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Erratum to: Local-duality QCD sum rules for strong isospin breaking in the decay constants of heavy–light mesons

  • Wolfgang Lucha
  • Dmitri Melikhov
  • Silvano Simula
Open Access
Erratum
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1 Erratum to: Eur. Phys. J. C (2018) 78:168 https://doi.org/10.1140/epjc/s10052-018-5637-z

We correct Eq. (1) of the original paper, where the term describing nonperturbative power corrections was not displayed (although taken into account in the analysis). In Eqs. (33) and (34) of the original paper, the references to the wrong bibitems were shown; these are corrected. All material of the paper, except for these typos, remains valid and unchanged.

I. In Eq. (1) of the original paper, the term describing power corrections, \(\Pi ^{(N)}_\mathrm{power}\), was not shown. The correct Eq. (1) reads
$$\begin{aligned}&f_H^2 (M_H^2)^N \mathrm{e}^{-M_H^2 \tau } \nonumber \\&\quad = \int \limits _{(m_Q+m_q)^2}^{s^{(N)}_\mathrm{eff}(\tau , m_Q, m_q, \alpha _s)} \mathrm{d}s \mathrm{e}^{-s \tau } s^N \rho _{\mathrm{pert}}(s, m_Q, m_q, \alpha _s) \nonumber \\&\qquad +\, \Pi ^{(N)}_{\mathrm{power}}(\tau ,m_Q,m_q,\alpha _s,\langle \bar{q}q\rangle ,\ldots ). \end{aligned}$$
(1)
II. In Eqs. (33) and (34) of the original paper, the references were not linked correctly. The references in Eq. (33) should read:
$$\begin{aligned}&(\overline{m}_d - \overline{m}_u) (2\;\mathrm{GeV}) = (2.67 \pm 0.22)\;\mathrm{MeV} ~[2,3], \nonumber \\&\overline{m}_{ud}(2\;\mathrm{GeV}) \equiv \frac{\overline{m}_u + \overline{m}_d}{2} = (3.70 \pm 0.17)\;\mathrm{MeV} ~[2,3],\;\nonumber \\&\overline{m}_s(2\;\mathrm{GeV}) = (93.9 \pm 1.1)\;\mathrm{MeV} ~[2,3],\nonumber \\&\overline{m}_c(\overline{m}_c) = (1.275 \pm 0.025)\;\mathrm{GeV} ~ [4], \nonumber \\&\overline{m}_b(\overline{m}_b) = (4.247 \pm 0.034)\ \mathrm{GeV} ~ [5],\nonumber \\&\alpha _\mathrm{s}(M_Z) = 0.1182 \pm 0.0012 ~ , \end{aligned}$$
(33)
whereas the correct references in Eq. (34) are as follows:
$$\begin{aligned}&f_D=(212.15\pm 1.45)~\mathrm{MeV},\quad \frac{f_{D_s}}{f_D}=1.1716\pm 0.0032 ~ [2,3],\nonumber \\&f_{D^*}=(223.5\pm 8.3)\;\mathrm{MeV},\quad \frac{f_{D^*_s}}{f_{D^*}}=1.203\pm 0.054 ~6, \nonumber \\&f_B=(186.0\pm 4.0)~\mathrm{MeV},\quad \frac{f_{B_s}}{f_B}=1.205\pm 0.007 ~ [2,3],\nonumber \\&f_{B^*}=(186.4\pm 7.1)~\mathrm{MeV},\quad \frac{f_{B^*_s}}{f_{B^*}}=1.197 \pm 0.055 ~ 6. \end{aligned}$$
(34)

References

  1. 1.
    S. Aoki et al., Eur. Phys. J. C 77, 112 (2017). arXiv:1607.00299 [hep-lat]ADSCrossRefGoogle Scholar
  2. 2.
    S. Aoki et al., Eur. Phys. J. C 74, 2890 (2014). arXiv:1310.8555 [hep-lat]ADSCrossRefGoogle Scholar
  3. 3.
    C. Patrignani et al. (Particle Data Group), Chin. Phys. C 40, 100001 (2016)Google Scholar
  4. 4.
    W. Lucha, D. Melikhov, S. Simula, Phys. Rev. D 88, 056011 (2013). arXiv:1305.709 [hep-ph]ADSCrossRefGoogle Scholar
  5. 5.
    V. Lubicz et al. (ETM Collaboration), Phys. Rev. D 96, 034524 (2017). arXiv:1707.04529 [hep-lat]

Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Authors and Affiliations

  • Wolfgang Lucha
    • 1
  • Dmitri Melikhov
    • 1
    • 2
    • 3
  • Silvano Simula
    • 4
  1. 1.Institute for High Energy PhysicsAustrian Academy of SciencesViennaAustria
  2. 2.D. V. Skobeltsyn Institute of Nuclear PhysicsM. V. Lomonosov Moscow State UniversityMoscowRussia
  3. 3.Faculty of PhysicsUniversity of ViennaViennaAustria
  4. 4.Istituto Nazionale di Fisica Nucleare, Sezione di Roma TreRomeItaly

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