Skip to main content
SpringerLink
Log in

Decay \({B \to K^\ast(\to K\pi)\ell^{+} \ell^{-}}\) in Covariant Quark Model

  • Published:
Few-Body Systems Aims and scope Submit manuscript

Abstract

Our article is devoted to the study of the rare \({B \to K^\ast \ell^+\ell^-}\) decay where \({\ell=e,\mu,\tau}\). We compute the relevant form factors in the framework of the covariant quark model with infrared confinement in the full kinematical momentum transfer region. The calculated form factors are used to evaluate branching fractions and polarization observables in the cascade decay \({B \to K^\ast(\to K\pi)\ell^+\ell^-}\). We compare the obtained results with available experimental data and the results from other theoretical approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Langenbruch, C. [LHCb Collaboration]: Latest results on rare decays from LHCb. arXiv:1505.04160 [hep-ex]

  2. Crivellin, A., Heeck, J., Stoffer, P.: A perturbed lepton-specific two-Higgs-doublet model facing experimental hints for physics beyond the Standard Model. arXiv:1507.07567 [hep-ph]

  3. Lees, J., et al. (BABAR Collaboration): Evidence for an excess of \({\bar{B} \to D^{(*)}\tau^-\bar{\nu}_\tau}\) decays. Phys. Rev. Lett. 109, 101802 (2012). arXiv:1205.5442 [hep-ex]

  4. Tanaka, M., Watanabe, R.: Tau longitudinal polarization in B -> D tau nu and its role in the search for charged Higgs boson. Phys. Rev. D 82, 034027 (2010). [arXiv:1005.4306 [hep-ph]]

  5. Fajfer, S., Kamenik, J.F., Nisandzic, I.: On the \({B \to D^{*} \tau \bar \nu_{\tau}}\) sensitivity to new physics. Phys. Rev. D 85, 094025 (2012). arXiv:1203.2654 [hep-ph]

  6. Kamenik, J.F., Mescia, F.: \({B \to D \tau \nu}\) branching ratios: opportunity for lattice QCD and Hadron colliders. Phys. Rev. D 78, 014003 (2008). arXiv:0802.3790 [hep-ph]

  7. Aaij, R., et al. [LHCb Collaboration]: Test of lepton universality using \({B^{+} \rightarrow K^{+} \ell^{+} \ell^{-}}\) decays. Phys. Rev. Lett. 113, 151601 (2014). [arXiv:1406.6482 [hep-ex]]

  8. Aaij, R., et al. [LHCb Collaboration]: Measurement of form-factor-independent observables in the decay \({B^{0} \to K^{*0} \mu^+ \mu^-}\). Phys. Rev. Lett. 111, 191801 (2013). [arXiv:1308.1707 [hep-ex]]

  9. Descotes-Genon, S., Matias, J., Virto, J.: Understanding the \({B \to K* \mu^+ \mu^-}\) Anomaly. Phys. Rev. D 88, 074002 (2013). [arXiv:1307.5683 [hep-ph]]

  10. Descotes-Genon, S., Hurth, T., Matias, J., Virto, J.: Optimizing the basis of \({{B} \to {K}^{*}\ell^+ \ell^-}\) observables in the full kinematic range. JHEP 1305, 137 (2013). [arXiv:1303.5794 [hep-ph]]

  11. Hurth, T., Mahmoudi, F.: On the LHCb anomaly in \({B \to K^*\ell^+\ell^-}\). JHEP 1404, 097 (2014). [arXiv:1312.5267 [hep-ph]]

  12. Bobeth, C., Hiller, G., van Dyk, D.: The Benefits of \({\bar{B} - > \bar{K}^* l^+ l^-}\) Decays at low recoil. JHEP 1007, 098 (2010) [arXiv:1006.5013 [hep-ph]]

  13. Bobeth, C., Hiller, G., van Dyk, D.: General analysis of \({\bar{B} \to \bar{K}^{(*)} \ell^+ \ell^-}\) decays at low recoil. Phys. Rev. D 87(3), 034016 (2013). [arXiv:1212.2321 [hep-ph]]

  14. Hiller, G., Zwicky, R.: (A)symmetries of weak decays at and near the kinematic endpoint. JHEP 1403, 042 (2014). [arXiv:1312.1923 [hep-ph]]

  15. Gratrex, J., Hopfer, M., Zwicky, R.: Generalised helicity formalism, higher moments and the \({B \to K_{J_K}(\to K\pi) \bar{\ell}_1\ell_2}\) angular distributions, arXiv:1506.03970 [hep-ph]

  16. Das, D., Hiller, G., Jung, M., Shires, A.: The \({\bar{B} \to \bar{K}\pi \ell \ell }\) and \({{\bar{B}}_s\ \to \bar{K}K\ell \ell}\) distributions at low hadronic recoil. JHEP 1409, 109 (2014). [arXiv:1406.6681 [hep-ph]]

  17. Hofer, L., Matias, J.: Exploiting the symmetries of P and S wave for \({B \to K{*}\mu^+ \mu^-}\). arXiv:1502.00920 [hep-ph]

  18. Descotes-Genon, S., Virto, J.: Time dependence in B V decays. JHEP 1504, 045 (2015). [arXiv:1502.05509 [hep-ph]]

  19. Descotes-Genon, S., Matias, J., Ramon, M., Virto, J.: Implications from clean observables for the binned analysis of \({B \to K*\mu^+\mu^-}\) at large recoil. JHEP 1301, 048 (2013). [arXiv:1207.2753 [hep-ph]]

  20. Altmannshofer, W., Straub, D.M.: New physics in \({B \to K^*\mu\mu}\). Eur. Phys. J. C 73, 2646 (2013) [arXiv:1308.1501 [hep-ph]]

  21. Mandal, R., Sinha, R., Das, D.: Testing new physics effects in \({B \to K^*\ell^+\ell^-}\). Phys. Rev. D 90, 096006 (2014). [arXiv:1409.3088 [hep-ph]]

  22. Körner, J.G., Schuler, G.A.: Exclusive semileptonic decays of bottom mesons in the spectator quark model. Z. Phys. C 38 (1988) 511 [Erratum-ibid. C 41 (1989) 690]

  23. Körner J.G., Schuler G.A.: Exclusive semileptonic heavy meson decays including Lepton mass effects. Z. Phys.C 46, 93 (1990)

    ADS  Google Scholar 

  24. Melikhov, D., Nikitin, N., Simula, S.: Probing right-handed currents in \({B \to K^*}\) lepton + lepton− transitions. Phys. Lett. B 442, 381 (1998) [hep-ph/9807464]

  25. Kruger, F., Sehgal, L.M., Sinha, N., Sinha, R.: Angular distribution and CP asymmetries in the decays anti-\({B \to K- \pi+ e- e4+}\) and anti-\({B \to \pi- \pi+ e- e+}\). Phys. Rev. D 61, 114028 (2000) [Erratum-ibid. D 63, 019901 (2001)] [ hep-ph/9907386]

  26. Kim, C.S., Kim, Y.G., Lu, C.D., Morozumi, T.: Azimuthal angle distribution in \({B \to K^* (\to K pi)}\) lepton + lepton− at low invariant m(lepton + lepton−) region. Phys. Rev. D 62, 034013 (2000) [hep-ph/0001151]

  27. Kruger, F., Matias, J.: Probing new physics via the transverse amplitudes of \({B0 \to K^*0 (\to K- \pi+) l+l-}\) at large recoil. Phys. Rev. D 71, 094009 (2005) [hep-ph/0502060]

  28. Kruger, F., Sehgal, L.M.: Lepton polarization in the decays \({b \to X(s) \mu+ \mu-}\) and \({B \to X(s) \tau+ \tau-}\). Phys. Lett. B 380, 199 (1996) [hep-ph/9603237]

  29. Matias, J., Mescia, F., Ramon, M., Virto, J.: Complete anatomy of \({\bar{B}_d ->\bar{K}^{* 0} (- > K \pi)l^+l^-}\) and its angular distribution. JHEP 1204, 104 (2012) [arXiv:1202.4266 [hep-ph]]

  30. Egede, U., Hurth, T., Matias, J., Ramon, M., Reece, W.: New physics reach of the decay mode \({\bar{B} \to \bar{K}^{*0} \ell^+\ell^-}\). JHEP 1010, 056 (2010) [arXiv:1005.0571 [hep-ph]]

  31. Beneke, M., Feldmann, T., Seidel, D.: Systematic approach to exclusive \({B \to Vl+ l-, V_\gamma}\) decays. Nucl. Phys. B 612, 25 (2001) [hep-ph/0106067]

  32. Asatryan, H.H., Asatrian, H.M., Greub, C., Walker, M.: Calculation of two loop virtual corrections to \({b \to s l+ l-}\) in the standard model. Phys. Rev. D 65, 074004 (2002). [hep-ph/0109140]

  33. Chen, C.H., Geng, C.Q.: Exclusive decays of \({B \to K^(*)}\) lepton + lepton- in the PQCD. Phys. Rev. D 63, 114025 (2001). [hep-ph/0103133]

  34. Chen, C.H., Geng, C.Q.: Analysis of \({B \to K^{*} \ell^{+} \ell^{-}}\) decays at large recoil region. Nucl. Phys. B 636, 338 (2002). [hep-ph/0203003]

  35. Ali, A., Safir, A.S.: Helicity analysis of the decays \({B \to K^{*} \ell^{+} \ell^{-}}\) and \({B \to \rho \ell \nu_{\ell}}\) in the large energy effective theory. Eur. Phys. J. C 25, 583 (2002). [hep-ph/0205254]

  36. Feldmann, T., Matias, J.: Forward backward and isospin asymmetry for \({B \to K* l+ l-}\) decay in the standard model and in supersymmetry. JHEP 0301, 074 (2003). [hep-ph/0212158]

  37. Ball, P., Zwicky, R.: \({B(D,S) \to \rho, \omega, K^*, \phi}\) decay form-factors from light-cone sum rules revisited. Phys. Rev. D 71, 014029 (2005) [hep-ph/0412079]

  38. Khodjamirian, A., Mannel, T., Offen, N.: Form-factors from light-cone sum rules with B-meson distribution amplitudes. Phys. Rev. D 75, 054013 (2007) [hep-ph/0611193]

  39. Ivanov, M.A., Kalinovsky, Y.L., Maris, P., Roberts, C.D.: Heavy meson to light meson transition form-factors. Phys. Rev. C 57, 1991 (1998) [nucl-th/9711023]

  40. Ivanov, M.A., Körner, J.G., Kovalenko, S.G., Roberts, C.D.: B- to light-meson transition form-factors. Phys. Rev. D 76, 034018 (2007) [nucl-th/0703094]

  41. Ebert, D., Faustov, R.N., Galkin, V.O.: Rare semileptonic decays of B and B c mesons in the relativistic quark model. Phys. Rev. D 82, 034032 (2010) [arXiv:1006.4231 [hep-ph]]

  42. Khodjamirian, A., Mannel, T., Pivovarov, A.A., Wang, Y.-M.: Charm-loop effect in \({B \to K^{(*)} \ell^{+} \ell^{-}}\) and \({B\to K^*\gamma}\). JHEP 1009, 089 (2010) [arXiv:1006.4945 [hep-ph]]

  43. Alok, A.K., Dighe A., Ghosh D., London D., Matias J., Nagashima M., Szynkman A.: New-physics contributions to the forward-backward asymmetry in \({B \rightarrow K^{\ast} ~\mu^{+} \mu^{-}}\). JHEP 1002, 053 (2010). doi:10.1007/JHEP02(2010)053. [arXiv:0912.1382 [hep-ph]]

  44. Beylich, M., Buchalla, G., Feldmann, T.: Theory of \({B \to K^{(*)} \ell^+ \ell^-}\) decays at high \({q^2}\) : OPE and quark-hadron duality. Eur. Phys. J. C 71 (2011) 1635. doi:10.1140/epjc/s10052-011-1635-0. [arXiv:1101.5118 [hep-ph]]

  45. Kang, X.W., Kubis, B., Hanhart, C., Meißner, U.G.:, \({B_{l4}}\) decays and the extraction of \({|V_{ub}|}\). Phys. Rev. D 89, 053015 (2014). doi:10.1103/PhysRevD.89.053015. [arXiv:1312.1193 [hep-ph]]

  46. Lyon, J., Zwicky, R.: Resonances gone topsy turvy - the charm of QCD or new physics in \({b \to s \ell^+ \ell^-}\)? (2014). arXiv:1406.0566 [hep-ph]

  47. Bharucha, A., Straub, D.M., Zwicky, R.: \({B\to V\ell^+\ell^-}\) in the standard model from light-cone sum rules (2015). arXiv:1503.05534 [hep-ph]

  48. Greub, C., Philipp, V., Schupbach, C.: Analytic calculation of two-loop QCD corrections to \({b \to sl+ l-}\) in the high \({{\rm q}^{2}}\) region. JHEP 0812, 040 (2008). doi:10.1088/1126-6708/2008/12/040. [arXiv:0810.4077 [hep-ph]]

  49. Descotes-Genon, S., Hofer, L., Martias, J., Virto, J.: Global analysis of \({b\to s\ell\ell}\) anomalies (2015). arXiv:1510.04239 [hep-ph].

  50. Faessler, A., Gutsche, T., Ivanov, M.A., Körner, J.G., Lyubovitskij, V.E.: The exclusive rare decays \({B \to {\text K(K*)} \bar{\ell} \ell}\) and \({B_c \to {\text D(D*)} \bar{\ell} \ell}\) in a relativistic quark model. Eur. Phys. J. direct C 4, 18 (2002) [hep-ph/0205287]

  51. Branz, T., Faessler, A., Gutsche, T., Ivanov, M.A., Körner, J.G., Lyubovitskij, V.E.: Relativistic constituent quark model with infrared confinement. Phys. Rev. D 81, 034010 (2010). [arXiv:0912.3710 [hep-ph]]

  52. Ivanov, M.A., Körner, J.G., Kovalenko, S.G., Santorelli, P., Saidullaeva, G.G.: Form factors for semileptonic, nonleptonic and rare B  (B s ) meson decays. Phys. Rev. D 85, 034004 (2012) [arXiv:1112.3536 [hep-ph]]

  53. Dubnička, S., Dubničková, A.Z., Ivanov, M.A., Liptaj, A.: Decays \({B_{s} \to J/\psi+\eta}\) and \({B_{s} \to J/\psi+\eta\prime}\) in the framework of covariant quark model. Phys. Rev. D 87, 074201 (2013). [arXiv:1301.0738 [hep-ph]]

  54. Issadykov, A., Ivanov, M.A., Sakhiyev, S.K.: Form factors of the B-S-transitions in the covariant quark model. Phys. Rev. D 91(7), 074007 (2015). [arXiv:1502.05280 [hep-ph]]

  55. Gutsche, T., Ivanov, M.A., Körner, J.G., Lyubovitskij, V.E., Santorelli, P.: Light baryons and their electromagnetic interactions in the covariant constituent quark model. Phys. Rev. D 86, 074013 (2012). [arXiv:1207.7052 [hep-ph]]

  56. Gutsche, T., Ivanov, M.A., Körner, J.G., Lyubovitskij, V.E., Santorelli, P.: Rare baryon decays \({\Lambda_b \to \Lambda {l^{+}l^{-}} (l=e, \mu, \tau)}\) and \({\Lambda_b \to \Lambda\gamma}\) : differential and total rates, lepton- and hadron-side forward-backward asymmetries. Phys. Rev. D 87, 074031 (2013) [arXiv:1301.3737 [hep-ph]]

  57. Gutsche, T., Ivanov, M.A., Körner, J.G., Lyubovitskij, V.E., Santorelli, P.: Polarization effects in the cascade decay \({\wedge {b} \to \wedge (\to {p} \pi^-) + {J}/\psi (\to \ell+\ell^-)}\) in the covariant confined quark model. Phys. Rev. D 88(11), 114018 (2013) [arXiv:1309.7879 [hep-ph]]

  58. Gutsche, T., Ivanov, M.A., Körner, J.G., Lyubovitskij, V.E., Santorelli, P.: Heavy-to-light semileptonic decays of \({\Lambda_b}\) and \({\Lambda_c}\) baryons in the covariant confined quark model. Phys. Rev. D 90(11), 114033 (2014) [arXiv:1410.6043 [hep-ph]]

  59. Gutsche, T., Ivanov, M.A., Körner, J.G., Lyubovitskij, V.E., Santorelli, P., Habyl, N.: Semileptonic decay \({\Lambda_b \to \Lambda_c + \tau^- + \bar{\nu_\tau}}\) in the covariant confined quark model. Phys. Rev. D 91(7), 074001 (2015) [arXiv:1502.04864 [hep-ph]]

  60. Dubnička, S., Dubničková, A.Z., Ivanov, M.A., Körner, J.G.: Quark model description of the tetraquark state X(3872) in a relativistic constituent quark model with infrared confinement. Phys. Rev. D 81, 114007 (2010) [arXiv:1004.1291 [hep-ph]]

  61. Dubnička, S., Dubničková, A.Z., Ivanov, M.A., Koerner, J.G., Santorelli, P., Saidullaeva, G.G.: One-photon decay of the tetraquark state \({X(3872) \to \gamma + J/\psi}\) in a relativistic constituent quark model with infrared confinement. Phys. Rev. D84, 014006 (2011). [arXiv:1104.3974 [hep-ph]]

  62. Dineykhan M., Ivanov M.A., Saidullaeva G.G.: Exotic states and rare B/s-decays in the covariant quark model. Phys. Part. Nucl. 43, 749 (2012)

    Article  Google Scholar 

  63. Efimov G.V., Ivanov M.A.: Confinement and quark structure of light hadrons. Int. J. Mod. Phys. A 4, 2031 (1989)

    Article  ADS  Google Scholar 

  64. Efimov G.V., Ivanov M.A.: The Quark Confinement Model of Hadrons. CRC Press, Boca Raton (1993)

    Google Scholar 

  65. Weinberg S.: Elementary particle theory of composite particles. Phys. Rev. 130, 776 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  66. Salam A.: Lagrangian theory of composite particles. Nuovo Cimento 25, 224 (1962)

    Article  MATH  Google Scholar 

  67. Hayashi, K., Hirayama, M., Muta, T., Seto, N., Shirafuji, T.: Compositeness criteria of particles in Quantum field theory and S-matrix theory. Fortsch. Phys. 15, 625 (1967)

  68. Vermaseren, J.A.M.: The FORM project. Nucl. Phys. Proc. Suppl. 183, 19 (2008). [arXiv:0806.4080 [hep-ph]]; arXiv:math-ph/0010025

  69. Ebert, D., Feldmann, T., Reinhardt, H.: Extended NJL model for light and heavy mesons without q anti-q thresholds. Phys. Lett. B 388, 154 (1996). [arXiv:hep-ph/9608223]

  70. Bedolla M.A., Cobos-Martnez J.J., Bashir A.: Charmonia in a contact interaction. Phys. Rev. D 92(5), 054031 (2015)

    Article  ADS  Google Scholar 

  71. Ganbold, G., Gutsche, T., Ivanov, M.A., Lyubovitskij, V.E.: On the meson mass spectrum in the covariant confined quark model. J. Phys. G 42(7):075002 (2015). [arXiv:1410.3741 [hep-ph]]

  72. Buchalla, G., Buras, A.J., Lautenbacher, M.E.: Weak decays beyond leading logarithms. Rev. Mod. Phys. 68, 1125 (1996). [hep-ph/9512380]

  73. Ali A., Mannel T., Morozumi T.: Forward backward asymmetry of dilepton angular distribution in the decay b → s l + l−. Phys. Lett. B 273, 505 (1991)

    Article  ADS  Google Scholar 

  74. Olive, K.A., et al. [Particle Data Group Collaboration]: Review of particle physics. Chin. Phys. C 38, 090001 (2014)

  75. Aaij, R., et al. [LHCb Collaboration]: Differential branching fractions and isospin asymmetries of \({B \to K^{(*)}\mu^+ \mu^-}\) decays. JHEP 1406, 133 (2014). [arXiv:1403.8044 [hep-ex]]

  76. Pescatore, L., [LHCb Collaboration]: Rare decays at the LHCb experiment. arXiv:1410.2411 [hep-ex]

  77. Ali, A., Lunghi, E., Greub, C., Hiller, G.: Improved model independent analysis of semileptonic and radiative rare B decays. Phys. Rev. D 66 (2002) 034002. [hep-ph/0112300]

  78. Ali, A., Ball, P., Handoko, L.T., Hiller, G.: A Comparative study of the decays \({B \to {\text (K, K^*)} \ell^+ \ell^-}\) in standard model and supersymmetric theories. Phys. Rev. D 61, 074024 (2000). [hep-ph/9910221]

  79. Melikhov, D., Nikitin, N., Simula, S.: Rare exclusive semileptonic b→ s transitions in the standard model. Phys. Rev. D 57, 6814 (1998). [hep-ph/9711362]

  80. Geng, C.Q., Kao, C.P.: Lepton polarization asymmetry in b → K(*) lepton+ lepton-. Phys. Rev. D 54, 5636 (1996). [hep-ph/9608466]

  81. Ivanov, M.A., Kalinovsky, Y.L., Roberts, C.D.: Survey of heavy meson observables. Phys. Rev. D 60, 034018 (1999). [nucl-th/9812063]

  82. Belle Collaboration: Measurement of the Differential branching fraction and forward-backward asymmetry for \({B \to K^{(*)}\ell^+\ell^-}\). Phys. Rev. Lett. 103, 171801 (2009) [arXiv:0904.0770 [hep-ex]]

  83. LHCb Collaboration: Differential branching fraction and angular analysis of the \({B^0\to K^{*0} \mu^+\mu^-}\) decay. Phys. Rev. Lett. 108, 181806 (2012), [LHCb-CONF-2012-008 and arXiv:1112.3515 [hep-ex]]

  84. CDF Collaboration: Measurements of the angular distributions in the decays \({B \to K^{(*)}\mu^+ \mu^-}\) at CDF. Phys. Rev. Lett. 108, 081807 (2012) [arXiv:1108.0695 [hep-ex]]

Download references

Author information

Authors and Affiliations

  1. Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia

    S. Dubnička & A. Liptaj

  2. Comenius University, Bratislava, Slovakia

    A. Z. Dubničková

  3. Al-Farabi Kazakh National University, Almaty, Kazakhstan

    N. Habyl & G. S. Nurbakova

  4. Joint Institute for Nuclear Research, Dubna, Russia

    M. A. Ivanov

Authors
  1. S. Dubnička
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Z. Dubničková
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Habyl
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. A. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Liptaj
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. G. S. Nurbakova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. A. Ivanov.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dubnička, S., Dubničková, A.Z., Habyl, N. et al. Decay \({B \to K^\ast(\to K\pi)\ell^{+} \ell^{-}}\) in Covariant Quark Model. Few-Body Syst 57, 121–143 (2016). https://doi.org/10.1007/s00601-015-1034-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00601-015-1034-4

Keywords

Search

Navigation