Model supersymetryczny z dodatkowa grupa U(1)

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Model supersymetryczny z dodatkowa grupa U(1)
Seminarium Fizyki Wysokich Energii, 30
kwietnia 2007
Jan Kalinowski
we wspólpracy z. S.Y. Choi, H.E. Haber i P.M.
Zerwas
hep-ph/0612218
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Plan seminarium

• Motywacja wyjscia poza MS
• Motywacja wyjscia poza MSSM
• Model z dodatkowa symetria U(1)
• Sektor Higgsa
• Sektor neutralin
• przyklad 2x2
• Troche fenomenologii
• Podsumowanie

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Motivation origin of mass ?
In the SM

• one Higgs doublet
• the potential
• if (why?) and
  (why?) then
• EWSB ltRe Ho gt v 246 GeV
• 4 dof gt 3 massive gauge bosons MW MZ
  cosqW gv/2
• one physical Higgs boson m2H l v2 /2

• but d m2H L2 gt hierarchy problem

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MSSM medication
In the MSSM the hierarchy is stabilised

• two Higgs doublets
• the superpotential
• nice feature radiative EWSB
• min. cond.
• negative Higgs searches gt little fine
  tuning

• but why m EW scale? gt the m
  problem

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Beyond MSSM

• NMSSM promote to vev of some scalar
  field S
• 
  
  l ltSgt

Bastero-Gil, Hugonie, King, Roy, Vempati 2000
tan b 5
New term increases the Higgs mass - allows
lighter stops reducing fine tuning

• But broken Z3 symmetry gt cosmological
  domain-wall problem

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U(1) extended SUSY

• Another way to avoid axion is to promote PQ
  to the U(1) gauge
• symmetry
• Gauge group USSMSU(3)xSU(2)xUY(1) x UX(1)
• New scalar S and gauge B superfields
• axion eaten-up by a
  massive Z gauge boson
• new fermions are needed to cancel anomalies
  assume heavy
• USSM a LE subset of E6SSM of
  King, Moretti, Nevzorov
• 
  hep-ph/0510419

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Kinetic term mixing
gauge kinetic term for B and B
l
can be converted to canonical form
the U(1) part of the covariant derivative gt
effective Qx charge
ll
gaugino masses
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Higgs sector
Two iso-doublets Hu , Hd and one scalar S
l
After spontaneous EW U(1)X symmetry breaking by
the doublet higgsino mass and higgsino-singlino
mass terms are generated
l
physical Higgs bosons three neutral scalars
two charged
one neutral
pseudoscalar
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Higgs sector
The USSM Higgs h1 mass bound
l
NMSSM USSM
hep-ph/0510419, hep-ph/0511256
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Neutralino sector
In the
basis, the neutralino mass matrix
where
and Higgs U(1)x charges
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Diagonalizing M6
For small mixing between
and

• diagonalize first 4x4
• and 2x2 blocks

- perform block-diagonalization
- eigenvalues only shifted
where
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How to solve for neutralino masses

• The neutralino mass term in the Lagrangian

Original fields Physical fields
where we require
Mathematically this is the Takagi diagonalization
of a general complex symmetric matrix (singular
value decomposition)
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Takagi diagonalization
We want to solve (to simplify notation
)

• Physical masses are not eigenvalues they are
  singular values and
• in general cannot be found by a similarity
  transformation.

To compute singular values
but U can be found this way only in some
particular cases
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Takagi diagonalization

• Example

Singular value 1 is doubly-degenerate
1, i.e. does not specify U
But
Theorem for any complex symmetric nxn matrix
there exists a unitary matrix
such that
with real, non-negative
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Proof

• can be rewritten as

Denoting k-th kolumn of U by we have

Any non-degenerate gt unique
up to a sign
(if 0, up to a phase)
Any degenerate gt invariant
subspace
take any orthonormal set of
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By construction

• Algorithm for constructing U rewrite
  as

can be diagonalized by an orthogonal
transformation
If is eigenvalue with eigenvector
, then
is eigenvalue with eigenvector

Therefore has equal number of
positive and negative eigenvalues and
even number of zero eigenvalues.
Recipe for constructing U
1) take eigenvectors
corresponding to positive 2) for
m0, are linearly dependent
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Example

• Consider

The eigenvalues of M are degenerate and zero, and
M has only one eigenvector (1, i ).
Thus M cannot be diagonalized by a similarity
transformation.
But M has two non-degenerate singular values 0
and 2 since
Solving we find
check
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Neutralino sector of U(1) extended SUSY
In the
basis, the neutralino mass matrix
where
and Higgs U(1)x charges
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Real symmetric M6 can always be diagonalized
For small mixing between
and

• diagonalize first 4x4
• and 2x2 blocks

the diagonal elements can be of
both signs

• perform block-diagonalization mixing between
  MSSM and new states

important if
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Illustrative example
Evolution of the neutralino mass spectrum as a
function of
We take a scenario with
At M10, the 4 and 5 states have negative
eigenvalues
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Neutralino production in ee-
l
via s-channel Z, Z and t-,u-channel selectron
Z exchange
Z, Z gt mass eigenstates Z1, Z2 with mixing
angle
l
selectron exchange
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Neutralino production in ee-
in our scenario
The presence of 1 TeV Z2 strongly affects cross
sections e.g. for M10
Ecm800 GeV
although masses of are as in MSSM
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Neutralino decays
Phenomenology changes significantly only
selected examples

• Cascade decays - c.f. LHC celebrated case

• also possible

but
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Neutralino decays

• Radiative decays - important in cross-over
  zones

e.g. near M12.6 TeV 4-5 zone
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Summary

• USSM a well motivated and interesting scenario
• new states scalar Higgs, Z and two neutralinos
• Here exploratory studies of the USSM neutralino
  sector

• neutralino sector quite complicated
• in a weakly coupled regime under good
  theoretical control
• production and decay processes analysed
• phenomenology at ee- and LHC quite different
• a systematic survey needs more detailed analyses
• cosmological implications gt work in progress