Production of double P-wave heavy quarkonia at a super Z factory - Qi-Li Liao; Yan Yu (European Physical Journal C: Particles and Fields)
Abstract The production of double P-wave heavy quarkonia is studied systematically within the framework of non-relativistic quantum chromodynamics at the exclusive process of the electron–positron collision annihilation at the CM energy $$\sqrt{s}=91.1876$$ s = 91.1876 GeV of the $$Z^0$$ Z 0 pole, i.e., double P-wave charmonia, double P-wave $$B_c$$ B c mesons, and double P-wave bottomonia in $$e^+e^-\rightarrow \gamma ^*/Z^0 \rightarrow |(Q\bar{Q'})[n]\rangle +|(Q'\bar{Q})[n^\prime ]\rangle $$ e + e - → γ ∗ / Z 0 → | ( Q Q ′ ¯ ) [ n ] ⟩ + | ( Q ′ Q ¯ ) [ n ′ ] ⟩ ( $$Q/Q'=c$$ Q / Q ′ = c - or b-quarks) at a future super Z factory, where [n] or $$[n^\prime ]$$ [ n ′ ] stands for the color-singlet $$[^1P_1]$$ [ 1 P 1 ] and $$[^3P_J]$$ [ 3 P J ] ( $$J=0,1,2$$ J = 0 , 1 , 2 ) Fock states. As an improved trace technology is useful for calculating the complicated double P-wave channels, the analytical result can be obtained at the amplitude level. According to our study, the generation rates for the double P-wave heavy quarkonia at the future super Z factory are considerable. The values obtained for the total cross sections of the double P-wave charmonium for $$\sigma {(|(c\bar{c})[1]\rangle +|(c\bar{c})[1]\rangle )}=4.191^{+0.489}_{-0.498}\times 10^{-3}~fb$$ σ ( | ( c c ¯ ) [ 1 ] ⟩ + | ( c c ¯ ) [ 1 ] ⟩ ) = 4 . 191 - 0.498 + 0.489 × 10 - 3 f b , the total cross sections of the double P-wave $$B_c$$ B c mesons for $$\sigma {(|(c\bar{b})[1]\rangle +|(b\bar{c})[1]\rangle )}=0.2045^{+0.0084}_{-0.0080}~fb$$ σ ( | ( c b ¯ ) [ 1 ] ⟩ + | ( b c ¯ ) [ 1 ] ⟩ ) = 0 . 2045 - 0.0080 + 0.0084 f b , and the total cross sections of the double P-wave bottomonium for $$\sigma {(|(b\bar{b})[1]\rangle +|(b\bar{b})[1]\rangle )}=5.244^{+0.134}_{-0.136}\times 10^{-3}~fb$$ σ ( | ( b b ¯ ) [ 1 ] ⟩ + | ( b b ¯ ) [ 1 ] ⟩ ) = 5 . 244 - 0.136 + 0.134 × 10 - 3 f b . The main uncertainties come from the mass of heavy quarkonia and the corresponding first-derivative radial wave functions at the origin under the Buchmüller–Tye (BT) potential. The number of events in the production of double P-wave charmonium, $$B_c$$ B c -meson, and bottomonium states via $$e^-e^+\rightarrow \gamma ^*/Z^0 \rightarrow |(Q\bar{Q}')[n]\rangle + |(Q'\bar{Q})[n^\prime ]\rangle $$ e - e + → γ ∗ / Z 0 → | ( Q Q ¯ ′ ) [ n ] ⟩ + | ( Q ′ Q ¯ ) [ n ′ ] ⟩ at the integrated luminosity $$\mathcal{L}\approx 10^{34}cm^{-2}s^{-1}$$ L ≈ 10 34 c m - 2 s - 1 at the super Z factory is almost unobservable.