Heavy-quark QCD vacuum polarisation function: analytical results at four loops

We determine the charm quark massm c from QCD sum rules of the moments of the vector current correlator calculated in perturbative QCD at O(α 3 s ). Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules, including the one for the zeroth moment. Existing data from the continuum region can then be used to bound the theoretic uncertainty. Our result iŝ m c (m c ) = 1272 ± 8 MeV forα s (M Z ) = 0.1182, where the central value is in very good agreement with other recent determinations based on the relativistic sum rule approach. On the other hand, there is considerably less agreement regarding the theory dominated uncertainty and we pay special attention to the question how to quantify and justify it.

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“…These results are displayed in Fig. 6 together with our final result forα s (M Z ) = 0.1182 (16) [8].…”

Section: Comparison With Previous Worksupporting

confidence: 56%

“…TheĈ n are known up to O(α 3 s ) for n ≤ 3 [14][15][16][17][18], and up to O(α 2 s ) for the rest [19,20]. For the convenience of the reader we collect the numerical values of the coefficients C (i) n required for our analysis in Table 2.…”

Section: Formalism and Charm-mass Determinationmentioning

confidence: 99%

Charm quark mass with calibrated uncertainty

2017

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“…In the formula below we have used finding of Refs. [21,22] to display the ∆ MS,4 in a completely analytical form (it was also done in Ref. [23]).…”

Section: Pos(ll2016)010mentioning

confidence: 99%

Multiloop Renormalization Group: new results

Chetyrkin¹,

Baikov²,

Kühn³

2016

Proceedings of Loops and Legs in Quantum Field Theory — PoS(LL2016)

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“…The theoretical expression for the moments is related to derivatives of the vacuum polarization function at q 2 = 0. Four-loop [O(α s 3 )] results for the vacuum polarization function have appeared for the first moment [240][241][242], second moment [243], third moment [244], and approximate results for higher moments [245,246]. All those four-loop results are used in the most recent low-momentum sum-rule determinations of the heavy-quark masses reported below.…”

Section: • Momentsmentioning

confidence: 99%

Heavy quarkonium: progress, puzzles, and opportunities

Brambilla¹,

Eidelman²,

Heltsley³

et al. 2011

Advances in the Physics of Particles and Nuclei

103

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A golden age for heavy quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The early years of this period were chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in 2004, which presented a comprehensive review of the status of the field at that time and provided specific recommendations for further progress. However, the broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles could only be partially anticipated. Since the release of the YR, the BESII program concluded only to give birth to BESIII; the B-factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the deconfinement regime. All these experiments leave legacies of quality, precision, and unsolved mysteries for quarkonium physics, and therefore beg for continuing investigations at BESIII, the LHC, RHIC, FAIR, the Super Flavor and/or Tau-Charm factories, JLab, the ILC, and beyond. The list of newly-found conventional states expanded to include hc(1P ), χc2(2P ), B + c , and η b (1S). In addition, the unexpected and still-fascinating X(3872) has been joined by * Editors † Section coordinators ‡ Corresponding author: bkh2@cornell.edu more than a dozen other charmonium-and bottomonium-like "XY Z" states that appear to lie outside the quark model. Many of these still need experimental confirmation. The plethora of new states unleashed a flood of theoretical investigations into new forms of matter such as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the spectroscopy, decays, production, and in-medium behavior of cc, bb, and bc bound states have been shown to validate some theoretical approaches to QCD and highlight lack of quantitative success for others. Lattice QCD has grown from a tool with computational possibilities to an industrialstrength effort now dependent more on insight and innovation than pure computational power. New effective field theories for the description of quarkonium in different regimes have been developed and brought to a high degree of sophistication, thus enabling precise and solid theoretical predictions. Many expected decays and transitions have either been measured with precision or for the first time, but the confusing patterns of decays, both above and below open-flavor thresholds, endure and have deepened. The intriguing details of quarkonium suppression in heavy-ion collisions that have emerged from RHIC have elevated the importance of separating hotand cold-nuclear-matter effects in quark-gluon plasma studies. This review systematically addresses all these matters and concludes by prioritizing directions for ongoing and future efforts.

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Heavy-quark QCD vacuum polarisation function: analytical results at four loops

Abstract: Fully analytical results for the first two moments of the heavy-quark vacuum polarisation function at four loops in quantum chromo-dynamics are presented.

Cited by 36 publications

References 27 publications

Charm quark mass with calibrated uncertainty

Charm quark mass with calibrated uncertainty

Multiloop Renormalization Group: new results

Heavy quarkonium: progress, puzzles, and opportunities

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