Rare Meson Decays in Theories Beyond the Standard Model

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Rare Meson Decays in Theories Beyond the
Standard Model

• A. Ali (DESY), A. V. Borisov,
• M. V. Sidorova (MSU)

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SM
Beyond the SM

• Massive Majorana neutrinos
• R-parity-violating SUSY

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Feynman diagrams for the rare meson decay
mediated by Majorana neutrinos
tree
box
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1. Rare Meson Decays mediated by massive
Majorana neutrinos
The width of the decay
- tree diagram
- box diagram
- lepton tensor
- hadron tensor
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LEPTON TENSOR
- neutrino mixing matrix
the relative CP-phases,
-
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HADRON TENSOR
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The Bethe-Salpeter Formalism
Mesons as bound states of a quark and an
antiquark
- the center-of-mass
- the relative coordinates
- color index
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-
-group factor

• the mass of the meson M

-
quark masses
- the relative 4-momentum
- the total 4-momentum of the meson
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- model dependent scalar function
- parameter of the model
The definition of the decay constant of the
meson
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Amplitude for tree and box diagrams of the meson
decay
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Heavy neutrinos
In this case the total decay width is model
independent
-
the effective inverse Majorana mass
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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
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From the heavy neutral Majorana lepton detecting
experiments
Assuming one heavy neutrino scenario
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Experimental and indirect bounds on the branching
ratios for the rare meson decays mediated by
heavy Majorana neutrinos
Exp. upper bounds on
Ind. Bounds on
Rare decay






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Light neutrinos
t-amplitude is model independent
b-amplitude is model dependent
- the effective Majorana mass
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- 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
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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
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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
Ind. Bounds on






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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 Rp1 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 doesnt
require Rp conservation.
The most general gauge invariant form of the
superpotential in minimal SUSY SM is
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L
B
- generation indices
are lepton and quark doublet superfields
are lepton and up, down quark singlet superfields.
and
All are the coupling constants.
MSSM
Rp
An alternative discrete symmetry with the same
physical result, for example
proton stability
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Lagrangian, that yields contributions to the decay
The lepton number violating part of the
Lagrangian has the form
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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
.
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Feynman diagrams for the rare meson decay
in SUSY model
tree
box
3
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- the 4-momentum of the initial and final mesons
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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.
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Bounds on the branching ratios for the rare meson
decays in SUSY theories with R-parity
non-conservation.

Rare decay