The NLO contributions to the scalar pion form factors and the O(αs2){\cal O}(\alpha_s^2) annihilation corrections to the B→ππB\to \pi\pi decays

In this paper, by employing the $k_{T}$ factorization theorem, we made the first calculation for the space-like scalar pion form factor $Q^2 F(Q^2)$ at the leading order (LO) and the next-to-leading order (NLO) level, and then found the time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ by analytic continuation from the space-like one. From the analytical evaluations and the numerical results, we found the following points: (a) the NLO correction to the space-like scalar pion form factor has an opposite sign with the LO one but is very small in magnitude, can produce at most $10\%$ decrease to LO result in the considered $Q^2$ region; (b) the NLO time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ describes the ${\cal O}(\alpha_s^2)$ contribution to the factorizable annihilation diagrams of the considered $B \to \pi\pi$ decays, i.e. the NLO annihilation correction; (c) the NLO part of the form factor $F'^{(1)}_{\rm a,I}$ is very small in size, and is almost independent with the variation of cutoff scale $\mu_0$, but this form factor has a large strong phase around $-55^\circ$ and may play an important role in producing large CP violation for $B\to \pi\pi$ decays; and (d) for $B^0 \to \pi^+\pi^-$ and $\pi^0\pi^0$ decays, the newly known NLO annihilation correction can produce only a very small enhancement to their branching ratios, less than $3\%$ in magnitude, and therefore we could not interpret the well-known $\pi\pi$-puzzle by the inclusion of this NLO correction to the factorizable annihilation diagrams.Comment: 26 pages, 12 figures, 1 Table; Minor correction

Establishment and simulation of dynamic model of backfilling hydraulic support with six pillars

A backfilling hydraulic support with six pillars used for working face roof support and goaf backfilling in coal mine is designed, and the structure and working principle of the backfilling hydraulic support are described. In order to improve the working stability of backfilling hydraulic support, the differential equations of motion and the state space model of backfilling hydraulic support are established based on Lagrange method and space coordinate system. According to the support structure and related parameters, the differential equation of motion of the system is solved by MATLAB. The influence law of disturbance frequency and amplitude on the top beam vertical vibration, roll and pitch vibration is obtained. The results show that the vertical vibration and roll vibration of the top beam are more severe in the low frequency range. And the degree of vibration gradually decreases as the disturbance frequency increases. As the disturbance amplitude increases, the vibration of the top beam is more severe. The vibration of the backfilling hydraulic support and the deformation distribution nephogram of the top beam are obtained by the finite element analysis, the validity of the dynamic model is verified by finite element simulation. The results provide the basis for the optimization design and the stability evaluation of backfilling hydraulic support

Systematic investigation of the rotational bands in nuclei with Z≈100Z \approx 100 using a particle-number conserving method based on a cranked shell model

The rotational bands in nuclei with $Z \approx 100$ are investigated systematically by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($\kappa$ and $\mu$) and deformation parameters ($\varepsilon_2$ and $\varepsilon_4$) are proposed. The experimental kinematic moments of inertia for the rotational bands in even-even, odd-$A$ and odd-odd nuclei, and the bandhead energies of the 1-quasiparticle bands in odd-$A$ nuclei, are reproduced quite well by the PNC-CSM calculations. By analyzing the $\omega$-dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals in each major shell to the angular momentum alignment, the upbending mechanism in this region is understood clearly.Comment: 21 pages, 24 figures, extended version of arXiv: 1101.3607 (Phys. Rev. C83, 011304R); added refs.; added Fig. 4 and discussions; Phys. Rev. C, in pres

Nuclear superfluidity for antimagnetic rotation in 105^{105}Cd and 106^{106}Cd

The effect of nuclear superfluidity on antimagnetic rotation bands in $^{105}$Cd and $^{106}$Cd are investigated by the cranked shell model with the pairing correlations and the blocking effects treated by a particle-number conserving method. The experimental moments of inertia and the reduced $B(E2)$ transition values are excellently reproduced. The nuclear superfluidity is essential to reproduce the experimental moments of inertia. The two-shears-like mechanism for the antimagnetic rotation is investigated by examining the shears angle, i.e., the closing of the two proton hole angular momenta, and its sensitive dependence on the nuclear superfluidity is revealed.Comment: 14 pages, 4 figure

Rotational properties of the superheavy nucleus 256Rf and its neighboring even-even nuclei in particle-number conserving cranked shell model

The ground state band was recently observed in the superheavy nucleus 256Rf. We study the rotational properties of 256Rf and its neighboring even-even nuclei by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method in which the blocking effects are taken into account exactly. The kinematic and dynamic moments of inertia of the ground state bands in these nuclei are well reproduced by the theory. The spin of the lowest observed state in 256Rf is determined by comparing the experimental kinematic moments of inertia with the PNC-CSM calculations and agrees with previous spin assignment. The effects of the high order deformation varepsilon6 on the angular momentum alignments and dynamic moments of inertia in these nuclei are discussed.Comment: 7 pages, 6 figures; References and discussion about the cranking Nilsson model added, Fig. 3 modified and Figs. 5 and 6 added; Phys. Rev. C, in pres

Rotation and alignment of high-jj orbitals in transfermium nuclei

The structure of nuclei with $Z\sim100$ is investigated systematically by the Cranked Shell Model (CSM) with pairing correlations treated by a Particle-Number Conserving (PNC) method. In the PNC method, the particle number is conserved and the Pauli blocking effects are taken into account exactly. By fitting the experimental single-particle spectra in these nuclei, a new set of Nilsson parameters ($\kappa$ and $\mu$) is proposed. The experimental kinematic moments of inertia and the band-head energies are reproduced quite well by the PNC-CSM calculations. The band crossing, the effects of high-$j$ intruder orbitals and deformation are discussed in detail.Comment: To appear in the Proceedings of the International Nuclear Physics Conference (INPC2013), June 2-7, 2013, Florence, Ital