Heavy quarkonium production at the LHC through W boson decays

The production of the heavy (c (c) over bar)-quarkonium, (c (b) over bar)-quarkonium, and (b (b) over bar)-quarkonium states [(Q (Q) over bar') quarkonium for short], via the W+ semi-inclusive decays, has been systematically studied within the framework of the nonrelativistic QCD. In addition to the two color-singlet S-wave states, we also discuss the production of the four color-singlet P-wave states vertical bar(Q (Q) over bar') (P-1(1))(1)> and vertical bar(Q (Q) over bar') (P-3(1))(1)> [with J = (0, 1, 2)] together with the two color-octet components vertical bar(Q (Q) over bar') (S-1(0))(8)> and vertical bar(Q (Q) over bar') (S-3(1))(8)>. Improved trace technology is adopted to derive the simplified analytic expressions at the amplitude level, which shall be useful for dealing with the following cascade decay channels. At the LHC with the luminosity L-proportional to 10(34) cm(-2) s(-1) and the center-of-mass energy root S = 14 TeV, sizable heavy-quarkonium events can be produced through the W+ boson decays; i.e., 2.57 x 10(6) eta(c), 2.65 x 10(6) J/Psi, and 2.40 x 10(6) P-wave charmonium events per year can be obtained, and 1.01 x 10(5) B-c, 9.11 x 10(4) B-c*, and 3.16 x 10(4) P-wave (c (b) over bar -quarkonium events per year can be obtained. Main theoretical uncertainties have also been discussed. By adding the uncertainties caused by the quark masses in quadrature, we obtain Gamma(W+ ->) ((c (c) over bar)) (+ c (s) over bar) = 524.8(-258.4)(+396.3) KeV, Gamma(W+ ->) ((c (b) over bar)) (+) (b (s) over bar) = 13.5(-3.29)(+4.73) KeV, Gamma(W+ ->) ((c (b) over bar)) (+ c (c) over bar) = 1.74(-0.73)(+1.98) KeV, and Gamma(W+ ->) ((b (b) over bar)) (+) (c (b) over bar) = 38.6(-9.69)(+13.4) eV.