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Rare Meson Decays in Theories Beyond the Standard Model

Rare Meson Decays in Theories Beyond the Standard Model. A. Ali (DESY), A. V. Borisov, M. V. Sidorova (MSU). SM. Beyond the SM:. Massive Majorana neutrinos R-parity-violating SUSY. Feynman diagrams for the rare meson decay mediated by Majorana neutrinos. tree. box.

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Rare Meson Decays in Theories Beyond the Standard Model

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  1. Rare Meson Decays in Theories Beyondthe Standard Model A. Ali (DESY), A. V. Borisov, M. V. Sidorova (MSU) 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  2. SM Beyond the SM: • Massive Majorana neutrinos • R-parity-violating SUSY 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  3. Feynman diagrams for the rare meson decay mediated by Majorana neutrinos tree box 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  4. 1. Rare Meson Decays mediated by massive Majorana neutrinos The width of the decay: - tree diagram - box diagram - lepton tensor - hadron tensor 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  5. LEPTON TENSOR - neutrino mixing matrix - the relative CP-phases, 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  6. HADRONTENSOR 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  7. The Bethe-Salpeter Formalism Mesons as bound states of a quark and an antiquark: - the center-of-mass - the relative coordinates - color index 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  8. - -group factor • the mass of the meson M - quark masses - the relative 4-momentum - the total 4-momentum of the meson 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  9. - model dependent scalarfunction - parameter of the model The definition of the decay constant of the meson: 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  10. Amplitude for tree and box diagrams of the meson decay 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  11. Heavy neutrinos In this case the total decay width is model independent - the effective inverse Majorana mass 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  12. The branching ratios Using bounds on matrix elements from the othersprocesses one can obtain indirect bounds on the branching ratios. The bound from of nucleus: Also there are bounds on other mixing parameters: 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  13. From the heavy neutral Majorana lepton detecting experiments: Assuming one heavy neutrino scenario: 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  14. Experimental and indirect bounds on the branching ratios for the rare meson decays mediated by heavy Majorana neutrinos Ind. Bounds on Rare decay 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  15. Light neutrinos t-amplitudeis model independent b-amplitude is model dependent - the effective Majorana mass 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  16. - 1-dimensional integral The numerical calculations of multidimensional phase integ- rals were carried out using the program VEGAS based on Monte-Carlo mechanism. - 6-dimensional integral - 5-dimensional integral 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  17. The bound from: From cosmological data and neutrino oscillation experiments, assuming the existence of 3 light massive neutrino the constraint Taking into account Using the best fit of mixing matrix from neutrino oscillation experiments 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  18. Contribution of tree, box diagrams, their interference and indirect bounds on the branching ratios for the rare meson decays mediated by light Majorana neutrinos Ind. Bounds on 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  19. 2. Rare Meson Decays in R-parity-violating SUSY Theories R-parity is a discrete, multiplicative symmetrydefined as S, B, L – spin, barion and lepton quantum numbers The SM fields, including additional Higgs boson fields appearing in the extended gauge models, have Rp=+1 while their superpartners have Rp=-1. This symmetry has been imposed on the minimal supersymmetric SM to ensure B and L number conservation. However, SUSY doesn’t require Rp conservation. The most general gauge invariant form of the superpotential in minimal SUSY SM is 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  20. L B - generation indices; are lepton andquark doublet superfields and arelepton and up, down quark singlet superfields. All arethe coupling constants. MSSM Rp An alternative discrete symmetry with the same physical result, for example: proton stability 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  21. Lagrangian, that yields contributions to the decay The lepton number violating part of the Lagrangian has the form: 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  22. The Lagrangian terms corresponding to gluino and neutralino interactions with fermionsandtheir superpartners are , , Here are 3x3 Gell-Mann matrices. - neutralino coupling constants. Here and are the electric charge and weak isospin of the field . 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  23. Feynman diagrams for the rare meson decay in SUSY model tree box 3 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  24. - the 4-momentum of the initial and finalmesons 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  25. Using the input parameters for mesons: values of neutralino mixing matrix elements (hep-ph/0311123): Bounds on RPV couplings and the masses of the various superpartners to be comparable the SUSY mass scale Wefound that these R-parity violating contributionscould be muchlarger then those from massive neutrinos. 2-nd Vienna Central European Seminar, Nov 25-27, 2005

  26. Bounds on the branching ratios for the rare meson decays in SUSY theories with R-parity non-conservation. Rare decay 2-nd Vienna Central European Seminar, Nov 25-27, 2005

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