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Induced by three gluons symmetry, Mandelstam variables s, t, u symmetric expressions are widely involved in collider physics, especially in heavy quarkonium physics. In this work we study the general form of s, t, u symmetric polynomials, and find that they can be expressed as polynomials where the symmetry is manifest. The general form is then used to simplify expressions which asymptotically reduces the length of original expression to one-sixth. Based on the general form, we reproduce the exact differential cross section of J/? hadron production at leading order in ν2 up to four unknown constant numbers by simple analysis. Furthermore, we prove that differential cross section at higher order in ν2 is proportional to that at leading order. This proof explains the proportion relation at next-to-leading order in ν2 found in previous work and generalizes it to all order. [ABSTRACT FROM AUTHOR]

We analytically calculate the cross sections of double charmonium production in e+e- → J/ψ(ψ(2S))χcJ (J = 0, 1, 2) at next-to-leading order (NLO) in αs in nonrelativistic QCD, and confirm factorization of these processes. In contrast to χc0 production, for which the NLO correction is large and positive, the NLO corrections for χc1,2 production can be negative, resulting in decreased K factors of 0.91 and 0.78 for J = 1 and 2, respectively, when μ = 2mc. Consequently, the NLO QCD corrections markedly enlarge the difference between cross sections of χc0 and χc1,2. This may explain why e+e- → J/ψ(ψ(2S))χc0 but not e+e- → J/ψ(ψ(2S))χc1,2 is observed experimentally. Moreover, for J/ψ(ψ(2S))χc1,2, the NLO QCD corrections substantially reduce the μ dependence and lead to predictions with small theoretical uncertainties. [ABSTRACT FROM AUTHOR]

We study O(αsv2) corrections to decays of 1S0 heavy quarkonium into light hadrons and two photons within the framework of nonrelativistic QCD and find these O(αsv2) corrections to have significant contributions especially for the decay into light hadrons. With these new results, experimental measurements of the hadronic width and the γγ width of ηc can be described more consistently. By fitting experimental data, we find the long-distance matrix elements of ηc to be ∣Rηc(0)∣2=0.834-0.197+0.281??GeV3 and «v2»ηc=0.232-0.098+0.121. Moreover, ηc(2S) is also discussed and the γγ decay width is predicted to be 3.34-2.10+2.06??KeV. [ABSTRACT FROM AUTHOR]

The widely used nonrelativistic QCD (NRQCD) factorization theory now encounters some notable difficulties in describing quarkonium production. This may be due to the inadequate treatment of soft hadrons emitted in the hadronization process, which causes bad convergence of velocity expansion in NRQCD. In this paper, starting from QCD we propose a rigorously defined factorization approach, soft gluon factorization (SGF), to better deal with the effects of soft hadrons. After a careful velocity expansion, the SGF can be as simple as the NRQCD factorization in phenomenological studies, but has a much better convergence. The SGF may provide a new insight to understand the mechanisms of quarkonium production and decay. [ABSTRACT FROM AUTHOR]

High-order calculation at the semihard scale in high-energy collisions is very important, but a satisfactory calculation framework is still missing. We propose a systematic method to regularize the rapidity divergence in color glass condensate (CGC) factorization, which makes higher-order calculation rigorous and straightforward. By applying this method to the single hadron production in the pA collision, we find the kinematic constraint effect introduced by hand in previous works comes out automatically, but with different values. The difference is crucial for our next-to-leading-order result to have a smaller theoretical uncertainty compared with leading-order result, which makes the high-order calculation in CGC factorization be useful. As a byproduct, the negativity problem found in the literature can also be overcome in our framework by properly choosing the factorization scale. [ABSTRACT FROM AUTHOR]

High-order calculation at the semihard scale in high-energy collisions is very important, but a satisfactory calculation framework is still missing. We propose a systematic method to regularize the rapidity divergence in color glass condensate (CGC) factorization, which makes higher-order calculation rigorous and straightforward. By applying this method to the single hadron production in the pA collision, we find the kinematic constraint effect introduced by hand in previous works comes out automatically, but with different values. The difference is crucial for our next-to-leading-order result to have a smaller theoretical uncertainty compared with leading-order result, which makes the high-order calculation in CGC factorization be useful. As a byproduct, the negativity problem found in the literature can also be overcome in our framework by properly choosing the factorization scale. [ABSTRACT FROM AUTHOR]