Journal of High Energy Physics

, 2016:179 | Cite as

Perturbative corrections to Λ b → Λ form factors from QCD light-cone sum rules

  • Yu-Ming WangEmail author
  • Yue-Long Shen
Open Access
Regular Article - Theoretical Physics


We compute radiative corrections to Λ b → Λ from factors, at next-to-leading logarithmic accuracy, from QCD light-cone sum rules with Λ b -baryon distribution amplitudes. Employing the diagrammatic approach factorization of the vacuum-to-Λ b -baryon correlation function is justified at leading power in Λ/m b , with the aid of the method of regions. Hard functions entering the factorization formulae are identical to the corresponding matching coefficients of heavy-to-light currents from QCD onto soft-collinear effective theory. The universal jet function from integrating out the hard-collinear fluctuations exhibits richer structures compared with the one involved in the factorization expressions of the vacuum-to-B-meson correlation function. Based upon the QCD resummation improved sum rules we observe that the perturbative corrections at \( \mathcal{O}\left({\alpha}_s\right) \) shift the Λ b → Λ from factors at large recoil significantly and the dominant contribution originates from the next-to-leading order jet function instead of the hard coefficient functions. Having at hand the sum rule predictions for the Λ b → Λ from factors we further investigate several decay observables in the electro-weak penguin Λ b → Λ + transitions in the factorization limit (i.e., ignoring the “non-factorizable” hadronic effects which cannot be expressed in terms of the Λ b → Λ from factors), including the invariant mass distribution of the lepton pair, the forward-backward asymmetry in the dilepton system and the longitudinal polarization fraction of the leptonic sector.


Resummation Heavy Quark Physics Perturbative QCD 


Open Access

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  1. [1]
    T. Mannel and Y.-M. Wang, Heavy-to-light baryonic form factors at large recoil, JHEP 12 (2011) 067 [arXiv:1111.1849] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  2. [2]
    T. Feldmann and M.W.Y. Yip, Form factors for Lambda b → Λ transitions in SCET, Phys. Rev. D 85 (2012) 014035 [Erratum ibid. D 86 (2012) 079901] [arXiv:1111.1844] [INSPIRE].
  3. [3]
    W. Wang, Factorization of heavy-to-light baryonic transitions in SCET, Phys. Lett. B 708 (2012) 119 [arXiv:1112.0237] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    C.-S. Huang and H.-G. Yan, Exclusive rare decays of heavy baryons to light baryons: Λb → Λγ and Λb → Λ + , Phys. Rev. D 59 (1999) 114022 [Erratum ibid. D 61 (2000) 039901] [hep-ph/9811303] [INSPIRE].
  5. [5]
    C.-H. Chen and C.Q. Geng, Baryonic rare decays of Λb → Λ + , Phys. Rev. D 64 (2001) 074001 [hep-ph/0106193] [INSPIRE].
  6. [6]
    P. Böer, T. Feldmann and D. van Dyk, Angular analysis of the decay Λb → Λ(→ N π) + , JHEP 01 (2015) 155 [arXiv:1410.2115] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    T. Gutsche, M.A. Ivanov, J.G. Korner, V.E. Lyubovitskij and P. Santorelli, Rare baryon decays Λb → Λ + ( = e, μ, τ ) and Λb → Λγ: differential and total rates, lepton- and hadron-side forward-backward asymmetries, Phys. Rev. D 87 (2013) 074031 [arXiv:1301.3737] [INSPIRE].ADSGoogle Scholar
  8. [8]
    A. Khodjamirian, T. Mannel and N. Offen, B-meson distribution amplitude from the Bπ form-factor, Phys. Lett. B 620 (2005) 52 [hep-ph/0504091] [INSPIRE].
  9. [9]
    A. Khodjamirian, T. Mannel and N. Offen, Form-factors from light-cone sum rules with B-meson distribution amplitudes, Phys. Rev. D 75 (2007) 054013 [hep-ph/0611193] [INSPIRE].
  10. [10]
    F. De Fazio, T. Feldmann and T. Hurth, Light-cone sum rules in soft-collinear effective theory, Nucl. Phys. B 733 (2006) 1 [Erratum ibid. B 800 (2008) 405] [hep-ph/0504088] [INSPIRE].
  11. [11]
    F. De Fazio, T. Feldmann and T. Hurth, SCET sum rules for BP and BV transition form factors, JHEP 02 (2008) 031 [arXiv:0711.3999] [INSPIRE].CrossRefGoogle Scholar
  12. [12]
    M. Beneke, T. Feldmann and D. Seidel, Systematic approach to exclusive BV ℓ + , V γ decays, Nucl. Phys. B 612 (2001) 25 [hep-ph/0106067] [INSPIRE].
  13. [13]
    Y.-M. Wang and Y.-L. Shen, QCD corrections to Bπ form factors from light-cone sum rules, Nucl. Phys. B 898 (2015) 563 [arXiv:1506.00667] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
  15. [15]
    P. Ball, V.M. Braun and E. Gardi, Distribution amplitudes of the Λb baryon in QCD, Phys. Lett. B 665 (2008) 197 [arXiv:0804.2424] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    Y.-M. Wang, Y.-L. Shen and C.-D. Lu, Λbp, Λ transition form factors from QCD light-cone sum rules, Phys. Rev. D 80 (2009) 074012 [arXiv:0907.4008] [INSPIRE].ADSGoogle Scholar
  17. [17]
    P. Guo, H.-W. Ke, X.-Q. Li, C.-D. Lu and Y.-M. Wang, Diquarks and the semi-leptonic decay of Λb in the hyrid scheme, Phys. Rev. D 75 (2007) 054017 [hep-ph/0501058] [INSPIRE].
  18. [18]
    C.-D. Lu, Y.-M. Wang, H. Zou, A. Ali and G. Kramer, Anatomy of the pQCD approach to the baryonic decays Λbpπ, pK, Phys. Rev. D 80 (2009) 034011 [arXiv:0906.1479] [INSPIRE].ADSGoogle Scholar
  19. [19]
    G. Bell, T. Feldmann, Y.-M. Wang and M.W.Y. Yip, Light-cone distribution amplitudes for heavy-quark hadrons, JHEP 11 (2013) 191 [arXiv:1308.6114] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    V.M. Braun, S.E. Derkachov and A.N. Manashov, Integrability of the evolution equations for heavy-light baryon distribution amplitudes, Phys. Lett. B 738 (2014) 334 [arXiv:1406.0664] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    M. Knodlseder and N. Offen, Renormalisation of heavy-light light ray operators, JHEP 10 (2011) 069 [arXiv:1105.4569] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  22. [22]
    W. Detmold, C.-J.D. Lin, S. Meinel and M. Wingate, Λb → Λ + form factors and differential branching fraction from lattice QCD, Phys. Rev. D 87 (2013) 074502 [arXiv:1212.4827] [INSPIRE].ADSGoogle Scholar
  23. [23]
    Y.-M. Wang, Y. Li and C.-D. Lu, Rare decays of Λb → Λ + γ and Λb → Λ + + in the light-cone sum rules, Eur. Phys. J. C 59 (2009) 861 [arXiv:0804.0648] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    Y.-L. Liu, C.-Y. Cui and M.-Q. Huang, Higher order light-cone distribution amplitudes of the Λ baryon, Eur. Phys. J. C 74 (2014) 3041 [arXiv:1407.4889] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    V.L. Chernyak and I.R. Zhitnitsky, Nucleon wave function and nucleon form-factors in QCD, Nucl. Phys. B 246 (1984) 52 [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    T.M. Aliev, K. Azizi and M. Savci, Analysis of the Lambda b → Λ + decay in QCD, Phys. Rev. D 81 (2010) 056006 [arXiv:1001.0227] [INSPIRE].ADSGoogle Scholar
  27. [27]
    L.-F. Gan, Y.-L. Liu, W.-B. Chen and M.-Q. Huang, Improved light-cone QCD sum rule analysis of the rare decays Λb → Λγ and Λb → Λ + , Commun. Theor. Phys. 58 (2012) 872 [arXiv:1212.4671] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    V.M. Braun, A. Lenz and M. Wittmann, Nucleon form factors in QCD, Phys. Rev. D 73 (2006) 094019 [hep-ph/0604050] [INSPIRE].
  29. [29]
    X.-G. He, T. Li, X.-Q. Li and Y.-M. Wang, PQCD calculation for Λb → Λγ in the standard model, Phys. Rev. D 74 (2006) 034026 [hep-ph/0606025] [INSPIRE].
  30. [30]
    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].
  31. [31]
    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].ADSCrossRefzbMATHGoogle Scholar
  32. [32]
    B.L. Ioffe, On the choice of quark currents in the QCD sum rules for baryon masses, Z. Phys. C 18 (1983) 67 [INSPIRE].ADSGoogle Scholar
  33. [33]
    Y. Chung, H.G. Dosch, M. Kremer and D. Schall, Baryon sum rules and chiral symmetry breaking, Nucl. Phys. B 197 (1982) 55 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    V.L. Chernyak, A.A. Ogloblin and I.R. Zhitnitsky, Wave functions of octet baryons, Z. Phys. C 42 (1989) 569 [Yad. Fiz. 48 (1988) 1410] [Sov. J. Nucl. Phys. 48 (1988) 896] [INSPIRE].
  35. [35]
    V. Braun, R.J. Fries, N. Mahnke and E. Stein, Higher twist distribution amplitudes of the nucleon in QCD, Nucl. Phys. B 589 (2000) 381 [Erratum ibid. B 607 (2001) 433] [hep-ph/0007279] [INSPIRE].
  36. [36]
    S. Wandzura and F. Wilczek, Sum rules for spin dependent electroproduction: test of relativistic constituent quarks, Phys. Lett. B 72 (1977) 195 [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    G. Bonneau, Zimmermann identities and renormalization group equation in dimensional renormalization, Nucl. Phys. B 167 (1980) 261 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    G. Bonneau, Trace and axial anomalies in dimensional renormalization through Zimmermann like identities, Nucl. Phys. B 171 (1980) 477 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
  40. [40]
    M. Beneke, Y. Kiyo and D.s. Yang, Loop corrections to subleading heavy quark currents in SCET, Nucl. Phys. B 692 (2004) 232 [hep-ph/0402241] [INSPIRE].
  41. [41]
    G. Bell, M. Beneke, T. Huber and X.-Q. Li, Heavy-to-light currents at NNLO in SCET and semi-inclusive \( \overline{B}\to {X}_s{\ell}^{+}{\ell}^{-} \) decay, Nucl. Phys. B 843 (2011) 143 [arXiv:1007.3758] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  42. [42]
    M. Beneke and J. Rohrwild, B meson distribution amplitude from Bγℓν, Eur. Phys. J. C 71 (2011) 1818 [arXiv:1110.3228] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, A formalism for the systematic treatment of rapidity logarithms in quantum field theory, JHEP 05 (2012) 084 [arXiv:1202.0814] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  44. [44]
    H.-N. Li, Y.-L. Shen and Y.-M. Wang, Resummation of rapidity logarithms in B meson wave functions, JHEP 02 (2013) 008 [arXiv:1210.2978] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    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].ADSCrossRefGoogle Scholar
  46. [46]
    Y.-L. Shen and Y.-M. Wang, Rapidity resummation for B-meson wave functions, EPJ Web Conf. 80 (2014) 00047 [arXiv:1409.1048] [INSPIRE].CrossRefGoogle Scholar
  47. [47]
    LHCb collaboration, Measurement of the differential branching fraction of the decay Λ b0 → Λμ + μ , Phys. Lett. B 725 (2013) 25 [arXiv:1306.2577] [INSPIRE].
  48. [48]
    LHCb collaboration, Differential branching fraction and angular analysis of Λ b0 → Λμ + μ decays, JHEP 06 (2015) 115 [arXiv:1503.07138] [INSPIRE].
  49. [49]
    CDF collaboration, T. Aaltonen et al., Observation of the baryonic flavor-changing neutral current decay Λb → Λμ + μ , Phys. Rev. Lett. 107 (2011) 201802 [arXiv:1107.3753] [INSPIRE].
  50. [50]
    M. Beneke and T. Feldmann, Symmetry breaking corrections to heavy to light B meson form-factors at large recoil, Nucl. Phys. B 592 (2001) 3 [hep-ph/0008255] [INSPIRE].
  51. [51]
    S. Groote, J.G. Korner and O.I. Yakovlev, An analysis of diagonal and nondiagonal QCD sum rules for heavy baryons at next-to-leading order in α s, Phys. Rev. D 56 (1997) 3943 [hep-ph/9705447] [INSPIRE].
  52. [52]
    Y.-L. Liu and M.-Q. Huang, Distribution amplitudes of Σ and Λ and their electromagnetic form factors, Nucl. Phys. A 821 (2009) 80 [arXiv:0811.1812] [INSPIRE].ADSCrossRefGoogle Scholar
  53. [53]
    M. Beneke, A. Maier, J. Piclum and T. Rauh, The bottom-quark mass from non-relativistic sum rules at NNNLO, Nucl. Phys. B 891 (2015) 42 [arXiv:1411.3132] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    A. Khodjamirian, T. Mannel, N. Offen and Y.-M. Wang, Bπℓν width and |V ub| from QCD light-cone sum rules, Phys. Rev. D 83 (2011) 094031 [arXiv:1103.2655] [INSPIRE].ADSGoogle Scholar
  55. [55]
    A. Khodjamirian, T. Mannel, A.A. Pivovarov and Y.-M. Wang, Charm-loop effect in BK (∗) + and BK γ, JHEP 09 (2010) 089 [arXiv:1006.4945] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  56. [56]
    H.-N. Li, Y.-L. Shen and Y.-M. Wang, Next-to-leading-order corrections to Bπ form factors in k T factorization, Phys. Rev. D 85 (2012) 074004 [arXiv:1201.5066] [INSPIRE].ADSGoogle Scholar
  57. [57]
    W.-F. Wang and Z.-J. Xiao, The semileptonic decays \( B/{B}_s\to \left(\pi,\ K\right)\left({\ell}^{+}{\ell}^{-},\ \ell \nu,\ \nu \overline{\nu}\right) \) in the perturbative QCD approach beyond the leading-order, Phys. Rev. D 86 (2012) 114025 [arXiv:1207.0265] [INSPIRE].ADSGoogle Scholar
  58. [58]
    S. Groote, J.G. Korner and O.I. Yakovlev, QCD sum rules for heavy baryons at next-to-leading order in α s, Phys. Rev. D 55 (1997) 3016 [hep-ph/9609469] [INSPIRE].
  59. [59]
    C. Bourrely, I. Caprini and L. Lellouch, Model-independent description of Bπℓν decays and a determination of |V ub|, Phys. Rev. D 79 (2009) 013008 [Erratum ibid. D 82 (2010) 099902] [arXiv:0807.2722] [INSPIRE].
  60. [60]
    W. Detmold, C. Lehner and S. Meinel, \( {\varLambda}_b\to p{\ell}^{-}{\overline{\nu}}_{\ell } \) and \( {\varLambda}_b\to\ {\varLambda}_c{\ell}^{-}{\overline{\nu}}_{\ell } \) form factors from lattice QCD with relativistic heavy quarks, Phys. Rev. D 92 (2015) 034503 [arXiv:1503.01421] [INSPIRE].ADSGoogle Scholar
  61. [61]
    Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  62. [62]
    W.A. Bardeen, E.J. Eichten and C.T. Hill, Chiral multiplets of heavy-light mesons, Phys. Rev. D 68 (2003) 054024 [hep-ph/0305049] [INSPIRE].
  63. [63]
    A.V. Manohar and M.B. Wise, Heavy quark physics, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 10 (2000) 1 [INSPIRE].Google Scholar
  64. [64]
    T. Mannel and S. Recksiegel, Flavor changing neutral current decays of heavy baryons: the case Λb → Λγ, J. Phys. G 24 (1998) 979 [hep-ph/9701399] [INSPIRE].
  65. [65]
    F. Hussain, D.-S. Liu, M. Krämer, J.G. Korner and S. Tawfiq, General analysis of weak decay form-factors in heavy to heavy and heavy to light baryon transitions, Nucl. Phys. B 370 (1992) 259 [INSPIRE].ADSCrossRefGoogle Scholar
  66. [66]
    Y.-M. Wang, Beauty baryon decays: a theoretical overview, J. Phys. Conf. Ser. 556 (2014) 012050 [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    CDF collaboration, H. Miyake, S. Kim and F. Ukegawa, Precise measurements of exclusive b + μ decay amplitudes using the full CDF data set, public note 10894, Fermilab, Batavia U.S.A. (1992).
  68. [68]
    LHCb collaboration, Determination of the quark coupling strength |V ub| using baryonic decays, Nature Phys. 11 (2015) 743 [arXiv:1504.01568] [INSPIRE].

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Authors and Affiliations

  1. 1.Fakultät für PhysikUniversität WienViennaAustria
  2. 2.Physik Department T31Technische Universität MünchenGarchingGermany
  3. 3.College of Information Science and EngineeringOcean University of ChinaQingdaoP.R. China

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