P-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy

Abstract

We compute the heavy quarkonium mass of $l\ne 0$ (angular momentum) states, with otherwise arbitrary quantum numbers, with next-next-to-next-to-leading logarithmic (N${}^3$LL) accuracy. This constitutes the first observable in heavy quarkonium for which two orders of the weak-coupling expansion sensitive to the ultrasoft scale are known and the resummation of ultrasoft logarithms is made. We also obtain, for the first time, resummed N${}^3$LL expressions for the different fine and hyperfine energy splittings of these states, which are not sensitive to the ultrasoft scale but still require resummation of (hard) logarithms. We do this analysis for the equal and non-equal mass cases. We also study an alternative computational scheme that treats the static potential exactly. We then perform a comprehensive phenomenological analysis: we apply these results to the $n=2$, $l=1$ bottomonium, $B_c$ and charmonium systems and study their convergence.

arXiv comment49 pages, 15 figures, 1 table

References in corpus (72)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• Potential NRQCD: an effective theory for heavy quarkonium
• Effective field theories for heavy quarkonium
• Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED
• The Pole Mass of The Heavy Quark. Perturbation Theory and Beyond
• The static potential in QCD to two loops
• Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
• A quark mass definition adequate for threshold problems
• The static quark-antiquark potential in QCD to three loops
• The HQET/NRQCD Lagrangian to order alpha/m^3
• Renormalization group scaling in nonrelativistic QCD
• Three-loop static potential
• The infrared behaviour of the static potential in perturbative QCD
• B decay and the Upsilon mass
• Static QCD potential at three-loop order
• Complete O(v^2) corrections to the static interquark potential from SU(3) gauge theory
• Determination of the bottom quark mass from the ${\rm Y}(1S)$ system
• The QCD Potential at $O(1/m)$
• Potential NRQCD and Heavy-Quarkonium Spectrum at Next-to-Next-to-Next-to-Leading Order
• Potential NRQED: The Positronium Case
• The Heavy Quarkonium Spectrum at Order $m{\alpha }_s^5\ln {\alpha }_s$
• Fermionic contributions to the three-loop static potential
• Positronium S state spectrum: analytic results at O(m alpha^6)
• Spin-dependent potentials from lattice QCD
• Quarkonia and the Pole Mass
• Heavy Quarkonium Spectrum at $\mathcal{O}({\alpha }_s^5{m}_q)$ and Bottom/Top Quark Mass Determination
• Third-order Coulomb corrections to the S-wave Green function, energy levels and wave functions at the origin
• Calculation of Quarkonium Spectrum and $m_b,m_c$ to Order ${\alpha }_s^4$
• The Renormalization Group Improvement of the QCD Static Potentials
• Quarkonium spectroscopy and perturbative QCD: massive quark-loop effects
• Review of Heavy Quarkonium at weak coupling
• Quarkonium Spectroscopy and Perturbative QCD: A New Perspective
• $M({\eta }_b)$ and ${\alpha }_s$ from Nonrelativistic Renormalization Group
• Matching at one loop for the four-quark operators in NRQCD
• The NRQED lagrangian at order 1/M^4
• The static potential: lattice versus perturbation theory in a renormalon-based approach
• The QCD static energy at NNNLL
• Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum
• Nonabelian alpha_s^3/(m_q r^2) heavy-quark-antiquark potential
• Rigourous QCD Evaluation of Spectrum and Other Properties of Heavy Quarkonium Systems; II Bottomium with n=2, l=0,1
• Heavy Quarkonium Spectrum and Production/Annihilation Rates to order ${\beta }_0^3{\alpha }_s^3$
• Spin Dependence of Heavy Quarkonium Production and Annihilation Rates: Complete Next-to-Next-to-Leading Logarithmic result
• Renormalization Group Scaling of the 1/m^2 HQET Lagrangian
• Fine and Hyperfine Splittings of Charmonium and Bottomonium: An Improved Perturbative QCD Approach
• Two-Loop Anomalous Dimension of the Chromo-Magnetic Moment of a Heavy Quark
• Logarithms of alpha in QED bound states from the renormalization group
• Improved determination of Heavy Quarkonium magnetic dipole transitions in pNRQCD
• $M(B_c^{\ast })-M(B_c)$ Splitting from Nonrelativistic Renormalization Group
• R-evolution: Improving perturbative QCD
• The charm/bottom quark mass from heavy quarkonium at N${}^3$LO
• On The Spin-Dependent Potential Between Heavy Quark And Antiquark
• Bottom and Charm Mass determinations from global fits to $Q\bar{Q}$ bound states at N${}^3$LO
• Spectator Effects in the Heavy Quark Effective Theory
• HQET chromomagnetic interaction at two loops
• Perturbative heavy quarkonium spectrum at next-to-next-to-next-to-leading order
• Full Formula for Heavy Quarkonium Energy Levels at Next-to-next-to-next-to-leading Order
• Relations between Heavy-light Meson and Quark Masses
• Improved determination of inclusive electromagnetic decay ratios of heavy quarkonium from QCD
• Improved Perturbative QCD Approach to the Bottomonium Spectrum
• Potential NRQCD for unequal masses and the $B_c$ spectrum at NNNLO
• The 1P quarkonium fine splittings at NLO
• The static hybrid potential in D dimensions at short distances
• Ultrasoft NLL Running of the Nonrelativistic O(v) QCD Quark Potential
• Renormalizing the heavy quark effective field theory Lagrangian to order 1/m^2
• Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case
• Quarkonium $h$ States As Arbiters of Exoticity
• Two-Loop Ultrasoft Running of the O(v^2) QCD Quark Potentials
• The chromo-polarizabilities of a heavy quark at weak coupling
• More nonperturbative corrections to the fine and hyperfine splitting in the heavy quarkonium
• HQET renormalization group improved Lagrangian at $\mathcal{O}(1/m^3)$ with leading logarithmic accuracy: Spin-dependent case
• Spectator effects in the HQET renormalization group improved Lagrangian at $\mathcal{O}(1/m^3)$ with leading logarithmic accuracy: Spin-dependent case
• Spectator Effects in Heavy Quark Effective Theory at O(1/m_Q^3)

Cited by in corpus (16)

• The $XYZ$ states: experimental and theoretical status and perspectives
• 50 Years of Quantum Chromodynamics
• Bottomonium suppression in an open quantum system using the quantum trajectories method
• Spectroscopy of ${\mathbf{B}}_{\mathbf{c}}$ mesons and the possibility of finding exotic ${\mathbf{B}}_{\mathbf{c}}$-like structures
• Exotic to standard bottomonium transitions
• The proton radius (puzzle?) and its relatives
• Calibrating the Naïve Cornell Model with NRQCD
• Towards the discovery of novel $B_c$ states: radiative and hadronic transitions
• Electric dipole transitions of $1P$ bottomonia
• $B_c$ meson spectroscopy motivated by general features of pNRQCD
• Matching coefficients in NRQCD to two-loop accuracy
• The bottom-charmed meson spectrum from a QCD approach based on Tamm--Dancoff approximation
• Can the hyperfine mass splitting formula in heavy quarkonia be applied to the $B_c$ system?
• S-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy
• Highly excited $B$, $B_s$ and $B_c$ meson spectroscopy from lattice QCD
• Study of charmonium production using decays to hadronic final states with the LHCb experiment