Gravitational microlensing in Verlinde's emergent gravity

We propose gravitational microlensing as a way of testing the emergent gravity theory recently proposed by Eric Verlinde~\cite{Verlinde:2016toy}. We consider two limiting cases: the dark mass of maximally anisotropic pressures (Case I) and of isotropic pressures (Case II). Our analysis of perihelion advancement of a planet shows that only Case I yields a viable theory. In this case the metric outside a star of mass $M_*$ can be modeled by that of a point-like global monopole whose mass is $M_*$ and a deficit angle $\Delta = \sqrt{(2GH_0M_*)/(3c^3)}$, where $H_0$ is the Hubble rate and $G$ the Newton constant. This deficit angle can be used to test the theory since light exhibits additional bending around stars given by, $\alpha_D\approx -\pi\Delta/2$. This angle is independent on the distance from the star and it affects equally light and massive particles. The effect is too small to be measurable today, but should be within reach of the next generation of high resolution telescopes. Finally we note that the advancement of periastron of a planet orbiting around a star or black hole, which equals $\pi\Delta$ per period, can be also used to test the theory.Comment: 19 pages, 2 figure

Pion-nucleon Sigma Term in the Global Color Model of QCD

We study the pion-nucleon sigma term in vacuum and in nuclear matter in the framework of global color model of QCD. With the effective gluon propagator being taken as the $\delta$-function in momentum space of Munczek-Nomirovsky model, we estimate that the sigma term at chiral limit in the vacuum is 9/2 times the current quark mass and it decreases with the nuclear matter density. With the presently obtained in-medium pion-nucleon sigma term, we study the in-medium chiral quark condensate and obtain a reasonable variation behavior against the nuclear matter density.Comment: 17 pages, 3 figure

The primordial black hole from running curvaton

In light of our previous work \cite{Liu:2019xhn}, we investigate the possibility of the formation of a primordial black-hole during preheating period, in which we have implemented the instability of the Mathieu equation. For generating sufficient enough enhanced power spectrum, we choose some proper parameters belonging to the narrow resonance. To characterize the full power spectrum, the enhanced part of the power spectrum is depicted by the $\delta$ function at some specific scales, which is highly relevant to the mass of the inflaton due to the explicit coupling between the curvaton and inflaton. After the inflationary period, the effective mass of inflaton is determined by its derivative with potential, thus the mass of inflaton can vary from the initial value satisfying with the COBE normalization up to the vanishing. Thanks to the huge choices for this mass parameter, we can simulate the value of abundance of primordial black holes nearly covering all of the mass ranges, in which we have given three special cases. One case could account for the dark matter in some sense since the abundance of a primordial black hole is about $75\%$. At late times, the relic of exponential potential could be approximated to a constant of the order of cosmological constant dubbed as a role of dark energy. Thus, our model could unify dark energy and dark matter from the perspective of phenomenology. Finally, it sheds new light on exploring Higgs physics.Comment: 23 pages 4 figures, discussion significantly improved, some errors are change

Inflation in an effective gravitational model & asymptotic safety

We consider an inflationary model motivated by quantum effects of gravitational and matter fields near the Planck scale. Our Lagrangian is a re-summed version of the effective Lagrangian recently obtained by Demmel, Saueressig and Zanusso~\cite{Demmel:2015oqa} in the context of gravity as an asymptotically safe theory. It represents a refined Starobinsky model, ${\cal L}_{\rm eff}=M_{\rm P}^2 R/2 + (a/2)R^2/[1+b\ln(R/\mu^2)]$, where $R$ is the Ricci scalar, $a$ and $b$ are constants and $\mu$ is an energy scale. By implementing the COBE normalisation and the Planck constraint on the scalar spectrum, we show that increasing $b$ leads to an increased value of both the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$. Requiring $n_s$ to be consistent with the Planck collaboration upper limit, we find that $r$ can be as large as $r\simeq 0.01$, the value possibly measurable by Stage IV CMB ground experiments and certainly from future dedicated space missions. The predicted running of the scalar spectral index $\alpha=d n_s/d\ln(k)$ is still of the order $-5\times 10^{-4}$ (as in the Starobinsky model), about one order of magnitude smaller than the current observational bound.Comment: 29 pages, 6 figure

Charm-strange baryon strong decays in a chiral quark model

The strong decays of charm-strange baryons up to N=2 shell are studied in a chiral quark model. The theoretical predictions for the well determined charm-strange baryons, $\Xi_c^*(2645)$, $\Xi_c(2790)$ and $\Xi_c(2815)$, are in good agreement with the experimental data. This model is also extended to analyze the strong decays of the other newly observed charm-strange baryons $\Xi_c(2930)$, $\Xi_c(2980)$, $\Xi_c(3055)$, $\Xi_c(3080)$ and $\Xi_c(3123)$. Our predictions are given as follows. (i) $\Xi_c(2930)$ might be the first $P$-wave excitation of $\Xi_c'$ with $J^P=1/2^-$, favors the $|\Xi_c'\ ^2P_\lambda 1/2^->$or$|\Xi_c'\ ^4P_\lambda 1/2^->$state. (ii)$\Xi_c(2980)$might correspond to two overlapping$P$-wave states$|\Xi_c'\ ^2P_\rho 1/2^->$and$|\Xi_c'\ ^2P_\rho 3/2^->$, respectively. The$\Xi_c(2980)$observed in the$\Lambda_c^+\bar{K}\pi$final state is most likely to be the$|\Xi_c'\ ^2P_\rho 1/2^->$state, while the narrower resonance with a mass$m\simeq 2.97$GeV observed in the$\Xi_c^*(2645)\pi$channel favors to be assigned to the$|\Xi_c'\ ^2P_\rho 3/2^->$state. (iii)$\Xi_c(3080)$favors to be classified as the$|\Xi_c\ S_{\rho\rho} 1/2^+>$state, i.e., the first radial excitation (2S) of$\Xi_c$. (iv)$\Xi_c(3055)$is most likely to be the first$D$-wave excitation of$\Xi_c$with$J^P=3/2^+$, favors the$|\Xi_c\ ^2D_{\lambda\lambda} 3/2^+>$state. (v)$\Xi_c(3123)$might be assigned to the$|\Xi_c'\ ^4D_{\lambda\lambda} 3/2^+>$,$|\Xi_c'\ ^4D_{\lambda\lambda} 5/2^+>$, or$|\Xi_c\ ^2D_{\rho\rho} 5/2^+>$state. As a by-product, we calculate the strong decays of the bottom baryons$\Sigma_b^{\pm}$,$\Sigma_b^{*\pm}$and$\Xi_b^*$, which are in good agreement with the recent observations as well.Comment: 15 pages, 9 figure