also fully resolve $2.5\sigma$7 but again at the expense of renewed CMB tension (Sotudeh et al., 1 Oct 2025).

6. Dark-matter and indirect-detection realizations

HTH has also been developed as a dark-matter framework in which annihilation proceeds through a hadronic twin shower. In that realization, the twin sector contains three twin generations of quarks, no light twin leptons or twin photons, and twin pions as the lightest twin particles. Two benchmark WIMP candidates were analyzed: a Dirac twin lepton $2.5\sigma$8 and a Majorana state $2.5\sigma$9. Freeze-out occurs through annihilation into twin quarks via twin electroweak interactions, followed by twin hadronization into a multiplicity of twin pions and heavier hadrons. The showering and hadronization were simulated with a custom Pythia8 implementation adapted to the twin sector (Freytsis et al., 2016).

The resulting photon phenomenology is dominated, for appropriate masses, by $\sigma_8$0. The summary reports that the gamma-ray spectra can fit the Fermi-LAT Galactic Center Excess for dark-matter masses $\sigma_8$1, with twin QCD scales slightly above the Standard Model and $\sigma_8$2. In the Dirac scenario, the fit to the Galactic Center Excess, the relic-density requirement, and minimal fine-tuning overlap for $\sigma_8$3; in the Majorana scenario, the masses in the fit region overclose the Universe. The same work states that direct detection through the Higgs portal lies below current LUX bounds but may be accessible in future experiments, while mediator searches at the LHC, $\sigma_8$4-factories, beam-dump experiments, and rare meson decays can probe much of the portal parameter space (Freytsis et al., 2016).

7. Phenomenological status and conceptual scope

The phenomenological profile of HTH is shaped by a tension between invisibility and testability. The intrinsic twin sector is difficult to probe at colliders because it lacks Standard Model charges and, in the minimal version, lacks light visible final states. The 2025 cosmology study therefore identifies cosmological observables as the key probe and points to future precision programs such as CMB-S4, DESI, and Euclid through predicted shifts in $\sigma_8$5, $\sigma_8$6, and structure formation. At the same time, earlier dark-shower studies emphasize that the auxiliary portals required for twin-hadron decay can themselves introduce experimentally accessible mediators, so collider and intensity-frontier signatures are not excluded in UV-complete realizations (Sotudeh et al., 1 Oct 2025).

A recurrent misconception is to treat HTH as merely the MTH with altered parameters. The supplied literature instead presents a structural distinction: HTH is defined by a hadronic twin sector without a gauged twin hypercharge and without light twin leptons, so its cosmological behavior is not that of a fully mirrored plasma. Another common overstatement is that any Twin Higgs explanation of the $\sigma_8$7 tension must rely on extra dark radiation. The HTH cosmology analysis explicitly claims the opposite for the minimal model: $\sigma_8$8 at recombination and BBN, partial resolution of the $\sigma_8$9 tension, and concurrent alleviation of $SU(4)\rightarrow SU(3)$0. Full $SU(4)\rightarrow SU(3)$1 resolution reappears only in an extended HTH sector with light twin leptons, where the gain in $SU(4)\rightarrow SU(3)$2 is offset by renewed tension with CMB constraints (Sotudeh et al., 1 Oct 2025).