Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors

By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like $\gamma^*\gamma\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow \gamma+ Q\bar{Q}$,~and~$H/Z^0\rightarrow \gamma+ Q\bar{Q}$, heavy quarkonium exclusive decays, and also the CP-even heavy quarkonium inclusive production and decays.Comment: 23 pages, 3 figures, more discussions and references adde

Heating and cooling of coronal loops observed by SDO

Context: One of the most prominent processes suggested to heat the corona to well above 10^6 K builds on nanoflares, short bursts of energy dissipation. Aims: We compare observations to model predictions to test the validity of the nanoflare process. Methods: Using extreme UV data from AIA/SDO and HMI/SDO line-of-sight magnetograms we study the spatial and temporal evolution of a set of loops in active region AR 11850. Results: We find a transient brightening of loops in emission from Fe xviii forming at about 7.2 MK while at the same time these loops dim in emission from lower temperatures. This points to a fast heating of the loop that goes along with evaporation of material that we observe as apparent upward motions in the image sequence. After this initial phases lasting for some 10 min, the loops brighten in a sequence of AIA channels showing cooler and cooler plasma, indicating the cooling of the loops over a time scale of about one hour. A comparison to the predictions from a 1D loop model shows that this observation supports the nanoflare process in (almost) all aspects. In addition, our observations show that the loops get broader while getting brighter, which cannot be understood in a 1D model.Comment: 9 pages, 7 figures, accepted by A&

Annihilation Rates of Heavy 1−−1^{--} S-wave Quarkonia in Salpeter Method

The annihilation rates of vector $1^{--}$ charmonium and bottomonium $^3S_1$ states $V \rightarrow e^+e^-$ and $V\rightarrow 3\gamma$, $V \rightarrow \gamma gg$ and $V \rightarrow 3g$ are estimated in the relativistic Salpeter method. We obtained $\Gamma(J/\psi\rightarrow 3\gamma)=6.8\times 10^{-4}$ keV, $\Gamma(\psi(2S)\rightarrow 3\gamma)=2.5\times 10^{-4}$ keV, $\Gamma(\psi(3S)\rightarrow 3\gamma)=1.7\times 10^{-4}$ keV, $\Gamma(\Upsilon(1S)\rightarrow 3\gamma)=1.5\times 10^{-5}$ keV, $\Gamma(\Upsilon(2S)\rightarrow 3\gamma)=5.7\times 10^{-6}$ keV, $\Gamma(\Upsilon(3S)\rightarrow 3\gamma)=3.5\times 10^{-6}$ keV and $\Gamma(\Upsilon(4S)\rightarrow 3\gamma)=2.6\times 10^{-6}$ keV. In our calculations, special attention is paid to the relativistic correction, which is important and can not be ignored for excited $2S$, $3S$ and higher excited states.Comment: 10 pages,2 figures, 5 table