Potential-model calculation of an order-v^2 NRQCD matrix element

Abstract

We present two methods for computing dimensionally-regulated NRQCD heavy-quarkonium matrix elements that are related to the second derivative of the heavy-quarkonium wave function at the origin. The first method makes use of a hard-cutoff regulator as an intermediate step and requires knowledge only of the heavy-quarkonium wave function. It involves a significant cancellation that is an obstacle to achieving high numerical accuracy. The second method is more direct and yields a result that is identical to the Gremm-Kapustin relation, but it is limited to use in potential models. It can be generalized to the computation of matrix elements of higher order in the heavy-quark velocity and can be used to resum the contributions to decay and production rates that are associated with those matrix elements. We apply these methods to the Cornell potential model and compute a matrix element for the J/psi state that appears in the leading relativistic correction to the production and decay of that state through the color-singlet quark-antiquark channel.

26 pages, 3 figures, Sec. IV completely re-written, published version in Phys. Rev. D

Cited by in corpus (31)

• Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium
• Relativistic corrections to $J/\psi$ exclusive and inclusive double charm production at B factories
• Double charm production e^+ e^- \to J/ψ+ c \bar{c} at B factories with next-to-leading order QCD corrections
• Resummation of Relativistic Corrections to e+ e- -> J/psi+eta_c
• QCD corrections to ${\mathbf{e}}^{+}{\mathbf{e}}^{-}\to \mathbf{J}/\mathbf{\psi gg}$ at B Factories
• Reconciling the light-cone and nonrelativistic QCD approaches to calculating e+ e- -> J/psi + eta_c
• The study of leading twist light cone wave function of η_c meson
• Factorization and NLO QCD correction in e^+ e^- \to J/ψ(ψ(2S))+ χ_{c0} at B Factories}
• The study of leading twist light cone wave functions of J/Psi meson
• Pair Production of Heavy Quarkonium and $B_c{(}^{\ast })$ Mesons at Hadron Colliders
• Interpretations for the X(4160) observed in the double charm production at B factories
• Relativistic effects in the production of pseudoscalar and vector doubly heavy mesons from e^+e^- annihilation
• Perturbative QCD analysis of exclusive J/ψ+η_c production in e^+e^- annihilation
• Leading twist distribution amplitudes of P-wave nonrelativistic mesons
• Exclusive $et{a}_b$ decay to double $J/\psi$ at next-to-leading order in $alph{a}_s$
• Exclusive heavy quarkonium + gamma production from e+ e- annihilation into a virtual photon
• Exclusive Two-Vector-Meson Production from e^+ e^- Annihilation
• Which hadronic decay modes are good for ${\eta }_b$ searching: double $J/\psi$ or something else?
• Inclusive Charm Production in chi_b Decays
• Relativistic description of the double charmonium production in $e^{+}{e}^{-}$ annihilation
• Spectroscopy, leptonic decays and the nature of heavy quarkonia
• The study of leading twist light cone wave functions of 2S state charmonium mesons
• Decay rates of quarkonia with NRQCD formalism using spectroscopic parameters of potential models
• Inclusive Charm Production in Upsilon(nS) Decay
• Precise Numerical Solutions of Potential Problems Using Crank-Nicholson Method
• Order-alpha_s corrections to the quarkonium electromagnetic current at all orders in the heavy-quark velocity
• The study of double vector charmonium mesons production at B-factories within light cone formalism
• Possible contributions to $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ due to intermediate meson rescatterings
• ${\rm Y}$ decay to two-charm quark jets as a Probe of the Color Octet Mechanism
• Invariant-mass distribution of cc-bar in Upsilon(1S) -> cc-bar + X
• Heavy Quarkonium Physics from Effective Field Theories