Analysis of the 12±{\frac{1}{2}}^{\pm} pentaquark states in the diquark model with QCD sum rules

In this article, we present the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type pentaquark configurations in the diquark model, and study the masses and pole residues of the $J^P={\frac{1}{2}}^\pm$ hidden-charmed pentaquark states in details with the QCD sum rules by extending our previous work on the $J^P={\frac{3}{2}}^-$ and ${\frac{5}{2}}^{+}$ hidden-charmed pentaquark states. We calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion by constructing both the scalar-diquark-scalar-diquark-antiquark type and scalar-diquark-axialvector-diquark-antiquark type interpolating currents. The present predictions of the masses can be confronted to the LHCb experimental data in the future.Comment: 20 pages, 17 figures. arXiv admin note: substantial text overlap with arXiv:1508.0146

Possible assignments of the X(3872)X(3872), Zc(3900)Z_c(3900) and Zb(10610)Z_b(10610) as axial-vector molecular states

In this article, we construct both the color singlet-singlet type and octet-octet type currents to interpolate the $X(3872)$, $Z_c(3900)$, $Z_b(10610)$, and calculate the vacuum condensates up to dimension-10 in the operator product expansion. Then we study the axial-vector hidden charmed and hidden bottom molecular states with the QCD sum rules, explore the energy scale dependence of the QCD sum rules for the heavy molecular states in details, and use the formula $\mu=\sqrt{M^2_{X/Y/Z}-(2{\mathbb{M}}_Q)^2}$ with the effective masses ${\mathbb{M}}_Q$ to determine the energy scales. The numerical results support assigning the $X(3872)$, $Z_c(3900)$, $Z_b(10610)$ as the color singlet-singlet type molecular states with $J^{PC}=1^{++}$, $1^{+-}$, $1^{+-}$, respectively, more theoretical and experimental works are still needed to distinguish the molecule and tetraquark assignments; while there are no candidates for the color octet-octet type molecular states.Comment: 20 pages, 20 figures, add detailed discussions. arXiv admin note: substantial text overlap with arXiv:1310.2422, arXiv:1312.2652, arXiv:1312.1537, arXiv:1311.104

Search for a heavy dark photon at future e+e−e^+e^- colliders

A coupling of a dark photon $A'$ from a $U(1)_{A'}$ with the standard model (SM) particles can be generated through kinetic mixing represented by a parameter $\epsilon$. A non-zero $\epsilon$ also induces a mixing between $A'$ and $Z$ if dark photon mass $m_{A'}$ is not zero. This mixing can be large when $m_{A'}$ is close to $m_Z$ even if the parameter $\epsilon$ is small. Many efforts have been made to constrain the parameter $\epsilon$ for a low dark photon mass $m_{A'}$ compared with the $Z$ boson mass $m_Z$. We study the search for dark photon in $e^+e^- \to \gamma A' \to \gamma \mu^+ \mu^-$ for a dark photon mass $m_{A'}$ as large as kinematically allowed at future $e^+e^-$ colliders. For large $m_{A'}$, care should be taken to properly treat possible large mixing between $A'$ and $Z$. We obtain sensitivities to the parameter $\epsilon$ for a wide range of dark photon mass at planed $e^+\;e^-$ colliders, such as Circular Electron Positron Collider (CEPC), International Linear Collider (ILC) and Future Circular Collider (FCC-ee). For the dark photon mass $20~\text{GeV}\lesssim m_{A^{\prime}}\lesssim 330~\text{GeV}$, the $2\sigma$ exclusion limits on the mixing parameter are $\epsilon\lesssim 10^{-3}-10^{-2}$. The CEPC with $\sqrt{s}=240~\text{GeV}$ and FCC-ee with $\sqrt{s}=160~\text{GeV}$ are more sensitive than the constraint from current LHCb measurement once the dark photon mass $m_{A^{\prime}}\gtrsim 50~\text{GeV}$. For $m_{A^{\prime}}\gtrsim 220~\text{GeV}$, the sensitivity at the FCC-ee with $\sqrt{s}=350~\text{GeV}$ and $1.5~\text{ab}^{-1}$ is better than that at the 13~TeV LHC with $300~\text{fb}^{-1}$, while the sensitivity at the CEPC with $\sqrt{s}=240~\text{GeV}$ and $5~\text{ab}^{-1}$ can be even better than that at 13~TeV LHC with $3~\text{ab}^{-1}$ for $m_{A^{\prime}}\gtrsim 180~\text{GeV}$.Comment: 21 pages, 5 figures, 2 table

Pion Electromagnetic Form Factor in the KTK_T Factorization Formulae

Based on the light-cone (LC) framework and the $k_T$ factorization formalism, the transverse momentum effects and the different helicity components' contributions to the pion form factor $F_{\pi}(Q^2)$ are recalculated. In particular, the contribution to the pion form factor from the higher helicity components ($\lambda_1+\lambda_2=\pm 1$), which come from the spin-space Wigner rotation, are analyzed in the soft and hard energy regions respectively. Our results show that the right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the $k_T$ dependence in the hard amplitude, and that the $k_T$ dependence in LC wavefunction affects the hard and soft contributions substantially. A model for the twist-3 wavefunction $\psi_p(x,\mathbf{k_\perp})$ of the pion has been constructed based on the moment calculation by applying the QCD sum rules, whose distribution amplitude has a better end-point behavior than that of the asymptotic one. With this model wavefunction, the twist-3 contributions including both the usual helicity components ($\lambda_1+\lambda_2=0$) and the higher helicity components ($\lambda_1+\lambda_2=\pm 1$) to the pion form factor have been studied within the modified pQCD approach. Our results show that the twist-3 contribution drops fast and it becomes less than the twist-2 contribution at $Q^2\sim 10GeV^2$. The higher helicity components in the twist-3 wavefunction will give an extra suppression to the pion form factor. When all the power contributions, which include higher order in $\alpha_s$, higher helicities, higher twists in DA and etc., have been taken into account, it is expected that the hard contributions will fit the present experimental data well at the energy region where pQCD is applicable.Comment: 4 pages, 2 figures, Prepared for International Conference on QCD and Hadronic Physics, Beijing, China, 16-20 June 200