$\overline{\mathrm{MS}}$ 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.

arXiv comment62 pages, 9 figures, 2 tables, typos corrected, version published in JHEP

References in corpus (73)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• Heavy quarkonium: progress, puzzles, and opportunities
• Potential NRQCD: an effective theory for heavy quarkonium
• Effective field theories for heavy quarkonium
• Renormalons
• QCD forces and heavy quark bound states
• RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses
• QCD and strongly coupled gauge theories: challenges and perspectives
• Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED
• Quarkonium Wave Functions at the Origin
• The static potential in QCD to two loops
• A quark mass definition adequate for threshold problems
• Version 3 of {\tt RunDec} and {\tt CRunDec}
• The HQET/NRQCD Lagrangian to order alpha/m^3
• Three-loop static potential
• The infrared behaviour of the static potential in perturbative QCD
• Two-loop Correction to the Leptonic Decay of Quarkonium
• Update: Precision D_s decay constant from full lattice QCD using very fine lattices
• Two-loop QCD corrections to the heavy quark pair production cross section in e+e- annihilation near the threshold
• Static QCD potential at three-loop order
• The QCD Potential at $O(1/m)$
• Top quark production near threshold and the top quark mass
• Potential NRQED: The Positronium Case
• Improved determination of color-singlet nonrelativistic QCD matrix elements for S-wave charmonium
• Top Quark Pair Production close to Threshold: Top Mass, Width and Momentum Distribution
• Rigourous QCD Evaluation of Spectrum and Ground State Properties of Heavy Quarkonium Systems; with a Precision Determination of the bottom quark mass and of the eta-b mass
• Fermionic contributions to the three-loop static potential
• The QCD potential at O(1/m^2): Complete spin-dependent and spin-independent result
• The b quark low-scale running mass from Upsilon sum rules
• Bottom quark pole mass and $|V_{cb}|$ matrix element from $R(e^{+}{e}^{-}\to b\bar{b})$ and ${\Gamma }_{sl}(b\to cl{\nu }_l)$ in the next-to-next-to-leading order
• Review of Heavy Quarkonium at weak coupling
• Top Quark Pair Production at Threshold: Complete Next-to-next-to-leading Order Relativistic Corrections
• Inclusive Decays of Heavy Quarkonium to Light Particles
• Quarkonium Decay Matrix Elements from Quenched Lattice QCD
• Matching at one loop for the four-quark operators in NRQCD
• QCD Radiative Corrections to the Leptonic Decay Rate of the B_c Meson
• Power Counting in Dimensionally Regularized NRQCD
• Nonabelian alpha_s^3/(m_q r^2) heavy-quark-antiquark potential
• Top quark production at threshold with O(alpha_s^2) accuracy
• Spin Dependence of Heavy Quarkonium Production and Annihilation Rates: Complete Next-to-Next-to-Leading Logarithmic result
• The QCD heavy-quark potential to order v^2: one loop matching conditions
• New predictions for inclusive heavy-quarkonium P-wave decays
• Dimensional Regularization in Quarkonium Calculations
• Charmonium decays: J/psi --> e+e- and eta_c --> gamma gamma
• Leptonic decay of the Upsilon(1S) meson at third order in QCD
• Can NRQCD explain the $\gamma {\gamma }^{\ast }\to {\eta }_c$ transition form factor data?
• Three-loop matching of the vector current
• The charm/bottom quark mass from heavy quarkonium at N${}^3$LO
• Bottomonium Decay Matrix Elements from Lattice QCD with Two Light Quarks
• 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
• Effective string theory constraints on the long distance behavior of the subleading potentials
• Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production
• Two-Loop Matching Coefficients for Heavy Quark Currents
• Relations between Heavy-light Meson and Quark Masses
• Improved determination of inclusive electromagnetic decay ratios of heavy quarkonium from QCD
• O(alpha_s^2) Corrections to e+e- to ttbar Total and Differential Cross Sections Near Threshold
• Decay and electromagnetic production of strongly coupled quarkonia in pNRQCD
• Top quark production near threshold: NNLO QCD correction
• Perturbative O(alpha_s^2) Corrections to the Hadronic Cross Section Near Heavy Quark-Antiquark Thresholds in e+e- Annihilation
• $O({\alpha }_s{v}^2)$ correction to pseudoscalar quarkonium decay to two photons
• Spin correlations and velocity-scaling in color-octet NRQCD matrix elements
• Analytical results for $e^{+}{e}^{-}\to t\bar{t}$ and $\gamma \gamma \to t\bar{t}$ observables near the threshold up to the next-to-next-to-leading order of NRQCD
• Relativistic corrections to light-cone distribution amplitudes of S-wave $B_c$ mesons and heavy quarkonia
• Potential NRQCD for unequal masses and the $B_c$ spectrum at NNNLO
• Quark-antiquark potential to order 1/m and heavy quark masses
• Renormalon Ambiguities in NRQCD Operator Matrix Elements
• 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
• Pseudoscalar Quarkonium+gamma Production at NLL+NLO accuracy
• Charmonium potentials: Matching perturbative and lattice QCD
• Top quark production near threshold
• Is there a linear potential at short distances?

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