Double Logarithms in $e^{+}{e}^{-}\to J/\psi +{\eta }_c$

Abstract

Double logarithms of $Q^2/m_c^2$ that appear in the cross section for $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ at next-to-leading order (NLO) in the strong coupling ${\alpha }_s$ account for the bulk of the NLO correction at $B$-factory energies. (Here, $Q^2$ is the square of the center-of-momentum energy, and $m_c$ is the charm-quark mass.) We analyze the double logarithms that appear in the contribution of each NLO Feynman diagram, and we find that the double logarithms arise from both the Sudakov and the end-point regions of the loop integration. The Sudakov double logarithms cancel in the sum over all diagrams. We show that the end-point region of integration can be interpreted as a pinch-singular region in which a spectator fermion line becomes soft or soft and collinear to a produced meson. This interpretation may be important in establishing factorization theorems for helicity-flip processes, such as $e^{+}{e}^{-}\to J/\psi +{\eta }_c$, and in resumming logarithms of $Q^2/m_c^2$ to all orders in ${\alpha }_s$.

31 pages, 4 figures, 1 table, minor revisions, version published in PRD

References in corpus (20)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• Observation of Double cc bar Production in e+ e- Annihilation at sqrt{s} ~ 10.6 GeV
• Exclusive Double-Charmonium Production from e^+ e^- Annihilation into a Virtual Photon
• Measurement of Double Charmonium Production in $e^{+}{e}^{-}$ Annihilations at $\sqrt{s}=10.6$ GeV
• Next-to-Leading Order QCD Correction to ${\mathbf{e}}^{+}{\mathbf{e}}^{-}\to \mathbf{J}/\mathbf{\psi }+{\mathbf{\eta }}_{\mathbf{c}}$ at $\sqrt{s}=10.6$GeV}
• Problems of Double Charm Production in $e^{+}{e}^{-}$ Annihilation at $\sqrt{s}=10.6$ GeV
• Order-v^4 Corrections to S-wave Quarkonium Decay
• Study of double charmonium production in e^+ e^- annihilation at \sqrt{s} ~ 10.6 GeV
• QCD corrections to J/psi plus eta_c production in e+e- annihilation at sqrt{s}=10.6 GeV
• Resummation of Relativistic Corrections to e+ e- -> J/psi+eta_c
• Potential-model calculation of an order-v^2 NRQCD matrix element
• Relativistic Corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ in a Potential Model
• $O({\alpha }_s{v}^2)$ correction to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ at $B$ factories
• Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production
• Factorization in exclusive quarkonium production
• Factorization theorems for exclusive heavy-quarkonium production
• Bridging light-cone and NRQCD approaches: asymptotic behavior of $B_c$ electromagnetic form factor
• $O({\alpha }_s)$ corrections to $J/\psi +{\chi }_{cJ}$ production at $B$ factories

Cited by in corpus (7)

• Next-to-leading order QCD corrections to paired $B_c$ production in $e^{+}{e}^{-}$ annihilation
• ${\alpha }_s{v}^2$ corrections to ${\eta }_c$ and ${\chi }_{cJ}$ production recoiled with a photon at $e^{+}{e}^{-}$ colliders
• Renormalization of the radiative jet function
• Analyticity, renormalization, and evolution of the soft-quark function
• Next-to-leading-order study of $J/\psi$ angular distributions in $e^{+}{e}^{-}\to J/\psi +{\eta }_c,{\chi }_{cJ}$ at $\sqrt{s}\approx 10.6$ GeV
• Two loop QCD corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ in asymptotic expansion
• $\mathcal{O}({\alpha }_s)$ corrections to $e^{+}{e}^{-}\to J/\psi +{\eta }_{c2}({\chi }_{c1}^{\prime })$ at $B$ factories