Abstract
In this paper, we carry out the next-to-leading-order (NLO) studies on Z rightarrow Upsilon (1S)+g+g via the color-singlet (CS) b{bar{b}} state. We find the newly calculated NLO QCD corrections to this process can significantly influence its leading-order (LO) results and greatly improve the dependence on the renormalization scale. By including the considerable feeddown contributions, the branching ratio {mathcal {B}}_{Z rightarrow Upsilon (1S)+g+g} is predicted to be (0.56–0.95) times 10^{-6}, which can reach up to 19–31% of the LO predictions given by the CS dominant process Z rightarrow Upsilon (1S)+b+{bar{b}}. Moreover, Z rightarrow Upsilon (1S)+g+g also seriously affects the CS predictions on the Upsilon (1S) energy distributions, especially when z is relatively small. In summary, for the inclusive Upsilon (1S) productions in Z decay, besides Z rightarrow Upsilon (1S)+b+{bar{b}}, the gluon radiation process Z rightarrow Upsilon (1S)+g+g can provide indispensable contributions as well.
Highlights
The L3 group at LEP has released the measurement on the total decay width of Z → Υ(1S) + X [1]BZ→Υ(1S)+X < 4.4 × 10−5.The leading-order (LO) color-singlet (CS) predictions obtained by calculating the CS dominant process Z → Υ(1S) + b + bare only at the 10−6 order [2,3,4]
The package MALT@FDC that has been employed to preform the NLO QCD corrections to several heavy quarkonium related processes [19,20,23,24,25] is used to deal with Virtual, ˆ S, and HC
The smallness of αs in Z → bb[1 S0[8],3 S1[8],3 PJ[8]] + g comparing to Z → bb[3 S1[1]] + g + g, together with the potential enhancement via the NLO corrections to these CO channels, may partly compensate for the suppression caused by long distance matrix elements (LDMEs), subsequently making the CO contributions nonnegligible
Summary
The L3 group at LEP has released the measurement on the total decay width of Z → Υ(1S) + X [1]. MΥ2 EΥ2 for large z [11,16,17], so the value of z concerning the maximum d dz should be small; as a result of the b quark fragmentation, the dominant contributions of Z → Υ + b + bexist in the region of large z. From these points of view, the process Z → Υ + g + g would be crucial for Z decaying to the inclusive Υ, deserving a separate investigation.
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