Rare Meson Decays in Theories Beyond the Standard

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

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

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

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

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

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

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

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

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

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

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

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: 12 2 -nd Vienna Central European Seminar, Nov 25 -27, 2005

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

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

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

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

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 17 2 -nd Vienna Central European Seminar, Nov 25 -27, 2005

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

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

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

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

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

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

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

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 We found that these R-parity violating contributions could be much larger then those from massive neutrinos. 25 2 -nd Vienna Central European Seminar, Nov 25 -27, 2005

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