Power expansion for heavy quarkonium production at next-to-leading order in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ annihilation

Abstract

We study heavy quarkonium production associated with gluons in ${\mathrm{e}}^{+}{\mathrm{e}}^{-}$ annihilation as an illustration of the perturbative QCD (pQCD) factorization approach, which incorporates the first nonleading power in the energy of the produced heavy quark pair. We show how the renormalization of the four-quark operators that define the heavy quark pair fragmentation functions using dimensional regularization induces "evanescent" operators that are absent in four dimensions. We derive closed forms for short-distance coefficients for quark pair production to next-to-leading order (${\alpha }_s^2$) in the relevant color singlet and octet channels. Using non-relativistic QCD (NRQCD) to calculate the heavy quark pair fragmentation functions up to $v^4$ in the velocity expansion, we derive analytical results for the differential energy fraction distribution of the heavy quarkonium. Calculations for ${}^3{S}_1^{[1]}$ and ${}^1{S}_0^{[8]}$ channels agree with analogous NRQCD analytical results available in the literature, while several color-octet calculations of energy fraction distributions are new. We show that the remaining corrections due to the heavy quark mass fall off rapidly in the energy of the produced state. To explore the importance of evolution at energies much larger than the mass of the heavy quark, we solve the renormalization group equation perturbatively to two-loop order for the ${}^3{S}_1^{[1]}$ case.

arXiv comment44 pages, 9 figures

References in corpus (31)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• Hard-scattering factorization with heavy quarks: A general treatment
• World data of J/psi production consolidate NRQCD factorization at NLO
• Evanescent Operators, Scheme Dependences and Double Insertions
• Fragmentation contributions to J/psi production at the Tevatron and the LHC
• Fragmentation, NRQCD and NNLO Factorization Analysis in Heavy Quarkonium Production
• Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium
• QCD radiative correction to color-octet $J/\psi$ inclusive production at B Factories
• Signature for Color-Octet Production of $J/\psi$ in $e^{+}{e}^{-}$ Annihilation
• Heavy Quarkonium Production at Collider Energies: Factorization and Evolution
• Prompt J/psi production at e^+e^- colliders
• Resumming the color-octet contribution to e+ e- -> J/psi + X
• QCD corrections to ${\mathbf{e}}^{+}{\mathbf{e}}^{-}\to \mathbf{J}/\mathbf{\psi gg}$ at B Factories
• Next-to-Leading-Order QCD Corrections to e^ + e^- -> J/ψ+gg at the B Factories
• Kinematic Enhancement of Non-Perturbative Corrections to Quarkonium Production
• Next-to-leading-order tests of nonrelativistic-QCD factorization with $J/\psi$ yield and polarization
• Heavy quarkonium fragmentation functions from a heavy quark pair. I. $S$ wave
• Color-Singlet ${\psi }_Q$ Production at $e^{+}{e}^{-}$ Colliders
• Relativistic corrections to Higgs boson decays to quarkonia
• Resummation of Large Endpoint Corrections to Color-Octet J/psi Photoproduction
• Dimensional Regularization in Quarkonium Calculations
• The Systematics of Quarkonium Production at the LHC and Double Parton Fragmentation
• Heavy Quarkonium Production at Collider Energies: Partonic Cross Section and Polarization
• Factorized power expansion for high-$p_T$ heavy quarkonium production
• Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production
• Heavy quarkonium fragmentation functions from a heavy quark pair. II. $P$ wave
• Anomalous dimensions of the double parton fragmentation functions
• New factorization theory for heavy quarkonium production and decay
• The color-singlet contribution to e^+ e^- ->J/psi + X at the endpoint
• Inclusive $h_c$ production and energy spectrum from $e^{+}{e}^{-}$ annihilation at Super $B$ factory
• Power corrections in semi-inclusive deep inelastic scatterings at fixed target energies

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