Exclusive charmonium production from $e^{+}{e}^{-}$ annihilation round the $Z^0$ peak

Abstract

We make a comparative and comprehensive study on the charmonium exclusive productions at the $e^{+}{e}^{-}$ collider with the collision energy either round the $Z^0$-boson mass for a super $Z$ factory or equals to 10.6 GeV for the $B$ factories as Belle and BABAR. We study the total cross sections for the charmonium production via the exclusive processes $e^{+}{e}^{-}\to {\gamma }^{\ast }/Z^0\to H_1+H_2$ and $e^{+}{e}^{-}\to {\gamma }^{\ast }/Z^0\to H_1+\gamma$, where $H_1$ and $H_2$ represent the dominant color-singlet $S$-wave and $P$-wave charmonium states respectively. Total cross sections versus the $e^{+}{e}^{-}$ collision energy $\sqrt{s}$, together with their uncertainties, are presented, which clearly show the relative importance of these channels. At the $B$ factory, the production channels via the virtual ${\gamma }^{\ast }$ propagator are dominant over the channels via the $Z^0$ propagator by about four orders. While, at the super $Z$ factory, due to the $Z^0$-boson resonance effect, the $Z^0$ boson channels shall provide sizable or even dominant contributions in comparison to the channels via the ${\gamma }^{\ast }$ propagator. Sizable exclusive charmonium events can be produced at the super $Z$ factory with high luminocity up to $10^{36}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$, especially for the channel of $e^{+}{e}^{-}\to Z^0\to H_1+\gamma$, e.g. by taking $m_c=1.50\pm 0.20$ GeV, we shall have $(5.0_{-0.6}^{+0.8})\times 10^4$ $J/\psi$, $(7.5_{-0.9}^{+1.1})\times 10^3$ ${\eta }_c$, $(6.2_{-1.9}^{+3.3})\times 10^3$ $h_c$, $(3.1_{-0.9}^{+1.7})\times 10^2$ ${\chi }_{c0}$, $(2.2_{-0.4}^{+1.0})\times 10^3$ ${\chi }_{c1}$, and $(7.7_{-2.4}^{+4.1})\times 10^2$ ${\chi }_{c2}$ events by one operation year. Thus, in addition to the $B$ factories as BABAR and Belle, such a super $Z$ factory shall provide another useful platform for studying the heavy quarkonium properties and for testing QCD theories.

Comments: 19 pages, 9 figures. References and discussions updated. To be published in Phys.Rev.D