Perturbations of Single-field Inflation in Modified Gravity Theory

In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form $f(R)$. Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f.) system, the (curvature) perturbations are not equivalent in two frames, so in despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the "real" ones as we always do for pure $f(R)$ theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there are large parameter space in these models, we show that it is easy to fit the data very well.Comment: 9 pages, 1 figure, substantially improved, matching with the published versio

Analysis of the tensor-tensor type scalar tetraquark states with QCD sum rules

In this article, we study the ground states and the first radial excited states of the tensor-tensor type scalar hidden-charm tetraquark states with the QCD sum rules. We separate the ground state contributions from the first radial excited state contributions unambiguously, and obtain the QCD sum rules for the ground states and the first radial excited states, respectively. Then we search for the Borel parameters and continuum threshold parameters according to four criteria and obtain the masses of the tensor-tensor type scalar hidden-charm tetraquark states, which can be confronted to the experimental data in the future.Comment: 12 pages, 4 figures. arXiv admin note: text overlap with arXiv:1607.0484

The decay width of the Zc(3900)Z_c(3900) as an axialvector tetraquark state in solid quark-hadron duality

In this article, we tentatively assign the $Z_c^\pm(3900)$ to be the diquark-antidiquark type axialvector tetraquark state, study the hadronic coupling constants $G_{Z_cJ/\psi\pi}$, $G_{Z_c\eta_c\rho}$, $G_{Z_cD \bar{D}^{*}}$ with the QCD sum rules in details. We take into account both the connected and disconnected Feynman diagrams in carrying out the operator product expansion, as the connected Feynman diagrams alone cannot do the work. Special attentions are paid to matching the hadron side of the correlation functions with the QCD side of the correlation functions to obtain solid duality, the routine can be applied to study other hadronic couplings directly. We study the two-body strong decays $Z_c^+(3900)\to J/\psi\pi^+$, $\eta_c\rho^+$, $D^+ \bar{D}^{*0}$, $\bar{D}^0 D^{*+}$ and obtain the total width of the $Z_c^\pm(3900)$. The numerical results support assigning the $Z_c^\pm(3900)$ to be the diquark-antidiquark type axialvector tetraquark state, and assigning the $Z_c^\pm(3885)$ to be the meson-meson type axialvector molecular state.Comment: 16 pages, 3 figure