The Bc→ψ(2S)πB_c\rightarrow \psi(2S)\pi, ηc(2S)π\eta_c(2S)\pi decays in the perturbative QCD approach

Nonleptonic two body $B_c$ decays including radially excited $\psi(2S)$ or $\eta_c(2S)$ mesons in the final state are studied using the perturbative QCD approach based on $k_T$ factorization. The charmonium distribution amplitudes are extracted from the $n = 2, l = 0$ Schr$\ddot{o}$dinger states for the harmonic oscillator potential. Utilizing these distribution amplitudes, we calculate the numerical results of the $B_c\rightarrow \psi(2S),\eta_c(2S)$ transition form factors and branching fractions of $B_c\rightarrow \psi(2S)\pi, \eta_c(2S)\pi$ decays. The ratio between two decay modes $B_c\rightarrow \psi(2S)\pi$ and $B_c\rightarrow J/\psi\pi$ is compatible with the experimental data within uncertainties, which indicate that the harmonic oscillator wave functions for $\psi(2S)$ and $\eta_c(2S)$ work well. It is found that the branching fraction of $B_c\rightarrow \eta_c(2S)\pi$, which is dominated by the twist-3 charmonium distribution amplitude, can reach the order of $10^{-3}$. We hope it can be measured soon in the LHCb experiment.Comment: 9 pages, 3 figures,3 Table

Collective unitary evolution with linear optics by Cartan decomposition

Unitary operation is an essential step for quantum information processing. We first propose an iterative procedure for decomposing a general unitary operation without resorting to controlled-NOT gate and single-qubit rotation library. Based on the results of decomposition, we design two compact architectures to deterministically implement arbitrary two-qubit polarization-spatial and spatial-polarization collective unitary operations, respectively. The involved linear optical elements are reduced from 25 to 20 and 21 to 20, respectively. Moreover, the parameterized quantum computation can be flexibly manipulated by wave plates and phase shifters. As an application, we construct the specific quantum circuits to realize two-dimensional quantum walk and quantum Fourier transformation. Our schemes are simple and feasible with the current technology.Comment: 9 figure