English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this work, the non-relativistic asymptotic behavior of the transition$q\overline{q}\rightarrow2g\rightarrow q\overline{q}$ in the $^1S_0$ channel isdiscussed. Different with the usual calculation which expands the physicalamplitude around the quark anti-quark threshold, we take the quark anti-quarkpairs as off shell and only expand the expression on the three-dimensionalmomenta of the quarks and anti-quarks. We calculate the results to order 6. Theimagine part of the results after applying the on shell conditions canreproduce the non-relativistic QCD (NRQCD) results in leading order of$\alpha_s$. The real part of the results can be used to estimate the mass shiftof the $^1S_0$ heavy quark anti-quark system due to the $2g$ annihilationeffect. The results can also be used to estimate the energy shifts of thepositronium system due to the two-photon annihilation.

Correction to the energy spectrum of $^1S_0$ heavy quarkonia due to two-gluon annihilation effect