$\overline{\mathrm{MS}}$ renormalization of $S$-wave quarkonium wavefunctions at the origin

Abstract

We compute $S$-wave quarkonium wavefunctions at the origin in the $\overline{\mathrm{MS}}$ scheme based on nonrelativistic effective field theories. We include the effects of nonperturbative long-distance behaviors of the potentials, while we determine the short-distance behaviors of the potentials in perturbative QCD. We obtain $\overline{\mathrm{MS}}$-renormalized quarkonium wavefunctions at the origin that have the correct scale dependences that are expected from perturbative QCD, so that the scale dependences cancel in physical quantities. Based on the calculation of the wavefunctions at the origin, we make model-independent predictions of decay constants and electromagnetic decay rates of $S$-wave charmonia and bottomonia, and compare them with measurements. We find that the poor convergence of perturbative QCD corrections are substantially improved when we include corrections to the wavefunctions at the origin in the calculation of decay constants and decay rates.

62 pages, 9 figures, 2 tables, typos corrected, version published in JHEP

References in corpus (13)

• Heavy quarkonium: progress, puzzles, and opportunities
• Update: Precision D_s decay constant from full lattice QCD using very fine lattices
• Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium
• Fermionic contributions to the three-loop static potential
• NRQCD matrix elements for S-wave bottomonia and Gamma[eta_b(nS) -> gamma gamma] with relativistic corrections
• $O({\alpha }_s{v}^2)$ Corrections to Hadronic and Electromagnetic Decays of ${}^1{S}_0$ Heavy Quarkonium
• Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production
• Two-Loop Matching Coefficients for Heavy Quark Currents
• Relativistic corrections to light-cone distribution amplitudes of S-wave $B_c$ mesons and heavy quarkonia
• Quark-antiquark potential to order 1/m and heavy quark masses
• Relativistic corrections to the static potential at O(1/m) and O(1/m^2)
• Order-alpha_s corrections to the quarkonium electromagnetic current at all orders in the heavy-quark velocity
• Charmonium potentials: Matching perturbative and lattice QCD

Cited by in corpus (14)

• Inclusive production of $J/\psi$, $\psi (2S)$, and ${\rm Y}$ states in pNRQCD
• Inclusive Production of Heavy Quarkonia in pNRQCD
• Indirect constraints on lepton-flavour-violating quarkonium decays
• Bound-state formation, dissociation and decays of darkonium with potential non-relativistic Yukawa theory for scalar and pseudoscalar mediators
• Improved evaluation of the electroweak contribution to muon $g-2$
• Next-to-next-to-leading-order QCD corrections to $J/\psi$ plus ${\eta }_c$ production at the $B$ factories
• $Z$ boson radiative decays to a $S$-wave quarkonium at NNLO and NLL accuracy
• $P$-wave quarkonium wavefunctions at the origin in the $\overline{\mathrm{MS}}$ scheme
• Three-loop matching coefficients for heavy flavor-changing currents and the phenomenological applications
• Next-to-leading-order QCD corrections to a vector bottomonium radiative decay into a charmonium
• Next-to-next-to-leading-order QCD corrections to double $J/\psi$ production at the $B$ factories
• Color-octet nonrelativistic QCD matrix elements for heavy quarkonium decays in the refined Gribov-Zwanziger theory
• Quarkonium production in pNRQCD: the $P$-wave case
• Prospects for observing the ${\eta }_t$ $\to$ $W^{+}{W}^{-}$ decay at the HL-LHC