Erratum to “<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mi>B</mml:mi><mml:mi>c</mml:mi><mml:mo>∗</mml:mo></mml:msubsup><mml:mo stretchy="false">)</mml:mo><mml:mtext>–</mml:mtext><mml:mi>M</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mi>B</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math> splitting from nonrelativistic renormalization group” [Ph

Penin, Alexander A.; Pineda, A. Morelos; Smirnov, Vladimir A.; Steinhauser, M.

doi:10.1016/j.physletb.2009.12.035

Cited by 12 publications

(26 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is enough for P-wave analyses [7], where such corrections produce a N 3 LL shift to the energy. Nevertheless, it is not so for S-wave states, as already noted in [9,10] for the case of the hyperfine splitting. The reason is the generation of singular potentials through divergent ultrasoft loops.…”

Section: Introductionmentioning

confidence: 87%

“…is indeed known with the required N 3 LL accuracy [9,10] (one should be careful when comparing though, as there is a change in the basis of potentials used there, compared with the one we use here). In terms ofD…”

Section: Pnrqcd Lagrangianmentioning

confidence: 99%

“…The spin-dependent case was computed in [9,10]. Explicit expressions for the potentials can be found in the Appendix of [36].…”

Section: Nrqcd-pnrqcd Matching Spin-independentmentioning

confidence: 99%

“…The missing link to obtain the complete N 3 LL pNRQCD Lagrangian is the N 3 LL running of the delta(-like) potentials 1 . For the spin-dependent case, such precision for the running has already been achieved in [9,10]. Therefore, what is left is to obtain the N 3 LL result for the spin-independent delta potential.…”

Section: Introductionmentioning

confidence: 99%

“…This, indeed, is what is needed to achieve NNLL precision for non-relativistic sum rules and t-t production near threshold. As the spin-dependent (and l = 0) contribution has already been computed in earlier papers [9,10,7], we only consider here energy averages of S-wave states where the spin-dependent contributions vanish, and only include terms relevant for the N 3 LL S-wave spin-average energy.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

2018

Self Cite

View full text Add to dashboard Cite

We obtain the Potential NRQCD Lagrangian relevant for S-wave states with next-next-to-next-to-leading logarithmic (NNNLL) accuracy. We compute the heavy quarkonium mass of spin-averaged l = 0 (angular momentum) states, with otherwise arbitrary quantum numbers, with NNNLL accuracy. These results are complete up to a missing contribution of the two-loop soft running. 1 We use the term "delta(-like) potentials" for the delta potential and the potentials generated by the Fourier transform of ln n k (in practice only ln k). 2 These are known at O(1/m) [11], O(1/m 2 ) [12, 13] and O(1/m 3 ) [14].

show abstract

Section: Introductionmentioning

confidence: 87%

Section: Pnrqcd Lagrangianmentioning

confidence: 99%

“…The spin-dependent case was computed in [9,10]. Explicit expressions for the potentials can be found in the Appendix of [36].…”

Section: Nrqcd-pnrqcd Matching Spin-independentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

2018

Self Cite

View full text Add to dashboard Cite

show abstract

Higher-order QCD perturbation theory in different schemes: from FOPT to CIPT to FAPT

Bakulev¹,

Михайлов²,

Stefanis

2010

J. High Energ. Phys.

View full text Add to dashboard Cite

Results on the resummation of non-power-series expansions of the Adler function of a scalar, D S , and a vector, D V , correlator are presented within fractional analytic perturbation theory (FAPT). The first observable can be used to determine the decay width Γ H→bb of a scalar Higgs boson to a bottom-antibottom pair, while the second one is relevant for the e + e − annihilation cross section. The obtained estimates are compared with those from fixed-order (FOPT) and contour-improved perturbation theory (CIPT), working out the differences. We prove that although FAPT and CIPT are conceptually different, they yield identical results. The convergence properties of these expansions are discussed and predictions are extracted for the resummed series of R S and D V using one-and two-loop coupling running, and making use of appropriate generating functions for the coefficients of the perturbative series.Since the original work of Shirkov and Solovtsov [1] appeared in 1997, the analytic approach to QCD perturbation theory has evolved and progressed considerably. At the heart of this approach is the spectral density which provides the means to define an analytic running coupling in the Euclidean space via a dispersion relation in accordance with causality and renormalization-group (RG) invariance. Using the same spectral density one can also define the running coupling in Minkowski space by employing the dispersion relation for the Adler function [2][3][4][5]. In parallel, this approach has been extended beyond the one-loop level [5,6] and analytic and numerical tools for its application have been developed [7][8][9][10][11][12]. These efforts culminated in a systematic calculational framework, termed Analytic Perturbation Theory (APT), recently reviewed in [13].The simple analytization of the running coupling and its integer powers has been generalized to the level of hadronic amplitudes [14,15] as a whole and new techniques have been developed to deal with more than one (large) momentum scale [16][17][18] (for a brief exposition, see [19]). This encompassing version of analytization includes all terms that may contribute to the spectral density, i.e., affect the discontinuity across the cut along the negative real axis −∞ < Q 2 < 0. It turns out that logarithms of the second large scale, which can be the factorization scale in higher-order perturbative calculations or the evolution scale, correspond to non-integer indices of the analytic couplings, giving rise-in Euclidean space-to Fractional Analytic Perturbation Theory (FAPT) [20,21]. This concept was successfully extended to the timelike region and a unified description in the whole complex momentum space was achieved [22] (see also [23,24]). The issue of crossing heavy-flavor thresholds, naturally entering such calculations, has been considered within APT [13,18,25,26] and more recently also within FAPT [27].Another important topic, which is at the core of the present investigation, deals with the perturbative summation in (F)APT. As it has been demonstrated in [2...

show abstract

Heavy-Quark Hybrid Mass Splittings: Hyperfine and “Ultrafine”

Lebed

Swanson

2018

Few-Body Syst

View full text Add to dashboard Cite

It is argued that the heavy-quark limit of QCD requires a certain combination of hyperfine mass splittings in heavy-quark hybrid-meson multiplets to be unusually small. This observation will assist in the exploration of the heavy-quark hybrid spectrum at facilities such as PANDA. Alternatively, a large measured value for this mass splitting indicates that at least one member of the multiplet must contain significant light-quark degrees of freedom.

show abstract

Erratum to “M(Bc∗)–M(Bc) splitting from nonrelativistic renormalization group” [Ph

Cited by 12 publications

References 0 publications

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

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

Higher-order QCD perturbation theory in different schemes: from FOPT to CIPT to FAPT

Heavy-Quark Hybrid Mass Splittings: Hyperfine and “Ultrafine”

Contact Info

Product

Resources

About