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The D and B couplings from light-cone sum rules

A preprint version of the article is available at arXiv.

Abstract

We revisit the calculation of the strong couplings D and B from the QCD light-cone sum rules using the pion light-cone distribution amplitudes. The accuracy of the correlation function, calculated from the operator product expansion near the light-cone, is upgraded by taking into account the gluon radiative corrections to the twist-3 terms. The double spectral density of the correlation function, including the twist-2, 3 terms at \( \mathcal{O}\left({\alpha}_s\right) \) and the twist-4 LO terms, is presented in an analytical form for the first time. This form allows us to use various versions of the quark-hadron duality regions in the double dispersion relation underlying the sum rules. We predict \( {g}_{D^{\ast } D\pi}={14.1}_{-1.2}^{+1.3} \) and \( {g}_{B^{\ast } B\pi}={30.0}_{-2.4}^{+2.6} \) when the decay constants of heavy mesons entering the light-cone sum rule are taken from lattice QCD results. We compare our results with the experimental value for the charmed meson coupling and with the lattice QCD calculations.

References

  1. CLEO collaboration, First measurement of Γ(D∗+) and precision measurement of m(D∗+) − m(D0), Phys. Rev. D 65 (2002) 032003 [hep-ex/0108043] [INSPIRE].

  2. BaBar collaboration, Measurement of the D ∗ (2010)+ meson width and the D ∗ (2010)+ − D0 mass difference, Phys. Rev. Lett. 111 (2013) 111801 [arXiv:1304.5657] [INSPIRE].

  3. Particle Data Group collaboration, Review of particle physics, PTEP 2020 (2020) 083C01 [INSPIRE].

  4. G. Burdman and J. F. Donoghue, Union of chiral and heavy quark symmetries, Phys. Lett. B 280 (1992) 287 [INSPIRE].

    ADS  Article  Google Scholar 

  5. M. B. Wise, Chiral perturbation theory for hadrons containing a heavy quark, Phys. Rev. D 45 (1992) 2188 [INSPIRE].

    ADS  Article  Google Scholar 

  6. T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y.C. Lin and H.-L. Yu, Heavy quark symmetry and chiral dynamics, Phys. Rev. D 46 (1992) 1148 [Erratum ibid. 55 (1997) 5851] [INSPIRE].

  7. D. Becirevic, B. Blossier, E. Chang and B. Haas, \( {g}_{B^{\ast } B\pi} \)-coupling in the static heavy quark limit, Phys. Lett. B 679 (2009) 231 [arXiv:0905.3355] [INSPIRE].

    ADS  Article  Google Scholar 

  8. D. Becirevic and F. Sanfilippo, Theoretical estimate of the D→ Dπ decay rate, Phys. Lett. B 721 (2013) 94 [arXiv:1210.5410] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  9. K. U. Can, G. Erkol, M. Oka, A. Ozpineci and T. T. Takahashi, Vector and axial-vector couplings of D and Dmesons in 2 + 1 flavor lattice QCD, Phys. Lett. B 719 (2013) 103 [arXiv:1210.0869] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  10. W. Detmold, C. J. D. Lin and S. Meinel, Calculation of the heavy-hadron axial couplings g1, g2 and g3 using lattice QCD, Phys. Rev. D 85 (2012) 114508 [arXiv:1203.3378] [INSPIRE].

    ADS  Article  Google Scholar 

  11. ALPHA collaboration, Precision lattice QCD computation of the BBπ coupling, Phys. Lett. B 740 (2015) 278 [arXiv:1404.6951] [INSPIRE].

  12. RBC and UKQCD collaborations, The BBπ coupling using relativistic heavy quarks, Phys. Rev. D 93 (2016) 014510 [arXiv:1506.06413] [INSPIRE].

  13. V. M. Belyaev, V. M. Braun, A. Khodjamirian and R. Ruckl, DDπ and BBπ couplings in QCD, Phys. Rev. D 51 (1995) 6177 [hep-ph/9410280] [INSPIRE].

    ADS  Article  Google Scholar 

  14. I. I. Balitsky, V. M. Braun and A. V. Kolesnichenko, Σ+ → Pγ decay in QCD, (in Russian), Sov. J. Nucl. Phys. 44 (1986) 1028 [Yad. Fiz. 44 (1986) 1582] [INSPIRE].

  15. I. I. Balitsky, V. M. Braun and A. V. Kolesnichenko, Radiative decay Σ+ → pγ in quantum chromodynamics, Nucl. Phys. B 312 (1989) 509 [INSPIRE].

    ADS  Article  Google Scholar 

  16. V. L. Chernyak and I. R. Zhitnitsky, B meson exclusive decays into baryons, Nucl. Phys. B 345 (1990) 137 [INSPIRE].

    ADS  Article  Google Scholar 

  17. V. M. Braun and I. E. Filyanov, QCD sum rules in exclusive kinematics and pion wave function, Z. Phys. C 44 (1989) 157 [Sov. J. Nucl. Phys. 50 (1989) 511] [Yad. Fiz. 50 (1989) 818] [INSPIRE].

  18. A. Khodjamirian, R. Rückl, S. Weinzierl and O. I. Yakovlev, Perturbative QCD correction to the B → π transition form factor, Phys. Lett. B 410 (1997) 275 [hep-ph/9706303] [INSPIRE].

    ADS  Article  Google Scholar 

  19. E. Bagan, P. Ball and V. M. Braun, Radiative corrections to the decay B → πeν and the heavy quark limit, Phys. Lett. B 417 (1998) 154 [hep-ph/9709243] [INSPIRE].

    ADS  Article  Google Scholar 

  20. P. Ball and R. Zwicky, New results on B → π, K, η decay formfactors from light-cone sum rules, Phys. Rev. D 71 (2005) 014015 [hep-ph/0406232] [INSPIRE].

    ADS  Article  Google Scholar 

  21. G. Duplancic, A. Khodjamirian, T. Mannel, B. Melić and N. Offen, Light-cone sum rules for B → π form factors revisited, JHEP 04 (2008) 014 [arXiv:0801.1796] [INSPIRE].

    ADS  Article  Google Scholar 

  22. A. Khodjamirian, C. Klein, T. Mannel and N. Offen, Semileptonic charm decays D → πℓν and D → Klν from QCD light-cone sum rules, Phys. Rev. D 80 (2009) 114005 [arXiv:0907.2842] [INSPIRE].

    ADS  Article  Google Scholar 

  23. A. Khodjamirian, R. Ruckl, S. Weinzierl and O. I. Yakovlev, Perturbative QCD correction to the light cone sum rule for the BBπ and DDπ couplings, Phys. Lett. B 457 (1999) 245 [hep-ph/9903421] [INSPIRE].

    ADS  Article  Google Scholar 

  24. A. Khodjamirian, QCD sum rules for heavy flavor physics, AIP Conf. Proc. 602 (2001) 194 [hep-ph/0108205] [INSPIRE].

    ADS  Article  Google Scholar 

  25. D. Becirevic, J. Charles, A. LeYaouanc, L. Oliver, O. Pene and J. C. Raynal, Possible explanation of the discrepancy of the light cone QCD sum rule calculation of g(D) coupling with experiment, JHEP 01 (2003) 009 [hep-ph/0212177] [INSPIRE].

    ADS  Article  Google Scholar 

  26. A. V. Rusov, Higher-twist effects in light-cone sum rule for the B → π form factor, Eur. Phys. J. C 77 (2017) 442 [arXiv:1705.01929] [INSPIRE].

    ADS  Article  Google Scholar 

  27. A. Bharucha, Two-loop corrections to the Btoπ form factor from QCD sum rules on the light-cone and |Vub|, JHEP 05 (2012) 092 [arXiv:1203.1359] [INSPIRE].

    ADS  Article  Google Scholar 

  28. P. Gelhausen, A. Khodjamirian, A. A. Pivovarov and D. Rosenthal, Decay constants of heavy-light vector mesons from QCD sum rules, Phys. Rev. D 88 (2013) 014015 [Erratum ibid. 89 (2014) 099901] [Erratum ibid. 91 (2015) 099901] [arXiv:1305.5432] [INSPIRE].

  29. A. Y. Khodjamirian, Dispersion sum rules for the amplitudes of radiative transitions in quarkonium, Phys. Lett. B 90 (1980) 460 [INSPIRE].

    ADS  Article  Google Scholar 

  30. B. L. Ioffe and A. V. Smilga, Meson widths and form-factors at intermediate momentum transfer in nonperturbative QCD, Nucl. Phys. B 216 (1983) 373 [INSPIRE].

    ADS  Article  Google Scholar 

  31. V. A. Nesterenko and A. V. Radyushkin, Sum rules and pion form-factor in QCD, Phys. Lett. B 115 (1982) 410 [INSPIRE].

    ADS  Article  Google Scholar 

  32. P. Colangelo and A. Khodjamirian, QCD sum rules, a modern perspective, hep-ph/0010175 [INSPIRE].

  33. M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, QCD and resonance physics. Theoretical foundations, Nucl. Phys. B 147 (1979) 385 [INSPIRE].

    ADS  Article  Google Scholar 

  34. P. Ball, V. M. Braun and A. Lenz, Higher-twist distribution amplitudes of the K meson in QCD, JHEP 05 (2006) 004 [hep-ph/0603063] [INSPIRE].

    ADS  Article  Google Scholar 

  35. V. M. Braun and I. E. Filyanov, Conformal invariance and pion wave functions of nonleading twist, Z. Phys. C 48 (1990) 239 [Sov. J. Nucl. Phys. 52 (1990) 126] [Yad. Fiz. 52 (1990) 199] [INSPIRE].

  36. H.-D. Li, C.-D. Lü, C. Wang, Y.-M. Wang and Y.-B. Wei, QCD calculations of radiative heavy meson decays with subleading power corrections, JHEP 04 (2020) 023 [arXiv:2002.03825] [INSPIRE].

    ADS  Article  Google Scholar 

  37. A. Khodjamirian, C. Klein, T. Mannel and Y.-M. Wang, Form factors and strong couplings of heavy baryons from QCD light-cone sum rules, JHEP 09 (2011) 106 [arXiv:1108.2971] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  38. P. Ball and R. Zwicky, Improved analysis of B → πeν from QCD sum rules on the light cone, JHEP 10 (2001) 019 [hep-ph/0110115] [INSPIRE].

    ADS  Article  Google Scholar 

  39. M. Neubert, Heavy meson form-factors from QCD sum rules, Phys. Rev. D 45 (1992) 2451 [INSPIRE].

    ADS  Article  Google Scholar 

  40. B. Blok and M. A. Shifman, The Isgur-Wise function in the small velocity limit, Phys. Rev. D 47 (1993) 2949 [hep-ph/9207217] [INSPIRE].

    ADS  Article  Google Scholar 

  41. Flavour Lattice Averaging Group collaboration, FLAG review 2019, Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE].

  42. ETM collaboration, Masses and decay constants of \( {D}_{(s)}^{\ast } \) and \( {B}_{(s)}^{\ast } \) mesons with Nf = 2 + 1 + 1 twisted mass fermions, Phys. Rev. D 96 (2017) 034524 [arXiv:1707.04529] [INSPIRE].

  43. K. G. Chetyrkin, J. H. Kühn and M. Steinhauser, RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses, Comput. Phys. Commun. 133 (2000) 43 [hep-ph/0004189] [INSPIRE].

    ADS  MATH  Article  Google Scholar 

  44. B. L. Ioffe, Condensates in quantum chromodynamics, Phys. Atom. Nucl. 66 (2003) 30 [Yad. Fiz. 66 (2003) 32] [hep-ph/0207191] [INSPIRE].

  45. RQCD collaboration, Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD, JHEP 08 (2019) 065 [Addendum ibid. 11 (2020) 037] [arXiv:1903.08038] [INSPIRE].

  46. A. Khodjamirian, Form-factors of γρ → π and γγ → π0 transitions and light cone sum rules, Eur. Phys. J. C 6 (1999) 477 [hep-ph/9712451] [INSPIRE].

    ADS  Article  Google Scholar 

  47. S. S. Agaev, V. M. Braun, N. Offen and F. A. Porkert, BELLE data on the π0 γγ form factor: a game changer?, Phys. Rev. D 86 (2012) 077504 [arXiv:1206.3968] [INSPIRE].

    ADS  Article  Google Scholar 

  48. H.-N. Li, Y.-L. Shen and Y.-M. Wang, Joint resummation for pion wave function and pion transition form factor, JHEP 01 (2014) 004 [arXiv:1310.3672] [INSPIRE].

    ADS  Article  Google Scholar 

  49. Y.-M. Wang and Y.-L. Shen, Subleading power corrections to the pion-photon transition form factor in QCD, JHEP 12 (2017) 037 [arXiv:1706.05680] [INSPIRE].

    ADS  Article  Google Scholar 

  50. V. M. Braun, A. Khodjamirian and M. Maul, Pion form-factor in QCD at intermediate momentum transfers, Phys. Rev. D 61 (2000) 073004 [hep-ph/9907495] [INSPIRE].

    ADS  Article  Google Scholar 

  51. S. Cheng, A. Khodjamirian and A. V. Rusov, Pion light-cone distribution amplitude from the pion electromagnetic form factor, Phys. Rev. D 102 (2020) 074022 [arXiv:2007.05550] [INSPIRE].

    ADS  Article  Google Scholar 

  52. A. Khodjamirian, T. Mannel, N. Offen and Y. M. Wang, B → πℓνl width and |Vub| from QCD light-cone sum rules, Phys. Rev. D 83 (2011) 094031 [arXiv:1103.2655] [INSPIRE].

    ADS  Article  Google Scholar 

  53. A. Ali, V. M. Braun and H. Simma, Exclusive radiative B decays in the light cone QCD sum rule approach, Z. Phys. C 63 (1994) 437 [hep-ph/9401277] [INSPIRE].

    ADS  Article  Google Scholar 

  54. A. Khodjamirian, R. Ruckl and C. W. Winhart, The scalar B → π and D → π form-factors in QCD, Phys. Rev. D 58 (1998) 054013 [hep-ph/9802412] [INSPIRE].

    ADS  Article  Google Scholar 

  55. C. G. Boyd and B. Grinstein, Chiral and heavy quark symmetry violation in B decays, Nucl. Phys. B 442 (1995) 205 [hep-ph/9402340] [INSPIRE].

    ADS  Article  Google Scholar 

  56. R. Casalbuoni, A. Deandrea, N. Di Bartolomeo, R. Gatto, F. Feruglio and G. Nardulli, Phenomenology of heavy meson chiral Lagrangians, Phys. Rept. 281 (1997) 145 [hep-ph/9605342] [INSPIRE].

    ADS  Article  Google Scholar 

  57. J. Rohrwild, Determination of the magnetic susceptibility of the quark condensate using radiative heavy meson decays, JHEP 09 (2007) 073 [arXiv:0708.1405] [INSPIRE].

    ADS  Article  Google Scholar 

  58. I. Sentitemsu Imsong, A. Khodjamirian, T. Mannel and D. van Dyk, Extrapolation and unitarity bounds for the B → π form factor, JHEP 02 (2015) 126 [arXiv:1409.7816] [INSPIRE].

    ADS  Article  Google Scholar 

  59. X.-Q. Li, F. Su and Y.-D. Yang, Determination of the strong coupling \( {g}_{B^{\ast } B\pi} \) from semi-leptonic B → πℓν decay, Phys. Rev. D 83 (2011) 054019 [arXiv:1011.0269] [INSPIRE].

    ADS  Article  Google Scholar 

  60. C. Bourrely, I. Caprini and L. Lellouch, Model-independent description of B → πℓν decays and a determination of |Vub|, Phys. Rev. D 79 (2009) 013008 [Erratum ibid. 82 (2010) 099902] [arXiv:0807.2722] [INSPIRE].

  61. Fermilab Lattice and MILC collaborations, |Vub| from B → πℓν decays and (2 + 1)-flavor lattice QCD, Phys. Rev. D 92 (2015) 014024 [arXiv:1503.07839] [INSPIRE].

  62. P. Colangelo and F. De Fazio, QCD interactions of heavy mesons with pions by light cone sum rules, Eur. Phys. J. C 4 (1998) 503 [hep-ph/9706271] [INSPIRE].

    ADS  Article  Google Scholar 

  63. V. L. Eletsky and Y. I. Kogan, Calculation of D→ Dγ and D→ Dπ decay widths from QCD sum rules, Z. Phys. C 28 (1985) 155 [INSPIRE].

    ADS  Article  Google Scholar 

  64. P. Colangelo, F. De Fazio, G. Nardulli, N. Di Bartolomeo and R. Gatto, Strong coupling of excited heavy mesons, Phys. Rev. D 52 (1995) 6422 [hep-ph/9506207] [INSPIRE].

    ADS  Article  Google Scholar 

  65. A. G. Grozin and O. I. Yakovlev, Couplings of heavy hadrons with soft pions from QCD sum rules, Eur. Phys. J. C 2 (1998) 721 [hep-ph/9706421] [INSPIRE].

    ADS  Article  Google Scholar 

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Khodjamirian, A., Melić, B., Wang, YM. et al. The D and B couplings from light-cone sum rules. J. High Energ. Phys. 2021, 16 (2021). https://doi.org/10.1007/JHEP03(2021)016

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Keywords

  • NLO Computations
  • QCD Phenomenology