Abstract
The rare multi-body decays \( \overline{B}\to \overline{K}\pi \ell \ell \) and \( {\overline{B}}_s\ \to \overline{K}K\ell \ell \) are both important as backgrounds to precision analyses in the benchmark modes \( \overline{B}\to {\overline{K}}^{*}\ell \ell \) and \( {\overline{B}}_s\to \phi \ell \ell \) as well as sensitive probes of flavor physics in and beyond the standard model. We work out non-resonant contributions to \( \overline{B}\to \overline{K}\pi \ell \ell \) and \( {\overline{B}}_s\ \to \overline{K}K\ell \ell \) amplitudes, where ℓ = e,μ, at low hadronic recoil in a model-independent way. Using the operator product expansion in 1/m b , we present expressions for the full angular distribution. The latter allows to probe new combinations of |ΔB| = |ΔS| = 1 couplings and gives access to strong phases between non-resonant and resonant contributions. Exact endpoint relations between transversity amplitudes based on Lorentz invariance are obtained. Several phenomenological distri- butions including those from the angular projections to the S-, P-, D-waves are given. Standard model branching ratios for non-resonant \( \overline{B}\to \overline{K}\pi \ell \ell \) and \( {\overline{B}}_s\ \to \overline{K}K\ell \ell \) decays are found to be in the few 10−8 region, but drop significantly if cuts around the K * or ϕ mass are employed. Nevertheless, the non-resonant contributions to \( \overline{B}\to \overline{K}\pi \ell \ell \) provide the dominant background in the \( \overline{B}\to {\overline{K}}^{*}\ell \ell \) signal region with respect to the low mass scalars. In \( {\overline{B}}_s\ \to \overline{K}K\ell \ell \), the narrowness of the ϕ allows for more efficient background control. We briefly discuss lepton-flavor non-universal effects, also in view of the recent data on R K .
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Belle-II collaboration, T. Abe et al., Belle II Technical Design Report, arXiv:1011.0352 [INSPIRE].
LHCb collaboration, Implications of LHCb measurements and future prospects, Eur. Phys. J. C 73 (2013) 2373 [arXiv:1208.3355] [INSPIRE].
G. Buchalla and G. Isidori, Nonperturbative effects in \( \overline{B}\ \to\ X(s){\ell}^{+}{\ell}^{-} \) for large dilepton invariant mass, Nucl. Phys. B 525 (1998) 333 [hep-ph/9801456] [INSPIRE].
B. Grinstein and D. Pirjol, Exclusive rare B → K * ℓ + ℓ − decays at low recoil: Controlling the long-distance effects, Phys. Rev. D 70 (2004) 114005 [hep-ph/0404250] [INSPIRE].
M. Beylich, G. Buchalla and T. Feldmann, Theory of B → K *ℓ+ℓ− decays at high q 2 : OPE and quark-hadron duality, Eur. Phys. J. C 71 (2011) 1635 [arXiv:1101.5118] [INSPIRE].
C. Bobeth, G. Hiller and D. van Dyk, The benefits of \( \overline{B}\ \to\ {\overline{K}}^{*}{\ell}^{+}{\ell}^{-} \) decays at low recoil, JHEP 07 (2010) 098 [arXiv:1006.5013] [INSPIRE].
C. Bobeth, G. Hiller and D. van Dyk, General Analysis of \( \overline{B}\ \to\ {\overline{K}}^{*}{\ell}^{+}{\ell}^{-} \) Decays at Low Recoil, Phys. Rev. D 87 (2013) 034016 [arXiv:1212.2321] [INSPIRE].
G. Burdman and J.F. Donoghue, Union of chiral and heavy quark symmetries, Phys. Lett. B 280 (1992) 287 [INSPIRE].
C.L.Y. Lee, M. Lu and M.B. Wise, B l4 and D l4 decay, Phys. Rev. D 46 (1992) 5040 [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].
S. Faller, T. Feldmann, A. Khodjamirian, T. Mannel and D. van Dyk, Disentangling the Decay Observables in \( {B}^{-}\to {\pi}^{+}{\pi}^{-}{\ell}^{-}{\overline{\nu}}_{\ell } \), Phys. Rev. D 89 (2014) 014015 [arXiv:1310.6660] [INSPIRE].
X.-W. Kang, B. Kubis, C. Hanhart and U.-G. Meißner, B l4 decays and the extraction of |V ub |, Phys. Rev. D 89 (2014) 053015 [arXiv:1312.1193] [INSPIRE].
D. Becirevic and A. Tayduganov, Impact of B → K *0 ℓ + ℓ − on the New Physics search in B → K * 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 *0 ℓ + ℓ − angular observables, JHEP 03 (2013) 027 [arXiv:1210.5279] [INSPIRE].
G. Hiller and F. Krüger, More model independent analysis of \( \overrightarrow{b}s \) processes, Phys. Rev. D 69 (2004) 074020 [hep-ph/0310219] [INSPIRE].
C. Bobeth, G. Hiller and G. Piranishvili, Angular distributions of \( \overline{B}\to \overline{K}\ell \ell \) decays, JHEP 12 (2007) 040 [arXiv:0709.4174] [INSPIRE].
P.J. Fox, J. Liu, D. Tucker-Smith and N. Weiner, An effective Z’, Phys. Rev. D 84 (2011) 115006 [arXiv:1104.4127] [INSPIRE].
W. Altmannshofer, S. Gori, M. Pospelov and I. Yavin, Dressing L μ − L τ in Color, Phys. Rev. D 89 (2014) 095033 [arXiv:1403.1269] [INSPIRE].
G. Hiller and R. Zwicky, (A)symmetries of weak decays at and near the kinematic endpoint, JHEP 03 (2014) 042 [arXiv:1312.1923] [INSPIRE].
F.A. Berends, A. Donnachie and G.C. Oades, Theoretical Study of K l4 Decay, Phys. Rev. 171 (1968) 1457 [INSPIRE].
B. Grinstein and D. Pirjol, Symmetry breaking corrections to heavy meson form-factor relations, Phys. Lett. B 533 (2002) 8 [hep-ph/0201298] [INSPIRE].
Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
P. Böer, T. Feldmann and D. van Dyk, Angular Analysis of the Decays Λ b → Λ(→Nπ)l + l −, preprint QFET-2014-11, SI-HEP-2014-16, in preparation.
C. Bobeth, G. Hiller and G. Piranishvili, CP Asymmetries in bar \( B\ \to {\overline{K}}^{*}\left(\to \overline{K}\pi \right)\overline{\ell}\ell \) and Untagged \( {\overline{B}}_s,{B}_s\ \to\ \phi \left(\to {K}^{+}{K}^{-}\right)\overline{\ell}\ell \) Decays at NLO, JHEP 07 (2008) 106 [arXiv:0805.2525] [INSPIRE].
J. Lyon and R. Zwicky, Resonances gone topsy turvy - the charm of QCD or new physics in b → sℓ + ℓ − ?, arXiv:1406.0566[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].
C. Hambrock, G. Hiller, S. Schacht and R. Zwicky, B → K * Form Factors from Flavor Data to QCD and Back, Phys. Rev. D 89 (2014) 074014 [arXiv:1308.4379] [INSPIRE].
G. Burdman and G. Hiller, Semileptonic form-factors from B → K * gamma decays in the large energy limit, Phys. Rev. D 63 (2001) 113008 [hep-ph/0011266] [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].
T.M. Aliev, K. Azizi and M. Savci, Analysis of rare B → K *0 (1430)ℓ + ℓ − decay within QCD sum rules, Phys. Rev. D 76 (2007) 074017 [arXiv:0710.1508] [INSPIRE].
C.-H. Chen, C.-Q. Geng, C.-C. Lih and C.-C. Liu, Study of \( B\ \to\ {K}_0^{*}(1430)\ell \overline{\ell} \) decays, Phys. Rev. D 75 (2007) 074010 [hep-ph/0703106] [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].
C. Hambrock and G. Hiller, Extracting B → K * Form Factors from Data, Phys. Rev. Lett. 109 (2012) 091802 [arXiv:1204.4444] [INSPIRE].
LHCb collaboration, Differential branching fraction and angular analysis of the decay B 0 s → ϕμ + μ −, JHEP 07 (2013) 084 [arXiv:1305.2168] [INSPIRE].
R.A. Briceño, M.T. Hansen and A. Walker-Loud, Multichannel one-to-two transition form factors in a finite volume, arXiv:1406.5965 [INSPIRE].
LHCb collaboration, Test of lepton universality using B + → K + ℓ + ℓ − decays, arXiv:1406.6482 [INSPIRE].
CKMfitter Group collaboration, J. Charles et al., CP violation and the CKM matrix: assessing the impact of the asymmetric B factories, Eur. Phys. J. C 41 (2005) 1 [hep-ph/0406184] [INSPIRE], updated results and plots available at http://ckmfitter.in2p3.fr.
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].
J.M. Flynn et al., The B * Bπ coupling with relativistic heavy quarks, arXiv:1311.2251 [INSPIRE].
L. Widhalm, Analysis of the neutral K e4 decay at NA48, Ph.D. Thesis, Österreichische Akademie der Wissenschaften, Vienna, Austria (2001).
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].
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: 1406.6681
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
Das, D., Hiller, G., Jung, M. et al. The \( \overline{B}\to \overline{K}\pi \ell \ell \) and \( {\overline{B}}_s\ \to \overline{K}K\ell \ell \) distributions at low hadronic recoil. J. High Energ. Phys. 2014, 109 (2014). https://doi.org/10.1007/JHEP09(2014)109
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2014)109