Abstract
In the framework of the QCD light-cone sum rules (LCSRs) we present the analysis of all B, B s → η (′) and D, D s → η (′) form factors (f + , f 0 and f T) by including \( {m}_{\eta^{\left(\prime \right)}}^2 \) corrections in the leading (up to the twist-four) and next-to-leading order (up to the twist-three) in QCD, and two-gluon contributions to the form factors at the leading twist. The SU(3)-flavour breaking corrections and the axial anomaly contributions to the distribution amplitudes are also consistently taken into account. The complete results for the f 0 and f T form factors of B, B s → η (′) and D, D s → η (′) relevant for processes like B → η (′) τν τ or B s → η (′) l + l − are given for the first time, as well as the two-gluon contribution to the tensor form factors. The values obtained for the f + form factors are as follows: \( {f}_{B\eta}^{+}(0)=0.{168}_{-0.047}^{+0.042},\left|{f}_{B_s\eta}^{+}(0)\right|=0.{212}_{-0.013}^{+0.015},{f}_{B\eta \prime}^{+}(0)=0.13{0}_{-0.032}^{+0.036},{f}_{B_s\eta \prime}^{+}(0)=0.{252}_{-0.020}^{+0.023} \) and \( {f}_{D\eta}^{+}(0)=0.{429}_{-0.141}^{+0.165},\left|{f}_{D_s\eta}^{+}(0)\right|={0.495}_{-0.029}^{+0.030},{f}_{D\eta \prime}^{+}(0)={0.292}_{-0.104}^{+0.113},{f}_{D_s\eta \prime}^{+}(0)={0.558}_{-0.045}^{+0.047} \). Also phenomenological predictions for semileptonic B, B s → η (′) and D, D s → η (′) decay modes are given.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Particle Data Group collaboration, K.A. Olive et al., Review of Particle Physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
B. Melić, Nonfactorizable corrections to B → J/ψK, Phys. Rev. D 68 (2003) 034004 [hep-ph/0303250] [INSPIRE].
B. Melić, LCSR analysis of exclusive two body B decay into charmonium, Phys. Lett. B 591 (2004) 91 [hep-ph/0404003] [INSPIRE].
D. Bečirević, G. Duplančić, B. Klajn, B. Melić and F. Sanfilippo, Lattice QCD and QCD sum rule determination of the decay constants of η c , J/ψ and h c states, Nucl. Phys. B 883 (2014) 306 [arXiv:1312.2858] [INSPIRE].
P. Colangelo, F. De Fazio and W. Wang, Nonleptonic B s to charmonium decays: analyses in pursuit of determining the weak phase β s , Phys. Rev. D 83 (2011) 094027 [arXiv:1009.4612] [INSPIRE].
R. Fleischer, R. Knegjens and G. Ricciardi, Exploring CP-violation and η-η′ Mixing with the B 0 s,d → J/ψη (′) Systems, Eur. Phys. J. C 71 (2011) 1798 [arXiv:1110.5490] [INSPIRE].
LHCb collaboration, Study of η-η′ mixing from measurement of B 0(s) → J/ψη (′) decay rates, JHEP 01 (2015) 024 [arXiv:1411.0943] [INSPIRE].
I.I. Balitsky, V.M. Braun and A.V. Kolesnichenko, Radiative Decay σ + → pγ in Quantum Chromodynamics, Nucl. Phys. B 312 (1989) 509 [INSPIRE].
V.M. Braun and I.E. Filyanov, QCD Sum Rules in Exclusive Kinematics and Pion Wave Function, Z. Phys. C 44 (1989) 157 [INSPIRE].
V.L. Chernyak and I.R. Zhitnitsky, B meson exclusive decays into baryons, Nucl. Phys. B 345 (1990) 137 [INSPIRE].
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].
A. Khodjamirian, C. Klein, T. Mannel and N. Offen, Semileptonic charm decays D → πlν l and D → Klν l from QCD Light-Cone Sum Rules, Phys. Rev. D 80 (2009) 114005 [arXiv:0907.2842] [INSPIRE].
G. Duplančić, 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].
G. Duplančić and B. Melić, B, B(s) → K form factors: An Update of light-cone sum rule results, Phys. Rev. D 78 (2008) 054015 [arXiv:0805.4170] [INSPIRE].
S.S. Agaev, V.M. Braun, N. Offen, F. Porkert and A. Schäfer, Transition form factors γ * γ → η and γ * γ → η′ in QCD, Phys. Rev. D 90 (2014) 074019 [arXiv:1409.4311] [INSPIRE].
P. Ball and G.W. Jones, B → η (′) Form Factors in QCD, JHEP 08 (2007) 025 [arXiv:0706.3628] [INSPIRE].
P. Kroll and K. Passek-Kumericki, The Two gluon components of the η and η′ mesons to leading twist accuracy, Phys. Rev. D 67 (2003) 054017 [hep-ph/0210045] [INSPIRE].
T. Feldmann, P. Kroll and B. Stech, Mixing and decay constants of pseudoscalar mesons, Phys. Rev. D 58 (1998) 114006 [hep-ph/9802409] [INSPIRE].
F. Ambrosino et al., A Global fit to determine the pseudoscalar mixing angle and the gluonium content of the η′ meson, JHEP 07 (2009) 105 [arXiv:0906.3819] [INSPIRE].
C. Di Donato, G. Ricciardi and I. Bigi, η − η′ Mixing — From electromagnetic transitions to weak decays of charm and beauty hadrons, Phys. Rev. D 85 (2012) 013016 [arXiv:1105.3557] [INSPIRE].
ETM collaboration, C. Michael, K. Ottnad and C. Urbach, η and η′ mixing from Lattice QCD, Phys. Rev. Lett. 111 (2013) 181602 [arXiv:1310.1207] [INSPIRE].
V.N. Baier and A.G. Grozin, Meson Wave Functions With Two Gluon States, Nucl. Phys. B 192 (1981) 476 [INSPIRE].
B. Melić, B. Nizic and K. Passek, A Note on the factorization scale independence of the PQCD predictions for exclusive processes, Eur. Phys. J. C 36 (2004) 453 [hep-ph/0107311] [INSPIRE].
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].
M. Beneke and M. Neubert, Flavor singlet B decay amplitudes in QCD factorization, Nucl. Phys. B 651 (2003) 225 [hep-ph/0210085] [INSPIRE].
M. Jamin and B.O. Lange, f B and \( {f}_{B_s} \) from QCD sum rules, Phys. Rev. D 65 (2002) 056005 [hep-ph/0108135] [INSPIRE].
G.P. Lepage and S.J. Brodsky, Exclusive Processes in Quantum Chromodynamics: Evolution Equations for Hadronic Wave Functions and the Form-Factors of Mesons, Phys. Lett. B 87 (1979) 359 [INSPIRE].
G.P. Lepage and S.J. Brodsky, Exclusive Processes in Perturbative Quantum Chromodynamics, Phys. Rev. D 22 (1980) 2157 [INSPIRE].
A.V. Efremov and A.V. Radyushkin, Factorization and Asymptotical Behavior of Pion Form-Factor in QCD, Phys. Lett. B 94 (1980) 245 [INSPIRE].
A.V. Efremov and A.V. Radyushkin, Asymptotical Behavior of Pion Electromagnetic Form-Factor in QCD, Theor. Math. Phys. 42 (1980) 97 [Teor. Mat. Fiz. 42 (1980) 147] [INSPIRE].
M.V. Terentev, Factorization In Exclusive Processes. Form-factor Of Singlet Mesons In Quantum Chromodynamics (in Russian), Sov. J. Nucl. Phys. 33 (1981) 911 [Yad. Fiz. 33 (1981) 1692] [INSPIRE].
B. Melić, B. Nizic and K. Passek, BLM scale setting for the pion transition form-factor, Phys. Rev. D 65 (2002) 053020 [hep-ph/0107295] [INSPIRE].
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].
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. D 89 (2014) 099901] [arXiv:1305.5432] [INSPIRE].
HPQCD collaboration, R.J. Dowdall, C.T.H. Davies, R.R. Horgan, C.J. Monahan and J. Shigemitsu, B-Meson Decay Constants from Improved Lattice Nonrelativistic QCD with Physical u, d, s and c Quarks, Phys. Rev. Lett. 110 (2013) 222003 [arXiv:1302.2644] [INSPIRE].
Fermilab Lattice and MILC collaborations, A. Bazavov et al., Charmed and light pseudoscalar meson decay constants from four-flavor lattice QCD with physical light quarks, Phys. Rev. D 90 (2014) 074509 [arXiv:1407.3772] [INSPIRE].
N. Carrasco et al., Leptonic decay constants f K , f D , and \( {f}_{D_s} \) with N f = 2 + 1 + 1 twisted-mass lattice QCD, Phys. Rev. D 91 (2015) 054507 [arXiv:1411.7908] [INSPIRE].
N. Offen, F.A. Porkert and A. Schäfer, Light-cone sum rules for the D (s) → η (′) lν l form factor, Phys. Rev. D 88 (2013) 034023 [arXiv:1307.2797] [INSPIRE].
Y.-Y. Charng, T. Kurimoto and H.-n. Li, Gluonic contribution to B → η (′) form factors, Phys. Rev. D 74 (2006) 074024 [Erratum ibid. D 78 (2008) 059901] [hep-ph/0609165] [INSPIRE].
T.M. Aliev, I. Kanik and A. Ozpineci, Semileptonic B → ηlν decay in light cone QCD, Phys. Rev. D 67 (2003) 094009 [hep-ph/0210403] [INSPIRE].
T.M. Aliev and M. Savci, Form-factor for penguin-induced B → η transitions in light cone QCD sum rules, Eur. Phys. J. C 29 (2003) 515 [hep-ph/0302187] [INSPIRE].
P. Colangelo and F. De Fazio, D s decays to η and η′ final states: A Phenomenological analysis, Phys. Lett. B 520 (2001) 78 [hep-ph/0107137] [INSPIRE].
K. Azizi, R. Khosravi and F. Falahati, Exclusive D s → (η, η′)lν decays in light cone QCD, J. Phys. G 38 (2011) 095001 [arXiv:1011.6046] [INSPIRE].
G.S. Bali, S. Collins, S. Dürr and I. Kanamori, D s → η, η′ semileptonic decay form factors with disconnected quark loop contributions, Phys. Rev. D 91 (2015) 014503 [arXiv:1406.5449] [INSPIRE].
D. Bečirević and A.B. Kaidalov, Comment on the heavy → light form-factors, Phys. Lett. B 478 (2000) 417 [hep-ph/9904490] [INSPIRE].
G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380] [INSPIRE].
M.V. Carlucci, P. Colangelo and F. De Fazio, Rare B s decays to η and η′ final states, Phys. Rev. D 80 (2009) 055023 [arXiv:0907.2160] [INSPIRE].
CLEO collaboration, J. Yelton et al., Studies of D + → (η′, η, ϕ)e + ν e , Phys. Rev. D 84 (2011) 032001 [arXiv:1011.1195] [INSPIRE].
CLEO collaboration, J. Yelton et al., Absolute Branching Fraction Measurements for Exclusive D s Semileptonic Decays, Phys. Rev. D 80 (2009) 052007 [arXiv:0903.0601] [INSPIRE].
CLEO collaboration, N.E. Adam et al., A Study of Exclusive Charmless Semileptonic B Decay and |V ub |, Phys. Rev. Lett. 99 (2007) 041802 [hep-ex/0703041] [INSPIRE].
BaBar collaboration, P. del Amo Sanchez et al., Measurement of the B 0 → π ℓ ℓ + ν and B + → η (′) ℓ + ν Branching Fractions, the B 0 → π − ℓ + ν and B + → ηℓ + ν Form-Factor Shapes and Determination of |V ub |, Phys. Rev. D 83 (2011) 052011 [arXiv:1010.0987] [INSPIRE].
K. Azizi, R. Khosravi and F. Falahati, Rare Semileptonic B s Decays to η and η′ mesons in QCD, Phys. Rev. D 82 (2010) 116001 [arXiv:1008.3175] [INSPIRE].
H.-M. Choi, Exclusive Rare B s → (K, η, η′)ℓ + ℓ − Decays in the Light-Front Quark Model, J. Phys. G 37 (2010) 085005 [arXiv:1002.0721] [INSPIRE].
R.N. Faustov and V.O. Galkin, Rare B s decays in the relativistic quark model, Eur. Phys. J. C 73 (2013) 2593 [arXiv:1309.2160] [INSPIRE].
A. Khodjamirian, T. Mannel, N. Offen and Y.M. Wang, B → πℓν l Width and |V ub | from QCD Light-Cone Sum Rules, Phys. Rev. D 83 (2011) 094031 [arXiv:1103.2655] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1508.05287
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as 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.
About this article
Cite this article
Duplančić, G., Melić, B. Form factors of B, Bs → η (′) and D, Ds → η (′) transitions from QCD light-cone sum rules. J. High Energ. Phys. 2015, 138 (2015). https://doi.org/10.1007/JHEP11(2015)138
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)138