Abstract
We calculate the NLO corrections for the gluon fragmentation functions to a heavy quark-antiquark pair in 1S0[1] or 1S0[8] state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of z (light-cone momentum fraction carried by the quark-antiquark pair), which can not only give FFs results with very high precision at any value of z, but also provide fully analytical structure at these singularities. We find that the NLO corrections are significant, with K-factors larger than 2 in most regions. The NLO corrections may have important impact on heavy quarkonia (e.g. ηc and J/ψ) production at the LHC.
Highlights
The inclusive production differential cross section of a specific hadron H at high pT can be calculated in collinear factorization [27], dσA+B→H(pT )+X =
We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and set up differential equations for these MIs
Our results are expressed in terms of asymptotic expansions at singular points of z, which can give fragmentation functions (FFs) results with very high precision at any value of z, and provide fully analytical structure at these singularities
Summary
The definition of FF from a gluon to a hadron (quarkonium) is given by Collins and Soper [63], Dg→H (z, μ0). Aμ(x) is the matrix-valued gluon field in the adjoint representation: [Aμ(x)]ac = if abcAμb (x) From this definition, we can derive Feynman rules related to gauge link, which are shown, where n = (0, 1−, 0⊥), K and P denote momenta, μ and ν denote. With these Feynman rules, we can obtain the amplitude of all Feynman diagrams denoted as MλQλQλ0λi(P, ki, mQ), where λQ and λQare respectively spins of produced onshell heavy quark and heavy antiquark, λ0 and λi By summing over spin and color of initial-state and final-state particles, we get the squared amplitude. Where n is the number of final-state light particles, and dΦis similar to dΦ by changing all momenta to the dimensionless ones. In the rest of the paper, we will only use the rescaled momenta, but omitting the “ˆ” for simplicity
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