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

3. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 2 SM Beyond the SM: -Massive Majorana neutrinos -R-parity-violating SUSY

4. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 3 Feynman diagrams for the rare meson decay mediated by Majorana neutrinos tree box

5. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 4 1. Rare Meson Decays mediated by massive Majorana neutrinos - tree diagram - box diagram - lepton tensor - hadron tensor The width of the decay:

6. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 5 LEPTON TENSOR the relative CP-phases,- - neutrino mixing matrix

7. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 6 HADRON TENSOR

8. 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

9. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 8 - the mass of the meson M - the total 4-momentum of the meson quark masses - - the relative 4-momentum --group factor

10. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 9 - parameter of the model - model dependent scalar function The definition of the decay constant of the meson:

11. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 10 Amplitude for tree and box diagrams of the meson decay

12. 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

13. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 12 The branching ratios Using bounds on matrix elements from the others processes one can obtain indirect bounds on the branching ratios. The bound from of nucleus: Also there are bounds on other mixing parameters:

14. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 13 From the heavy neutral Majorana lepton detecting experiments: Assuming one heavy neutrino scenario:

15. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 14 Exp. upper bounds on Ind. Bounds on Rare decay Experimental and indirect bounds on the branching ratios for the rare meson decays mediated by heavy Majorana neutrinos

16. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 15 Light neutrinos b- amplitude is model dependent t-amplitude is model independent - the effective Majorana mass

17. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 16 - 1-dimensional integral - 5-dimensional integral - 6-dimensional integral The numerical calculations of multidimensional phase integ- rals were carried out using the program VEGAS based on Monte-Carlo mechanism.

18. 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

19. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 18 Rare d ecay Ind. Bounds on Contribution of tree, box diagrams, their interference and indirect bounds on the branching ratios for the rare meson decays mediated by light Majorana neutrinos

20. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 19 2. Rare Meson Decays in R- parity-violating SUSY Theories 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 R-parity is a discrete, multiplicative symmetry defined as

21. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 20 - generation indices;are lepton and quark doublet superfields are lepton and up, down quark singlet superfields. All are the coupling constants. MSSM proton stability LB and Rp An alternative discrete symmetry with the same physical result, for example:

22. 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:

23. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 22 The Lagrangian terms corresponding to gluino and neutralino interactions with fermions and their superpartners are, Here are 3x3 Gell-Mann matrices. - neutralino coupling constants. Here and are the electric charge and weak isospin of the field.,

24. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 23 Feynman diagrams for the rare meson decay in SUSY model tree box 3

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

26. 2-nd Vienna Central European Seminar, Nov 25-27, 2005 25 Using the input parameters for mesons: Bounds on RPV couplings and the masses of the various superpartners to be comparable the SUSY mass scale We found that these R-parity violating contributions could be much larger then those from massive neutrinos. values of neutralino mixing matrix elements (hep-ph/0311123):

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