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Exclusive double $B_c$ meson production from $e^+e^-$ annihilation into two virtual photons

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 Added by Fedor Martynenko
 Publication date 2019
  fields
and research's language is English




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We calculate cross sections of a pair $B_c$ meson production on the basis of two-photon mechanism from electron-positron annihilation. We investigate the production cross sections in nonrelativistic approximation and with the account of relativistic corrections. Relativistic production amplitudes of S-wave pair pseudoscalar, vector and pseudoscalar+vector $B_c$-mesons are constructed on the basis of relativistic quark model. Numerical values of the production cross sections are obtained at different center-of-mass energies. The comparison of one-photon and two-photon annihilation contributions is presented.



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Within the framework of the perturbative QCD approach, we calculate the time-like $B_cB_c(B_c^*)$ form factors $F(Q^2)$ and $A_2(Q^2)$. We include relativistic corrections and QCD corrections, either of which can give about $20%$ correction to the leading-order contribution, but there are cancellation effects between them. We calculate the cross sections of the $e^+e^-to B_c^-B_c^+(B_c^{*+})$ processes. The cross sections are enhanced at the $Z$ pole to be $sigma^{PP}(Q=m_Z) sim 1.3times10^{-5}text{pb}$ and $sigma^{PV}(Q=m_Z) sim 2.5times10^{-5}text{pb}$, which are still too small to be detected by proposed $e^+e^-$ colliders such as the Circular Electron Positron Collider.
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The $B_c$ meson is a doubly heavy quark-antiquark bound state and carries flavors explicitly, which provides a fruitful laboratory for testing potential models and understanding the weak decay mechanisms for heavy flavors. In view of the prospects in $B_c$ physics at the hadronic colliders as Tevatron and LHC, $B_c$ physics is attracting more and more attention. It has been shown that a high luminosity $e^+e^-$ collider running around the $Z^0$-peak is also helpful for studying the properties of $B_c$ meson and has its own advantages. For the purpose, we write down an event generator for simulating $B_c$ meson production through $e^+e^-$ annihilation according to relevant publications. We name it as BEEC, in which the color-singlet $S$-wave and $P$-wave $(cbar{b})$-quarkonium states together with the color-octet $S$-wave $(cbar{b})$-quarkonium states can be generated. BEEC can also be adopted to generate the similar charmonium and bottomnium states via the semi-exclusive channels $e^{+}+e^{-}rightarrow |(Qbar{Q})[n]rangle +Q +bar{Q}$ with $Q=b$ and $c$ respectively. To increase the simulation efficiency, we simplify the amplitude as compact as possible by using the improved trace technology. BEEC is a Fortran programme written in a PYTHIA-compatible format and is written in a modularization structure, one may apply it to various situations or experimental environments conveniently by using the GNU C compiler {bf make}. A method to improve the efficiency of generating unweighted events within PYTHIA environment has been suggested. Moreover, BEEC will generate a standard Les Houches Event data file that contains useful information of the meson and its accompanying partons, which can be conveniently imported into PYTHIA to do further hadronization and decay simulation.
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