Abstract
We analyse the \( \overline{B}_s^0\to {K^{+}}{l^{-}}\overline{\nu} \) and \( \overline{B}_s^0\to {K^{*+ }}\left( {\to K\pi } \right){\ell^{-}}\overline{\nu} \) decays that are valuable for extracting the CKM matrix element |V ub|. We calculate the differential and integrated partial widths in units of |V ub|2 based on various calculations of hadronic form factors and in particular the latest Lattice QCD calculation of the B s → K * form factors. For the decay \( \overline{B}_s^0\to K\pi \ell \overline{\nu} \), we formulate the general angular distributions with the inclusion of the various partial-wave Kπ contributions. Using the results for the Kπ scalar form factor calculated from unitarized chiral perturbation theory, we explore the S-wave effects on angular distribution variables and demonstrate that they may not be negligible, considering the high precision expected in future measurements. We also briefly discuss the impact of the S-wave ππ contributions in the \( {B^{-}}\to {\pi^{+}}{\pi^{-}}\ell \overline{v} \) decay and provide estimates for the mode \( {B^{-}}\to {K^{+}}{K^{-}}\ell \overline{\nu} \). The studies of these channels in future can not only be used to determine |V ub|, but may also provide valuable information on the Kπ and ππ phase shifts.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Heavy Flavor Averaging Group collaboration, Y. Amhis et al., Averages of B-Hadron, C-Hadron and tau-lepton properties as of early 2012, arXiv:1207.1158 [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
A. Khodjamirian, T. Mannel, N. Offen and Y.-M. Wang, B → πℓνl Width and |V ub| from QCD Light-Cone Sum Rules, Phys. Rev. D 83 (2011) 094031 [arXiv:1103.2655] [INSPIRE].
BaBar collaboration, P. del Amo Sanchez et al., Study of B → πℓν and B → ρℓν Decays and Determination of |V ub|, Phys. Rev. D 83 (2011) 032007 [arXiv:1005.3288] [INSPIRE].
A. Bharucha, Two-loop Corrections to the B → π Form Factor from QCD Sum Rules on the Light-Cone and |V (ub)|, JHEP 05 (2012) 092 [arXiv:1203.1359] [INSPIRE].
R.R. Horgan, Z. Liu, S. Meinel and M. Wingate, Lattice QCD calculation of form factors describing the rare decays B → K ∗ℓ+ℓ− and B s → ϕℓ+ℓ−, arXiv:1310.3722 [INSPIRE].
P. Ball and R. Zwicky, B D,S → ρ, ω, K ∗ , ϕ decay form-factors from light-cone sum rules revisited, Phys. Rev. D 71 (2005) 014029 [hep-ph/0412079] [INSPIRE].
W.-F. Wang and Z.-J. Xiao, The semileptonic decays B/B s → (π, K)(ℓ+ℓ− , ℓν, ν\( \overline{\nu} \)) in the perturbative QCD approach beyond the leading-order, Phys. Rev. D 86 (2012) 114025 [arXiv:1207.0265] [INSPIRE].
R. Faustov and V. Galkin, Charmless weak B s decays in the relativistic quark model, Phys. Rev. D 87 (2013) 094028 [arXiv:1304.3255] [INSPIRE].
H.-Y. Cheng, C.-K. Chua and C.-W. Hwang, Covariant light front approach for s wave and p wave mesons: Its application to decay constants and form-factors, Phys. Rev. D 69 (2004) 074025 [hep-ph/0310359] [INSPIRE].
C.-D. Lu, W. Wang and Z.-T. Wei, Heavy-to-light form factors on the light cone, Phys. Rev. D 76 (2007) 014013 [hep-ph/0701265] [INSPIRE].
R. Verma, Decay constants and form factors of s-wave and p-wave mesons in the covariant light-front quark model, J. Phys. G 39 (2012) 025005 [arXiv:1103.2973] [INSPIRE].
F. Krüger, L.M. Sehgal, N. Sinha and R. Sinha, Angular distribution and CP asymmetries in the decays \( \overline{B} \) → K −π+ e − e + and \( \overline{B} \) → π−π+ e − e +,Phys. Rev. D 61 (2000) 114028 [Erratum ibid. D 63 (2001) 019901] [hep-ph/9907386] [INSPIRE].
C.-D. Lu and W. Wang, Analysis of B → \( K_J^{*} \) (→ Kπ)μ + μ − in the higher kaon resonance region, Phys. Rev. D 85 (2012) 034014 [arXiv:1111.1513] [INSPIRE].
M. Döring, U.-G. Meißner and W. Wang, Chiral Dynamics and S-wave Contributions in Semileptonic B decays, JHEP 10 (2013) 011 [arXiv:1307.0947] [INSPIRE].
R.-H. Li, C.-D. Lu and W. Wang, Branching ratios, forward-backward asymmetries and angular distributions of B → \( K_2^{*} \) l + l − in the standard model and new physics scenarios, Phys. Rev. D 83 (2011) 034034 [arXiv:1012.2129] [INSPIRE].
D. Becirevic and A. Tayduganov, Impact of B → K 0ℓ+ℓ− on the New Physics search in B → \( K_0^{*} \)ℓ+ℓ− decay,Nucl. Phys. B 868 (2013) 368 [arXiv:1207.4004] [INSPIRE].
J. Matias, On the S-wave pollution of B → K ∗ℓ+ℓ− observables, Phys. Rev. D 86 (2012) 094024 [arXiv:1209.1525] [INSPIRE].
T. Blake, U. Egede and A. Shires, The effect of S-wave interference on the B 0 → K ∗0ℓ+ℓ− angular observables, JHEP 03 (2013) 027 [arXiv:1210.5279] [INSPIRE].
C. Bobeth, G. Hiller and D. van Dyk, General Analysis of \( \overline{B}\to {{\overline{K}}^{{\left( * \right)}}}{\ell^{+}}{\ell^{-}} \) Decays at Low Recoil, Phys. Rev. D 87 (2013) 034016 [arXiv:1212.2321] [INSPIRE].
S. Descotes-Genon, T. Hurth, J. Matias and J. Virto, Optimizing the basis of B → K ∗ℓ+ℓ− observables in the full kinematic range, JHEP 05 (2013) 137 [arXiv:1303.5794] [INSPIRE].
S. Descotes-Genon, J. Matias and J. Virto, Understanding the B → K ∗ μ + μ − Anomaly, Phys. Rev. D 88 (2013) 074002 [arXiv:1307.5683] [INSPIRE].
F. Berends, A. Donnachie and G. Oades, Theoretical Study of Kl-4 Decay, Phys. Rev. 171 (1968) 1457 [INSPIRE].
G. Kopp, G. Kramer, G. Schuler and W. Palmer, Angular correlations for semileptonic D meson decays, Z. Phys. C 48 (1990) 327 [INSPIRE].
C.L. Lee, M. Lu and M.B. Wise, B l4 and D l4 decay, Phys. Rev. D 46 (1992) 5040 [INSPIRE].
B. Ananthanarayan and K. Shivaraj, Comment on evidence for new interference phenomena in the decay D + → K −π+ μ +ν, Phys. Lett. B 628 (2005) 223 [hep-ph/0508116] [INSPIRE].
S. Faller, T. Feldmann, A. Khodjamirian, T. Mannel and D. van Dyk, Disentangling the Decay Observables in B − → π+π−ℓ− νℓ, arXiv:1310.6660 [INSPIRE].
X.-W. Kang, B. Kubis, C. Hanhart and U.-G. Meißner, B l4 decays and the extraction of |V u b|, arXiv:1312.1193 [INSPIRE].
P. Buettiker, S. Descotes-Genon and B. Moussallam, A new analysis of pi K scattering from Roy and Steiner type equations, Eur. Phys. J. C 33 (2004) 409 [hep-ph/0310283] [INSPIRE].
S. Descotes-Genon and B. Moussallam, The K 0(800) scalar resonance from Roy-Steiner representations of pi K scattering, Eur. Phys. J. C 48 (2006) 553 [hep-ph/0607133] [INSPIRE].
S. Gardner and U.-G. Meißner, Rescattering and chiral dynamics in B → ρπ decay, Phys. Rev. D 65 (2002) 094004 [hep-ph/0112281] [INSPIRE].
J. Gasser and U.G. Meißner, Chiral expansion of pion form-factors beyond one loop, Nucl. Phys. B 357 (1991) 90 [INSPIRE].
J. Oller, E. Oset and J. Palomar, Pion and kaon vector form-factors, Phys. Rev. D 63 (2001) 114009 [hep-ph/0011096] [INSPIRE].
U.-G. Meißner and J. Oller, J/ψ → ϕππ(K \( \overline{K} \)) decays, chiral dynamics and OZI violation, Nucl. Phys. A 679 (2001) 671 [hep-ph/0005253] [INSPIRE].
M. Frink, B. Kubis and U.-G. Meissner, Analysis of the pion kaon sigma term and related topics, Eur. Phys. J. C 25 (2002) 259 [hep-ph/0203193] [INSPIRE].
J. Bijnens and P. Talavera, K(l3) decays in chiral perturbation theory, Nucl. Phys. B 669 (2003) 341 [hep-ph/0303103] [INSPIRE].
T.A. Lähde and U.-G. Meißner, Improved Analysis of J/ψ Decays into a Vector Meson and Two Pseudoscalars, Phys. Rev. D 74 (2006) 034021 [hep-ph/0606133] [INSPIRE].
Z.-H. Guo, J. Oller and J. Ruiz de Elvira, Chiral dynamics in form factors, spectral-function sum rules, meson-meson scattering and semi-local duality, Phys. Rev. D 86 (2012) 054006 [arXiv:1206.4163] [INSPIRE].
J.F. Donoghue, J. Gasser and H. Leutwyler, The Decay of a Light Higgs Boson, Nucl. Phys. B 343 (1990) 341 [INSPIRE].
M. Jamin, J.A. Oller and A. Pich, S-wave Kπ scattering in chiral perturbation theory with resonances, Nucl. Phys. B 587 (2000) 331 [hep-ph/0006045] [INSPIRE].
M. Jamin, J.A. Oller and A. Pich, Strangeness changing scalar form-factors, Nucl. Phys. B 622 (2002) 279 [hep-ph/0110193] [INSPIRE].
M. Jamin, J. Oller and A. Pich, Scalar Kπ form factor and light quark masses, Phys. Rev. D 74 (2006) 074009 [hep-ph/0605095] [INSPIRE].
V. Bernard and E. Passemar, Matching chiral perturbation theory and the dispersive representation of the scalar K pi form-factor, Phys. Lett. B 661 (2008) 95 [arXiv:0711.3450] [INSPIRE].
V. Bernard and E. Passemar, Chiral Extrapolation of the Strangeness Changing K pi Form Factor, JHEP 04 (2010) 001 [arXiv:0912.3792] [INSPIRE].
BaBar collaboration, J. Lees et al., Evidence of B → τ ν decays with hadronic B tags, Phys. Rev. D 88 (2013) 031102 [arXiv:1207.0698] [INSPIRE].
Belle collaboration, I. Adachi et al., Measurement of B − → τ− \( {{\overline{\nu}}_{\tau }} \) with a Hadronic Tagging Method Using the Full Data Sample of Belle, Phys. Rev. Lett. 110 (2013) 131801 [arXiv:1208.4678] [INSPIRE].
T. Hurth and F. Mahmoudi, New physics search with flavour in the LHC era, Rev. Mod. Phys. 85 (2013) 795 [arXiv:1211.6453] [INSPIRE].
BaBar collaboration, J. Lees et al., Evidence for an excess of \( \overline{B}\to {D^{{\left( * \right)}}}{\tau^{-}}{{\overline{\nu}}_{\tau }} \) decays, Phys. Rev. Lett. 109 (2012) 101802 [arXiv:1205.5442] [INSPIRE].
Belle collaboration, A. Sibidanov et al., Study of Exclusive B → X u lν Decays and Extraction of |V ub| using Full Reconstruction Tagging at the Belle Experiment, Phys. Rev. D 88 (2013)032005 [arXiv:1306.2781] [INSPIRE].
H. Hatanaka and K.-C. Yang, Radiative and Semileptonic B Decays Involving Higher K-Resonances in the Final States, Eur. Phys. J. C 67 (2010) 149 [arXiv:0907.1496] [INSPIRE].
W. Wang, B to tensor meson form factors in the perturbative QCD approach, Phys. Rev. D 83 (2011) 014008 [arXiv:1008.5326] [INSPIRE].
K.-C. Yang, B to Light Tensor Meson Form Factors Derived from Light-Cone Sum Rules, Phys. Lett. B 695 (2011) 444 [arXiv:1010.2944] [INSPIRE].
C. Bouchard, G.P. Lepage, C.J. Monahan, H. Na and J. Shigemitsu, B and Bs semileptonic decay form factors with NRQCD/HISQ quarks, arXiv:1310.3207 [INSPIRE].
G. Duplancic and B. Melic, B, B s → K form factors: An Update of light-cone sum rule results, Phys. Rev. D 78 (2008) 054015 [arXiv:0805.4170] [INSPIRE].
Y.-Y. Keum, H.-n. Li and A. Sanda, Fat penguins and imaginary penguins in perturbative QCD, Phys. Lett. B 504 (2001) 6 [hep-ph/0004004] [INSPIRE].
Y. Keum, H.-N. Li and A. Sanda, Penguin enhancement and BKπ decays in perturbative QCD, Phys. Rev. D 63 (2001) 054008 [hep-ph/0004173] [INSPIRE].
C.-D. Lu, K. Ukai and M.-Z. Yang, Branching ratio and CP-violation of Bππ decays in perturbative QCD approach, Phys. Rev. D 63 (2001) 074009 [hep-ph/0004213] [INSPIRE].
C.-D. Lu and M.-Z. Yang, B → πρ, πω decays in perturbative QCD approach, Eur. Phys. J. C 23 (2002) 275 [hep-ph/0011238] [INSPIRE].
H.-n. Li, Y.-L. Shen and Y.-M. Wang, Next-to-leading-order corrections to B → π form factors in k T factorization, Phys. Rev. D 85 (2012) 074004 [arXiv:1201.5066] [INSPIRE].
C.-H. Chen, Y.-L. Shen and W. Wang, |V (ub)| and B → η(′) Form Factors in Covariant Light Front Approach, Phys. Lett. B 686 (2010) 118 [arXiv:0911.2875] [INSPIRE].
W. Wang, Y.-L. Shen and C.-D. Lu, Covariant Light-Front Approach for B(c) transition form factors, Phys. Rev. D 79 (2009) 054012 [arXiv:0811.3748] [INSPIRE].
X.-X. Wang, W. Wang and C.-D. Lu, B(c) to P-Wave Charmonia Transitions in Covariant Light-Front Approach, Phys. Rev. D 79 (2009) 114018 [arXiv:0901.1934] [INSPIRE].
C.-H. Chen and H.-N. Li, Three body nonleptonic B decays in perturbative QCD, Phys. Lett. B 561 (2003) 258 [hep-ph/0209043] [INSPIRE].
H.-Y. Cheng and C.-K. Chua, Branching Fractions and Direct CP-violation in Charmless Three-body Decays of B Mesons, arXiv:1308.5139 [INSPIRE].
Z.-H. Zhang, X.-H. Guo and Y.-D. Yang, CP violation in B ± → π±π+π− in the region with low invariant mass of one π+π− pair, Phys. Rev. D 87 (2013) 076007 [arXiv:1303.3676] [INSPIRE].
U.-G. Meißner and W. Wang, Novel Approach to Generalized Heavy-to-Light Form Factors, arXiv:1312.3087 [INSPIRE].
M. Diehl, Generalized parton distributions, Phys. Rept. 388 (2003) 41 [hep-ph/0307382] [INSPIRE].
H.-Y. Cheng, C.-K. Chua and K.-C. Yang, Charmless hadronic B decays involving scalar mesons: Implications to the nature of light scalar mesons, Phys. Rev. D 73 (2006) 014017 [hep-ph/0508104] [INSPIRE].
R.-H. Li, C.-D. Lu, W. Wang and X.-X. Wang, B → S Transition Form Factors in the PQCD approach, Phys. Rev. D 79 (2009) 014013 [arXiv:0811.2648] [INSPIRE].
J. Bijnens and I. Jemos, Hard Pion Chiral Perturbation Theory for B → π and D → π Formfactors, Nucl. Phys. B 840 (2010) 54 [Erratum ibid. B 844 (2011) 182] [arXiv:1006.1197] [INSPIRE].
J. Bijnens and I. Jemos, Vector Formfactors in Hard Pion Chiral Perturbation Theory, Nucl. Phys. B 846 (2011) 145 [arXiv:1011.6531] [INSPIRE].
J. Oller and E. Oset, Chiral symmetry amplitudes in the S wave isoscalar and isovector channels and the σ, f 0(980), a 0(980) scalar mesons, Nucl. Phys. A 620 (1997) 438 [Erratum ibid. A 652 (1999) 407] [hep-ph/9702314] [INSPIRE].
BaBar collaboration, P. del Amo Sanchez et al., Analysis of the D + → K −π+ e +νe decay channel, Phys. Rev. D 83 (2011) 072001 [arXiv:1012.1810] [INSPIRE].
LHCb collaboration, Differential branching fraction and angular analysis of the decay B 0 → K ∗0 μ + μ −, JHEP 08 (2013) 131 [arXiv:1304.6325] [INSPIRE].
J.M. Flynn, Y. Nakagawa, J. Nieves and H. Toki, |V (ub)| from Exclusive Semileptonic B→ρ Decays,Phys. Lett. B 675(2009)326[arXiv:0812.2795][INSPIRE].
M. Gronau and J.L. Rosner, B decays dominated by ω− ϕ mixing, Phys. Lett. B 666 (2008) 185 [arXiv:0806.3584] [INSPIRE].
Y. Li, C.-D. Lu and W. Wang, Revisiting B → ϕπ Decays in the Standard Model, Phys. Rev. D 80 (2009) 014024 [arXiv:0901.0648] [INSPIRE].
Z.-Q. Zhang, H.-F. Ou and L.-X. Lu, B → a 0(1450)ϕ decays: Dominated by the ω − ϕ mixing in the standard model, J. Phys. G 38 (2011) 095005 [INSPIRE].
Belle collaboration, I. Adachi et al., Measurement of exclusive B → X u lν decays using full-reconstruction tagging at Belle, arXiv:0812.1414 [INSPIRE].
A. Kucukarslan and U.-G. Meißner, Omega-phi mixing in chiral perturbation theory, Mod. Phys. Lett. A 21 (2006) 1423 [hep-ph/0603061] [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: 1311.5420
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Meißner, UG., Wang, W. B s → K (*)ℓ\( \overline{\nu} \), angular analysis, S-wave contributions and |V ub |. J. High Energ. Phys. 2014, 107 (2014). https://doi.org/10.1007/JHEP01(2014)107
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2014)107