Two Photon Transition Form Factor of cˉc\bar{c}c Quarkonia

The two photon transition of $\bar{c}c$ quarkonia are studied within a covariant approach based on the consistent truncation scheme of the quantum chromodynamics Dyson-Schwinger equation for the quark propagator and the Bethe--Salpeter equation for the mesons. We find the decay widths of $\eta_{c}^{} \to \gamma\gamma$ and $\chi_{c0,2}^{} \to \gamma\gamma$ in good agreement with experimental data. The obtained transition form factor of $\eta_{c}^{} \to \gamma\gamma^{\ast}$ for a wide range of space-like photon momentum transfer squared is also in agreement with the experimental findings of the BABAR experiment. As a by-product, the decay widths of $\eta_{b}^{},\chi_{b0,2}^{} \to \gamma\gamma$ and the transition form factor of $\eta_{b}^{}, \chi_{c0,b0}^{} \to\gamma\gamma^{\ast}$ are predicted, which await for experimental test

Leading-twist parton distribution amplitudes of S-wave heavy-quarkonia

The leading-twist parton distribution amplitudes (PDAs) of ground-state $^1S_0$ and $^3S_1$ $c\bar c$- and $b\bar b$-quarkonia are calculated using a symmetry-preserving continuum treatment of the meson bound-state problem which unifies the properties of these heavy-quark systems with those of light-quark bound-states, including QCD's Goldstone modes. Analysing the evolution of $^1S_0$ and $^3S_1$ PDAs with current-quark mass, $\hat m_q$, increasing away from the chiral limit, it is found that in all cases there is a value of $\hat m_q$ for which the PDA matches the asymptotic form appropriate to QCD's conformal limit and hence is insensitive to changes in renormalisation scale, $\zeta$. This mass lies just above that associated with the $s$-quark. At current-quark masses associated with heavy-quarkonia, on the other hand, the PDAs are piecewise convex-concave-convex. They are much narrower than the asymptotic distribution on a large domain of $\zeta$; but nonetheless deviate noticeably from $\varphi_{Q\bar Q}(x) = \delta(x-1/2)$, which is the result in the static-quark limit. There are also material differences between $^1S_0$ and $^3S_1$ PDAs, and between the PDAs for different vector-meson polarisations, which vanish slowly with increasing $\zeta$. An analysis of moments of the root-mean-square relative-velocity, $\langle v^{2m}\rangle$, in $^1S_0$ and $^3S_1$ systems reveals that $\langle v^4\rangle$-contributions may be needed in order to obtain a reliable estimate of matrix elements using such an expansion, especially for processes involving heavy pseudoscalar quarkonia.Comment: 6 pages, 2 figures, 3 table

Living in a changing Chinese urban landscape: The Dalian case study

Dalian is the second–most important city in the southern part of Liaoning Province in northeast China. The city can trace its history back to the Qingniwa settlement. This settlement was occupied from 1858 until 1950 in succession by the British, Japanese and Russian Empires, with each imposing its own building styles on the city. However, from 1950, when the city was finally returned to China by the Russians, who had captured it from the Japanese during the Second World War, most of the imperial buildings and sites were lost to redevelopment within the city. The most dramatic changes have taken place since 1984, when the city was declared a Special Economic Zone, and particularly during the 1990s, when Bo Xilai became the mayor and introduced parks, extensive motorways and many traffic circles. At present, having lost most of its traditional built environment, Dalian is a modern city marked by dramatic housing developments and dominated by multi-family high-rise buildings to accommodate its population of 5.72 million. In 2011, a survey was conducted among 400 inhabitants of the city to ascertain their perceptions concerning life in Dalian and the Dalian Development Zone, their living conditions and their level of satisfaction with their housing. From the survey, it was clear that the majority of the interviewees were uncertain about the variables concerning the structural quality of their housing units and the nature, quality and accessibility of the services provided. However, most of them indicated that public transport, open spaces, parks and recreational facilities were within easy reach of their housing units

Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions

The Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii-type conditions. Numerical example is given to indicate our results

Size dependence of static and dynamic magnetic properties in nanoscale square Permalloy antidot arrays

Permalloy antidot arrays with different square hole sizes (1200×1200, 800×800, and 400×400 nm2) have been fabricated by means of electron-beam lithography and lift-off techniques. The smaller square hole size results in enhanced remanence and reduced coercivity in the antidot array. Multiple resonance modes were clearly observed for the magnetic field applied normal to the array plane, and double uniform resonance modes occurred when the field deviated more than 30° from the normal to the plane. Two distinct dipolar field patterns with different orientations and magnitudes split the uniform resonance into double resonance modes. The double resonance modes show uniaxial in-plane anisotropy and the easy axes are orthogonal. The magnitude of the induced dipolar anisotropy remains almost constant with changes in the square hole size. The double resonance peaks move to low field with reduction of the square hole size