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  • Gravitational waves from equatorially eccentric extreme mass ratio inspirals around swirling-Kerr black holes
    2026, 50(2): 025107-025107-11. doi: 10.1088/1674-1137/ae1afc
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    The swirling-Kerr black hole is a novel solution of vacuum general relativity and has an extra swirling parameter characterizing the rotation of spacetime background. We study the gravitational waves generated by extreme mass ratio inspirals (EMRIs) along eccentric orbits on the equatorial plane in this novel swirling spacetime. Our findings indicate that this swirling parameter leads to a delayed phase shift in the gravitational waveforms. Furthermore, we investigate the effects of the swirling parameter on the potential issue of waveform confusion caused by the orbital eccentricity and semi-latus rectum parameters. As the swirling parameter increases, the relative variations in the eccentricity increase, whereas the variations in the semi-latus rectum rapidly decrease. The trends related to changes in the orbital eccentricity and semi-latus rectum with the swirling parameter resemble those observed with the MOG parameter in Scalar-Tensor-Vector-Gravity (STVG) theory but with different rates of change. Furthermore, our results also reveal that the effects of the background swirling parameter on the relative variations in the eccentricity and semi-latus rectum are distinct from those of the black hole spin parameter. These results provide deeper insights into the properties of EMRI gravitational waves and background swirling.
  • Investigation of resonances in the Σ(1/2) system based on the chiral quark model
    2026, 50(2): 023109-023109-11. doi: 10.1088/1674-1137/ae18af
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    In this work, we investigate the resonance structures in the $ \Sigma(1/2^-) $ system from both three-quark and five-quark perspectives within the framework of the chiral quark model. An accurate few-body computational approach, the Gaussian expansion method, is employed to construct the orbital wave functions of multiquark states. To reduce the model dependence on parameters, we fit two sets of parameters to check the stability of the results. The calculations show that our results remain stable despite changes in the parameters. In the three-quark calculations, two $ \Sigma(1/2^-) $ states are obtained with energies around 1.8 GeV, which are good candidates for the experimentally observed $ \Sigma(1750) $ and $ \Sigma(1900) $. In the five-quark configuration, several stable resonance states are identified, including $ \Sigma \pi $, $ N \bar{K} $, and $ N \bar{K}^{*} $. These resonance states survive the channel-coupling calculations under the complex-scaling framework and manifest as stable structures. Our results support the existence of a two-pole structure for the $ \Sigma(1/2^-) $ system, predominantly composed of $ \Sigma \pi $ and $ N \bar{K} $ configurations, analogous to the well-known $ \Lambda(1380) $-$ \Lambda(1405) $ ($ \Sigma \pi $-$ N \bar{K} $) system. On the other hand, although the energy of the $ N \bar{K}^{*} $ configuration is close to that of $ \Sigma(1750) $ and $ \Sigma(1900) $, the obtained width is not consistent with the experimental values. This suggests that the $ N \bar{K}^{*} $ state needs to mix with three-quark components to better explain the experimental $ \Sigma(1750) $ and $ \Sigma(1900) $ states. According to our decay width calculations, the predicted two resonance states are primarily composed of $ \Sigma \pi $ and $ N \bar{K} $, with their main decay channel being $ \Lambda \pi $. Therefore, we encourage experimental groups to search for the predicted two-pole structure of the $ \Sigma(1/2^-) $ system in the invariant mass spectrum of $ \Lambda \pi $.
  • Neutrino mass model at a three-loop level from a non-holomorphic modular A4 symmetry
    2026, 50(2): 023108-023108-9. doi: 10.1088/1674-1137/ae15ee
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    We study a three-loop induced neutrino mass scenario from a non-holomorphic modular A4 flavor symmetry and obtain the minimum scenario leading to predictions of the lepton masses, mixing angles, and Dirac and Majorana phases, which are shown through chi square analyses. In addition, we discuss the lepton flavor violations, muon anomalous magnetic moment, lepton universality, and relic density of the dark matter candidate. Moreover, we show that our model can be extended to satisfy the observed relic density of dark matter within the limit of perturbation by adding one singlet scalar boson without changing predictions in the neutrino sector.
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