arXiv subjects

Hai-Jun Li

Publications and source records attributed to Hai-Jun Li.

At least 19 recordsLinked to original sources

arXiv2026

Hierarchical Axiverse

String compactifications generically produce ${\cal O}(100)$ light axion-like particles, yet low-energy mixing has not previously been exploited as a structuring constraint on their spectrum. We show that the requirement of well-defined QCD-induced mass mixing forces the axion masses into a hierarchically spaced ordering, while stochastic mixing organizes the decay constants into a hierarchically split distribution -- two populations separated by an essentially empty window. Both patterns are insensitive to ultraviolet input and satisfy the relevant Swampland constraints within standard large-volume compactifications. We term this emergent pattern the hierarchical axiverse.

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arXiv2026

Stochastic Axion Mixing: A General Mechanism Beyond Decay Constant Constraints

We propose a novel and generalized mechanism, dubbed stochastic axion mixing. In a multi-axion framework, this mixing occurs naturally provided that the masses of all ultra-light axion-like particles (ALPs) are distinct and lighter than the zero-temperature mass of the QCD axion. Crucially, this mechanism is independent of the relative magnitudes of the axion decay constants. In contrast to the conventional maximal mixing scenario -- which strictly relies on specific decay constant hierarchies -- stochastic mixing represents a significantly broader formalism. Notably, maximal mixing emerges as a specific subset of stochastic mixing under restrictive conditions. This new mechanism offers profound implications for axion cosmology.

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arXiv2025

Some Properties of Multi-Component Axion Dark Matter

We introduce a mechanism for multi-component dark matter (DM) that originates from axion mixing and present some of its defining properties. In this context, multi-component DM implies that the cold DM is composed of the QCD axion and many ultra-light axion-like particles (ALPs). This framework can be realized in the type IIB string axiverse with hierarchical axion masses and decay constants. Our investigation reveals that in the light QCD axion scenario, the energy density of the lightest ALP often dominates after mixing. On the other hand, in the heavy QCD axion scenario, both the QCD axion and non-lightest ALPs may dominate, depending on the ALP decay constants. Under certain conditions, the QCD axion can dominate the DM budget. Finally, we briefly discuss a theoretical framework featuring $\sim\mathcal{O}(100)$ axions, with hierarchical axion masses and decay constants.

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arXiv2025

Toward the Effective Light and Heavy QCD Axion Scenarios

In this work, we investigate the effective parameter space associated with the axion mass and the axion decay constant in both the light and heavy QCD axion scenarios. We initiate our discussion by considering the simplest case of two axions, quantitatively analyzing the parameter space in these two distinct scenarios. We find that the axion mass ratios exhibit a high degree of similarity in these two situations. In contrast, the ratios of axion decay constants display a complete opposition. Furthermore, we generalize our conclusions to encompass the case of multiple axions.

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arXiv2025

Completing Axion Double Level Crossings

In this work, we present the refinement of axion double level crossings within the context of multi-axion mass mixing, specifically focusing on cases where the number of axions exceeds two. Our investigation reveals that double level crossings are a common phenomenon in the mass mixing of the $Z_{\mathcal N}$ axion and axion-like particles. Physically, these double level crossings involve a first level crossing at high temperatures followed by a second level crossing induced by the $Z_{\mathcal N}$ axion mass transition at $T_{\rm QCD}$. We introduce the general model for double level crossings, along with several toy examples, and redefine the light and heavy axion scenarios. In the light axion scenario, double level crossings can occur multiple times in the large ${\mathcal N}$ limit. However, excessively large values of ${\mathcal N}$ may also prevent the occurrence of double level crossings. Conversely, in the heavy axion scenario, excessively small ${\mathcal N}$ may similarly prevent their occurrence. Our findings also have some intriguing implications for axion cosmology.

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arXiv2025

Mass Mixing between QCD Axions

We introduce a novel level crossing phenomenon in the mass mixing between the QCD axions, one canonical QCD axion and one $Z_{\mathcal N}$ axion. The level crossing can take place at or slightly before the QCD phase transition critical temperature, depending on the ratio of the axion decay constants $\sim1.69$. The cosmological evolution of the mass eigenvalues in these two scenarios is similar; however, the transition of axion energy density differs significantly. Finally, we estimate the relic density of the QCD axion dark matter in this context. Additionally, this level crossing may have some interesting cosmological implications.

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arXiv2025

On the Temperature Effects in QCD Axion Mass Mixing

In this work, we extend the QCD axion mass mixing in the early Universe and investigate the temperature effects in the mixing. We explore the scenario where two $Z_{\mathcal N}$ QCD axions undergo mass mixing during the QCD phase transition, yielding three distinct mixing scenarios: the mixing I, II, and III. These scenarios are realized through fine-tuning of the axion decay constants, the temperature parameters, as well as the value of $\mathcal N$. We conduct a thorough analysis of the level crossing phenomena in these three mixing scenarios, detailing the conditions under which they occur. Notably, in the mixing I and II, the level crossing precedes the critical temperature of the QCD phase transition ($T_{\rm QCD}$), with minimal non-essential discrepancies in the cosmological evolution of the mass eigenvalues at $T_{\rm QCD}$. In contrast, the mixing III exhibits a unique double level crossings, occurring both before and at $T_{\rm QCD}$. Despite superficial similarities in axion evolution between the mixing II and III, we uncover fundamental differences between them. Additionally, we briefly address the transition in energy density between the two axions within our mixing scenarios. This work contributes to a deeper understanding of the role of the QCD axion in the early Universe and its potential implications for cold dark matter.

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arXiv2025

QCD Axion Dark Matter in the Dark Dimension

The recently proposed dark dimension scenario reveals that axions can be localized on the Standard Model brane, thereby predicting the quantum chromodynamics (QCD) axion decay constant from the Weak Gravity Conjecture: $f_a\lesssim M_5 \sim 10^{9}-10^{10}\, \rm GeV$, where $M_5$ is the five-dimensional Planck mass. When combined with observational lower bounds, this implies that $f_a$ falls within a narrow range $f_a\sim 10^{9}-10^{10}\, \rm GeV$, corresponding to the axion mass $m_a\sim 10^{-3}-10^{-2}\, \rm eV$. At this scale, the QCD axion constitutes a minor fraction of the total cold dark matter (DM) density $\sim 10^{-3}-10^{-2}$. In this work, we investigate the issue of QCD axion DM within the context of the dark dimension and demonstrate that the QCD axion in this scenario can account for the entire DM abundance through a simple two-axion mixing mechanism. Specifically, we consider the resonant conversion of an axion-like particle (ALP) into the QCD axion. We find that, in a scenario where the ALP possesses a mass of approximately $m_A \sim 10^{-5} \, \rm eV$ and a decay constant of $f_A \sim 10^{11} \, \rm GeV$, the QCD axion in the dark dimension can account for the overall DM. The ALP required within this specific range may originate from the grand unification of gauge forces in the dark dimension.

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arXiv2025

Axion Mixing in the String Axiverse

String axiverse provides a fascinating and complex landscape for axion physics. The requirement in type IIB string axiverse models necessitates at least two axions to ensure the presence of both a QCD axion candidate and an additional axion-like particle (ALP). In this work, we study axion mass mixing and adopt a bottom-up perspective to investigate what conditions an axion model must satisfy in order to exhibit maximal mixing -- the scenario where the degree of effective mixing is maximized. We find that maximal mixing occurs when the masses of all ALPs are smaller than the zero-temperature mass of the QCD axion, with no two ALP masses being equal, and when the decay constants of all ALPs are uniformly either smaller or larger than the decay constant of the QCD axion. Additionally, the transfer of axion energy density ultimately takes place only between the two axions with the closest masses. These findings provide critical insights into axion dynamics not only within type IIB string axiverse models but also in broader multi-axion mixing frameworks. The potential cosmological implications of axion mass mixing are also addressed at the end.

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arXiv2025

Axion effects on gamma-ray spectral irregularities. II: Implications of EBL absorption

The extragalactic background light (EBL) plays a crucial role in the propagation of high-energy particles throughout the Universe. In this work, we explore the impact of the EBL absorption effect on photon to axionlike particle (ALP) conversions from the very-high-energy gamma-ray spectral irregularities. For our purpose, we select four BL Lac blazars: Markarian 501, 1ES 0229+200, PKS 0301-243, and PKS 0447-439 for analysis. Their redshifts range from approximately 0.03 to 0.34. We first discuss the EBL absorption effect on the gamma-ray spectral energy distributions (SEDs) using three common EBL spectral models: Finke-10, Franceschini-17, and Saldana-Lopez-21. Then we consider the photon-ALP conversions in astrophysical magnetic fields. The best-fit chi-square distributions of these EBL models under the ALP assumption in the ALP parameter $\{m_a, g_{aγ}\}$ plane are provided, showing similar distributions. For comparison, we define a new delta chi-square, $χ_d^2$, to quantify the difference in chi-square values. The distributions of $χ_d^2$ and the gamma-ray SEDs corresponding to the maximum delta chi-square, $χ^2_{d, \rm max}$, are also presented for comparison. Our results indicate that the influence of these different EBL models is non-dominant at the low-redshift gamma-ray axionscope. In these cases, choosing the latest model, Saldana-Lopez-21, is sufficient. However, as the redshift of the sources increases, this influence becomes more significant.

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arXiv2025

QCD axion bubbles in the presence of ALP resonant conversion

The QCD axion bubbles can form due to an explicit breaking of the Peccei-Quinn symmetry in the early Universe. In this paper, we investigate the modified formation of QCD axion bubble in the presence of axionlike particle (ALP), considering its resonant conversion to QCD axion. We consider a general scenario where the QCD axion mixes with ALP before the QCD phase transition. In this scenario, the energy density of the ALP can be adiabatic transferred to the QCD axion at a temperature $T_R$, resulting in the suppression of the cosmic background temperature $T_B$ at which the energy density of the QCD axion equals that of the radiation. The QCD axion bubbles form when the QCD axions arise during the QCD phase transition. Finally, we briefly discuss the impact of the formation of QCD axion bubbles on the formation of primordial black holes.

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arXiv2025

Gravitational waves and primordial black holes from axion domain walls in level crossing

In this paper, we investigate the nano-Hertz gravitational waves (GWs) emission and the massive primordial black holes (PBHs) formation from the light QCD axion scenario. We consider the axion domain walls formation from the level crossing induced by the mass mixing between the light $Z_{\mathcal N}$ QCD axion and axion-like particle. A general mixing case is considered that the heavy and light mass eigenvalues do not necessarily have to coincide with the axion masses. In order to form the domain walls, the axions should start to oscillate slightly before the level crossing. The domain walls must annihilate before dominating the Universe to avoid the cosmological catastrophe. Then we focus our attention on the GWs emission from the domain walls annihilation and the PBHs formation from the domain walls collapse. We show the predicted GWs spectra with the peak frequency $\sim 0.2\, \rm nHz$ and the peak amplitude $\sim 5\times 10^{-9}$, which can be tested by the future pulsar timing array projects. In addition, during the domain walls annihilation, the closed walls could shrink to the Schwarzschild radius and collapse into the PBHs. We find that the PBHs in the mass range of $\mathcal{O}(10^5-10^8) M_\odot$ could potentially form in this scenario and account for a small fraction $\sim 10^{-5}$ of the cold dark matter.

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arXiv2024

Upper limit on the axion-photon coupling from Markarian 421

Markarian 421 is a well-known nearby BL Lac blazar at the redshift $z=0.031$. Many previous works were investigated to constrain the axion-photon coupling from its TeV gamma-ray observations, showing the upper limit on the coupling constant $g_{aγ} \lesssim 2.0\times 10^{-11} \rm \, GeV^{-1}$ for the axion mass $[5.0\times10^{-10} \, {\rm eV} \lesssim m_a \lesssim 5.0\times10^{-7} \, {\rm eV}]$. While in this work, we obtain a more stringent upper limit on the axion-photon coupling from the 1038 days gamma-ray observations of the blazar Markarian 421. The long-term gamma-ray spectra are measured by the collaborations Large Area Telescope on board NASA's Fermi Gamma-ray Space Telescope (Fermi-LAT) and High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory from 2015 June to 2018 July. We show the best-fit spectral energy distributions (SEDs) of Markarian 421 under the null and axion hypotheses. Then we set the axion-photon limit in the $\{m_a, \, g_{aγ}\}$ plane. The 99% $\rm C.L.$ upper limit set by Markarian 421 is $g_{aγ} \lesssim 4.0\times 10^{-12} \rm \, GeV^{-1}$ for the axion mass $[1.0\times10^{-9} \, {\rm eV} \lesssim m_a \lesssim 1.0\times10^{-8} \, {\rm eV}]$. It is the most stringent upper limit in this axion mass region.

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arXiv2024

Axion dark matter with explicit Peccei-Quinn symmetry breaking in the axiverse

It was shown that the required high quality of the Peccei-Quinn (PQ) symmetry can be a natural outcome of the multiple QCD axions model. In the axiverse, a hypothetical mass mixing between the QCD axions and axion-like particles (ALPs) can occur, which leads to an interesting phenomenon called the level crossing. In this paper, we investigate this mass mixing between one QCD axion and one ALP with the explicit PQ symmetry breaking in the early Universe. The dynamics of the axions and their cosmological evolutions when the level crossing occurs in this scenario are studied in detail. We show the evolution of the mass eigenvalues and the mass mixing angle. Then we check the condition for energy adiabatic transition with the corresponding parameter set. Finally, we estimate the relic density of the QCD axion and ALP dark matter through the misalignment mechanism. We find that, the QCD axion relic density can be suppressed, while the ALP relic density can be enhanced. The level crossing in our scenario may have some cosmological implications, such as the axion domain walls formation, the nano-Hertz gravitational waves emission, and also the primordial black holes formation.

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arXiv2024

Supermassive black holes triggered by QCD axion bubbles

The supermassive black holes (SMBHs) are ubiquitous in the center of galaxies, although the origin of their massive seeds is still unknown. In this paper, we investigate the SMBHs formation from the QCD axion bubbles. In this case, the primordial black holes (PBHs) are considered as the seeds of SMBHs, which are generated from the QCD axion bubbles due to an explicit Peccei-Quinn (PQ) symmetry breaking after inflation. The QCD axion bubbles are formed when the QCD axion starts to oscillate during the QCD phase transition. We consider a general case in which the axion bubbles are formed with the bubble effective angle $θ_{\rm eff}\in(0, \, π]$, leading to the minimum PBH mass $\sim\mathcal{O}(10^4-10^7)M_\odot$ for the axion decay constant $f_a\sim\mathcal{O}(10^{16})\, \rm GeV$. The PBHs at this mass region may account for the seeds of SMBHs.

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arXiv2024

Axion limits from the 10-year gamma-ray emission 1ES 1215+303

We present the limits on photon to axionlike particle (ALP) coupling from the 10-year period observations of the TeV BL Lacertae blazar 1ES 1215+303 (with redshift $z=0.130$). The contemporaneous gamma-ray spectra are measured by the collaborations Fermi-LAT and VERITAS with five flux phases from 2008 to 2017, including four low states and one flare. Using these flux phases, we show the spectral energy distributions (SEDs) under the null/ALP hypotheses and set the combined limit on ALP. The 95% $\rm C.L.$ combined limit set by 1ES 1215+303 with the 10-year gamma-ray data is roughly at the photon-ALP coupling constant $g_{aγ} \gtrsim 1.5\times 10^{-11} \rm \, GeV^{-1}$ for the ALP mass $5.0\times10^{-10} \, {\rm eV} \lesssim m_a \lesssim 1.0\times10^{-7} \, {\rm eV}$.

astro-ph.HE↗

arXiv2024

Light QCD Axion Dark Matter from Double Level Crossings

The even light QCD axion called the $Z_{\mathcal N}$ axion can both solve the strong CP problem and account for the dark matter (DM). We point out that the single and double level crossings can naturally take place in the mass mixing between the $Z_{\mathcal N}$ axion and axionlike particle (ALP). The first level crossing occurs much earlier than the QCD phase transition, while the second level crossing occurs exactly during the QCD phase transition if it exists. We also find that the single level crossing can transform into the double level crossings, depending on the ALP mass $m_A$ versus the zero-temperature $Z_{\mathcal N}$ axion mass $m_{a,0}$. Compared with the no level crossing case, the $Z_{\mathcal N}$ axion relic density can be suppressed in the single level crossing, and enhanced or suppressed in the double level crossings.

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arXiv2023

Axion effects on gamma-ray spectral irregularities with AGN redshift uncertainty

We investigate the photon-axionlike particle (ALP) oscillation effects on TeV gamma-ray spectral irregularities from the uncertain redshift active galactic nuclei (AGN) VER J0521+211. The gamma-ray spectra are measured by Fermi-LAT and VERITAS with the three flux states in 2013 and 2014. We set the combined constraints on the ALP parameter ($m_a, g_{aγ}$) space with these states and test the extragalactic background light (EBL) absorption effect on ALP constraints with the redshift limit scenarios $z_0\sim\mathcal{O}(0.1-0.3)$. The 99% $\rm C.L.$ photon-ALP combined constraints set by VER J0521+211 are roughly at $g_{aγ} \gtrsim 2.0\times 10^{-11} \rm \, GeV^{-1}$ for $1.0\times10^{-9} \, {\rm eV} \lesssim m_a \lesssim 1.0\times10^{-7} \, {\rm eV}$. We find no clear connection between the redshift limit scenarios and the photon-ALP constraints. Both the underestimated and overestimated redshifts can affect the constraint results.

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