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Using the fσ8(z) redshift space distortion (RSD) data, the $\sigma _8^0\!-\!\Omega _\mathrm{ m}^0$ tension is studied utilizing a parametrization of growth rate f(z) = Ωm(z)γ. Here, f(z) is derived from the expansion history H(z) which is reconstructed from the observational Hubble data applying the Gaussian process method. It is found that different priors of H0 have great influences on the evolution curve of H(z) and the constraint of $\sigma _8^0\!-\!\Omega _\mathrm{ m}^0$. When using a larger H0 prior, the low redshifts H(z) deviate significantly from that of the ΛCDM model, which indicates that a dark energy model different from the cosmological constant can help to relax the H0 tension problem. The tension between our best-fitting values of $\sigma _8^0\!-\!\Omega _\mathrm{ m}^0$ and that of the Planck 2018 ΛCDM (PLA) will disappear (less than 1σ) when taking a prior for H0 obtained from PLA. Moreover, the tension exceeds 2σ level when applying the prior H0 = 73.52 ± 1.62 km s−1 Mpc−1 resulted from the Hubble Space Telescope photometry. By comparing the $S_8\!-\!\Omega _\mathrm{ m}^0$ planes of our method with the results from KV450+DES-Y1, we find that using our method and applying the RSD data may be helpful to break the parameter degeneracies.

In practice the asymmetry, which is defined based on the angular distribution of the final states in scattering or decay processes, can be utilized to scrutinize underlying dynamics in and/or beyond the standard model (BSM). As one of the possible BSM physics which might be discovered early at the LHC, extra neutral gauge bosons Z ′ s are theoretical well motivated. Once Z ′ s are discovered at the LHC, it is crucial to discriminate different Z ′ s in various BSM. In principle such task can be accomplished by measuring the angular distribution of the final states which are produced via Z ′ -mediated processes. In the real data analysis, asymmetry is always adopted. In literature several asymmetries have been proposed at the LHC. Based on these works, we stepped further on to study how to optimize the asymmetries in the left-right model and the sequential standard model, as the examples of BSM. In this paper, we examined four kinds of asymmetries, namely rapidity-dependent forward-backward asymmetry, one-side forward-backward asymmetry, central charge asymmetry and edge charge asymmetry (see text for details), with ℓ + ℓ − (ℓ = e, µ), bb and tt as the final states. In the calculations with bb and tt final states, the QCD-induced higher order contributions to the asymmetric cross section were also included. For each kind of final states, we estimated the four kinds of asymmetries and especially the optimal cut usually associated with the definition of the asymmetry. Our numerical results indicated that the capacity to discriminate Z ′ models can be improved by imposing the optimal cuts.

In this brief report, we propose a new definition of charge asymmetry in top pair production at the LHC, namely the edge charge asymmetry (ECA). ECA utilizes the information of drifting direction only for single top (or anti-top) with hadronically decay. Therefore ECA can be free from the uncertainty arising from the missing neutrino in the tt event reconstruction. Moreover rapidity Y of top (or anti-top) is required to be greater than a critical value Y C in order to suppress the symmetric tt events mainly due to the gluongluon fusion process. In this paper ECA is calculated up to next-to-leading order QCD in the standard model and the choice of the optimal Y C is investigated. *