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Register a new userWhat are $Omh^2(z_1,z_2)$ and $Om(z_1,z_2)$ diagnostics telling us in light of $H(z)$ data?
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Two-point diagnostics $Om(z_i,z_j)$ and $Omh^2(z_i,z_j)$ have been introduced as an interesting tool for testing the validity of the $Lambda$CDM model. Quite recently, Sahni, Shafieloo $&$ Starobinsky (2014) combined two independent measurements of $H(z)$ from BAO data with the value of the Hubble constant $H_0$, and used the second of these diagnostics to test the $Lambda$CDM model. Their result indicated a considerable tension between observations and predictions of the $Lambda$CDM model. Since reliable data concerning expansion rates of the Universe at different redshifts $H(z)$ are crucial for the successful application of this method, we investigate both two-point diagnostics on the most comprehensive set of $N=36$ measurements of $H(z)$ coming from the BAO and differential ages (DA) of passively evolving galaxies. We discuss the uncertainties of two-point diagnostics and find that they are strongly non-Gaussian and follow the patterns deeply rooted in their very construction. Therefore we propose that non-parametric median statistics is the most appropriate way of treating this problem. Our results support the claims that $Lambda$CDM is in tension with $H(z)$ data according to the two-point diagnostics developed by Shafieloo, Sahni and Starobinsky. However, other alternatives to the $Lambda$CDM, such as wCDM or CPL models perform even worse. We also notice that there are serious systematic differences between BAO and DA methods which ought to be better understood before $H(z)$ measurements can become competitive to the other probes.
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We conjecture that $Z_c^-$(4100) found by LHCb group from a Dalitz plot analysis of $B^0to eta_c K^+pi^-$ decay is the charge conjugate of $Z_1^+$(4050) observed in $chi_{c1}pi^+$ distribution from Belle collaboration. Some interesting conclusions are inferred from this assumption. The $Z_2$(4250) would be assigned to be a $J^P = 1^+$ or $1^-$ state because of its absence in $eta_{c}pi^-$ invariant mass distribution, while $Z_1^+$(4050)/$Z_c^-$(4100) could be a $0^+$ or $1^-$ state but $2^+$ is unfavored because it would be coupled to $eta_{c}pi$ in $D$-wave. The null observation of $Z_1 Z_2$, $Z_1 Z_1$ and $Z_2 Z_2$ production in $e^+ e^-$ annihilation and $Upsilon(1S,2S)$ decay by Belle collaboration would further allocate the spin parity combination of $Z_1^+$(4050)/$Z_c^-$(4100) and $Z_2$(4250). Our deductions can be used to exclude a set of proposed models and could be further tested by future experiment, e.g. in $gamma gamma$ collisions.
We investigate the deep water abundance of Neptune using a simple 2-component (core + envelope) toy model. The free parameters of the model are the total mass of heavy elements in the planet (Z), the mass fraction of Z in the envelope (f_env), and the D/H ratio of the accreted building blocks (D/H_build ). We systematically search the allowed parameter space on a grid and constrain it using Neptunes bulk carbon abundance, D/H ratio, and interior structure models. Assuming solar C/O ratio and cometary D/H for the accreted building blocks forming the planet, we can fit all of median ~ 7%), and the rest the constraints if less than ~ 15% of Z is in the envelope (f_env is locked in a solid core. This model predicts a maximum bulk oxygen abundance in Neptune of 65 times solar value. If we assume a C/O of 0.17, corresponding to clathrate-hydrates building blocks, we predict a maximum oxygen abundance of 200 times solar value with a median value of ~ 140. Thus, both cases lead to an oxygen abundance significantly lower than the preferred value of Cavalie et al. (2017) (~ 540 times solar), inferred from model dependent deep CO observations. Such high water abundances are excluded by our simple but robust model. We attribute this discrepancy to our imperfect understanding of either the interior structure of Neptune or the chemistry of the primordial protosolar nebula.
Recently XENON1T Collaboration announced that they observed some excess in the electron recoil energy around a 2-3 keV. We show that this excess can be interpreted as exothermic scattering of excited dark matter (XDM), $XDM + e_{atomic} rightarrow DM + e_{free}$ on atomic electron through dark photon exchange. We consider DM models with local dark $U(1)$ gauge symmetry that is spontaneously broken into its $Z_2$ subgroup by Krauss-Wilczek mechanism. In order to explain the XENON1T excess with the correct DM thermal relic density within freeze-out scenario, all the particles in the dark sector should be light enough, namely $sim O(100)$ MeV for scalar DM and $sim O(1-10)$ MeV for fermion DM cases. And even lighter dark Higgs $phi$ plays an important role in the DM relic density calculation: $X X^dagger rightarrow Z phi$ for scalar DM ($X$) and $chi bar{chi} rightarrow phi phi$for fermion DM ($chi$) assuming $m_{Z} > m_chi$. Both of them are in the $p$-wave annihilation, and one can easily evade stringent bounds from Planck data on CMB on the $s$-wave annihilations, assuming other dangerous $s$-wave annihilations are kinematically forbidden.
We study Fayet-Iliopoulos (FI) terms of six-dimensional supersymmetric Abelian gauge theory compactified on a $T^2/Z_2$ orbifold. Such orbifold compactifications can lead to localized FI-terms and instability of bulk zero modes. We study 1-loop correction to FI-terms in more general geometry than the previous works. We find induced FI-terms depend on the complex structure of the compact space. We also find the complex structure of the torus can be stabilized at a specific value corresponding to a self-consistent supersymmetric minimum of the potential by such 1-loop corrections, which is applicable to the modulus stabilization.
In an earlier work it was shown that the IR singularities arising in the nonplanar one loop two point function of a noncommutative ${cal N}=2$ gauge theory can be reproduced exactly from the massless closed string exchanges. The noncommutative gauge theory is realised on a fractional $D_3$ brane localised at the fixed point of the $C^2/Z_2$ orbifold. In this paper we identify the contributions from each of the closed string modes. The sum of these adds upto the nonplanar two-point function.
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