Potential NRQCD and Heavy-Quarkonium Spectrum at Next-to-Next-to-Next-to-Leading Order

Abstract

The next-to-next-to-next-to-leading order (N^3LO) Hamiltonian of potential nonrelativistic QCD is derived. The complete matching of the Hamiltonian and the contribution from the ultrasoft dynamical gluons relevant for perturbative bound-state calculations is performed including one-, two-, and three-loop contributions. The threshold expansion is used to disentangle and match contributions of different scales in the effective-theory calculations. As a physical application, the heavy-quarkonium spectrum is obtained at N^3LO for the case of vanishing QCD beta function. Our results set the stage for a full N^3LO analysis of the heavy-quarkonium system.

29 pages (Latex), 4 figures (Axodraw)

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• The QCD heavy-quark potential to order v^2: one loop matching conditions
• Renormalization group analysis of the QCD quark potential to order v^2
• Running of the heavy quark production current and 1/k potential in QCD
• Bottom Quark Mass from Upsilon Mesons
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• Order (alpha^2 Gamma, alpha^3 Gamma) Binding Effects in Orthopositronium Decay
• O(alpha_s^2) Corrections to e+e- to ttbar Total and Differential Cross Sections Near Threshold
• Top quark production near threshold: NNLO QCD correction
• O(alpha_s^5 m) quarkonium 1S spectrum in large-beta_0 approximation and renormalon cancellation
• Top Quark Threshold Production at a gamma-gamma Collider at Next-to-Next-to-Leading Order
• Heavy Quarkonium Physics beyond the Next-to-Next-to-Leading Order of NRQCD

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• 50 Years of Quantum Chromodynamics
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• Fermionic contributions to the three-loop static potential
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• Review of Heavy Quarkonium at weak coupling
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• The bottom-quark mass from non-relativistic sum rules at NNNLO
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Connecting the Hadron Mass Scale to the Fundamental Mass Scale of Quantum Chromodynamics
• Heavy Quarkonium Spectrum and Production/Annihilation Rates to order ${\beta }_0^3{\alpha }_s^3$
• Variational Study of Weakly Coupled Triply Heavy Baryons
• Spin Dependence of Heavy Quarkonium Production and Annihilation Rates: Complete Next-to-Next-to-Leading Logarithmic result
• Ultrasoft contribution to quarkonium production and annihilation
• Determination of the top quark mass circa 2013: methods, subtleties, perspectives
• Long-range properties of $1S$ bottomonium states
• Leptonic decay of the Upsilon(1S) meson at third order in QCD
• Two-Loop Static QCD Potential for General Colour State
• $M(B_c^{\ast })-M(B_c)$ Splitting from Nonrelativistic Renormalization Group
• Analytic three-loop static potential
• Ultrasoft contribution to heavy-quark pair production near threshold
• QCD potential as a "Coulomb-plus-linear" potential
• Solving Recurrence Relations for Multi-Loop Feynman Integrals
• Electroweak non-resonant NLO corrections to e+ e- -> W+ W- b bbar in the t tbar resonance region
• Relativistic effects in the production of pseudoscalar and vector doubly heavy mesons from e^+e^- annihilation
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• Heavy-quarkonium creation and annihilation with O(alpha_s^3 ln(alpha_s)) accuracy
• Static QCD Potential at r < 1/Lambda_QCD: Perturbative expansion and operator-product expansion
• Hyperfine splitting in positronium to $\mathcal{O}({\alpha }^7{m}_e)$: one-photon annihilation contribution
• Violation of Casimir Scaling for Static QCD Potential at Three-loop Order
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• Calibrating the Naïve Cornell Model with NRQCD
• Fourth-order QCD renormalization group quantities in the {\rm{V}}-scheme and the relation of the $\beta$-function to the Gell-Mann--Low function in QED
• Fermionic Corrections to the Three-Loop Matching Coefficient of the Vector Current
• Gluinonia: Energy Levels, Production and Decay
• Bottom Quark Mass from ${\rm Y}$ Sum Rules to $\mathcal{O}({\alpha }_s^3)$
• Three-loop corrections to the muon and heavy quark decay rates
• Threshold production of unstable top
• Determination of $m_c$ and $m_b$ from quarkonium 1S energy levels in perturbative QCD
• Complete Higgs mass dependence of top quark pair threshold production to order $\alpha {\alpha }_s$
• Color Transfer Enhancement for Heavy Quarkonium Production
• Improved Perturbative QCD Approach to the Bottomonium Spectrum
• Potential NRQCD for unequal masses and the $B_c$ spectrum at NNNLO
• Quark-antiquark potential to order 1/m and heavy quark masses
• P-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy
• Heavy quarkonium photoproduction in ultrarelativistic heavy ion collisions
• Relativistic effects in the double S- and P-wave charmonium production in e^+e^- annihilation
• QCD moment sum rules for Coulomb systems: the charm and bottom quark masses
• Resummation of soft and Coulomb corrections for $t\bar{t}h$ production at the LHC
• Semi-inclusive radiative decays of Upsilon 1S
• Radiative decays and the nature of heavy quarkonia
• The 1P quarkonium fine splittings at NLO
• Soft, collinear and non-relativistic modes in radiative decays of very heavy quarkonium
• Relativistic effects in the processes of heavy quark fragmentation
• The nucleon-nucleon potential beyond the static approximation
• Mass of the bottom quark from Upsilon(1S) at NNNLO: an update
• Effective Field Theories for Heavy Quarkonium
• Two-Loop $\mathcal{O}(\alpha {\alpha }_s)$ Corrections to the On-Shell Fermion Propagator in the Standard Model
• Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case
• Quarkonium propagation in the quark gluon plasma
• Top mass determination and O (alpha_S^5 m) correction to toponium 1S energy level
• Quarkonium $h$ States As Arbiters of Exoticity
• Overview of Non-Relativistic QCD
• $\mathcal{O}(\alpha {\alpha }_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold
• Colour octet potential to three loops
• Comparing the QCD potential in Perturbative QCD and Lattice QCD at large distances
• Renormalization group improved pQCD prediction for ${\rm Y}(1S)$ leptonic decay
• Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation
• Estimate of the three-loop contribution to the QCD static potential from renormalon cancellation
• S-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy
• Coulomb Artifacts and Bottomonium Hyperfine Splitting in Lattice NRQCD
• Heavy quark mass determination from the quarkonium ground state energy: a pole mass approach
• $P$-wave quarkonium wavefunctions at the origin in the $\overline{\mathrm{MS}}$ scheme
• Baryons, multi-hadron systems, and composite dark matter in non-relativistic QCD
• Relativistic corrections to the static energy in terms of Wilson loops at weak coupling
• Bottomonium Hyperfine Splitting on the Lattice and in the Continuum
• From perturbative calculations of the QCD static potential towards four-loop pole-running heavy quarks masses relation
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• Overview of charmonium decays and production from Non-Relativistic QCD
• Supersymmetric Corrections to the Threshold Production of Top Quark Pairs
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• Bottonium mass - evaluation using renormalon cancellation
• Third order Coulomb correction to ttbar threshold cross section
• Mass shifts of ${}^3{P}_J$ heavy quarkonia due to the effect of two-gluon annihilation
• Applications of Nonrelativistic Effective Field Theories to quarkonium systems with a small radius
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• On enhanced corrections from quasi-degenerate states to heavy quarkonium observables
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• Potential Nonrelativistic QCD and Heavy Quarkonium Spectrum in Next-to-Next-to-Next-to-Leading Order