Accurate and precise measurements of masses of galaxy clusters are key to derive robust constraints on cosmological parameters. Rising evidence from observations, however, confirms that X-ray masses, obtained under the assumption of hydrostatic equilibrium, might be underestimated, as previously predicted by cosmological simulations. We analyse more than 300 simulated massive clusters, from 'The Three Hundred Project', and investigate the connection between mass bias and several diagnostics extracted from synthetic X-ray images of these simulated clusters. We find that the azimuthal scatter measured in 12 sectors of the X-ray flux maps is a statistically significant indication of the presence of an intrinsic (i.e. 3D) clumpy gas distribution. We verify that a robust correction to the hydrostatic mass bias can be inferred when estimates of the gas inhomogeneity from X-ray maps (such as the azimuthal scatter or the gas ellipticity) are combined with the asymptotic external slope of the gas density or pressure profiles, which can be respectively derived from X-ray and millimetric (Sunyaev-Zeldovich effect) observations. We also obtain that mass measurements based on either gas density and temperature or gas density and pressure result in similar distributions of the mass bias. In both cases, we provide corrections that help reduce both the dispersion and skewness of the mass bias distribution. These are effective even when irregular clusters are included leading to interesting implications for the modelling and correction of hydrostatic mass bias in cosmological analyses of current and future X-ray and SZ cluster surveys.

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The (g − 2)μ anomaly indicates that the second generation of leptons should have new interactions beyond the standard model. The high flux of νμ and $$ \overline{\nu} $$ ν ¯ μ at the forward experiments such as FASERν and SND@LHC makes them suitable setups to search for new interactions of the second generation leptons. In this paper, we build a model in which the second generation left-handed leptons couple to a new right-handed neutrino, N and a new Higgs doublet which also couples to the quarks. The scattering of high energy νμ off nuclei can produce N. We investigate how forward experiments can test this model by looking for the N production vertex followed by the displaced vertex of the N decay. Discovering even a single such event can be a harbinger to look for the spectacular signals of the new Higgs doublet production at the LHC. We discuss the possibility of explaining the (g − 2)μ anomaly by adding more generations of N which will lead to chain decays of N and multiple leptons with distinct signals both at forward experiments and at the CMS and ATLAS detectors. Finally, we show that by adding a new light singlet scalar mixed with the neutral component of the new Higgs doublet (i.e., 2HDM+S model), the statistics of the data sample can be dramatically increased.