Transcript スライド 1

D-term Dynamical Supersymmetry Breaking
with N. Maru (Keio U.)
• arXiv:1109.2276
• one in preparation
cf. K. Fujiwara and, H.I. and M. Sakaguchi
arXiv: hep-th/0409060, P. T. P. 113
arXiv: hep-th/0503113, N. P. B 723
H. I., K. Maruyoshi and S. Minato
arXiv:0909.5486, Nucl. Phys. B 830
I) Introduction
• spontaneous breaking of SUSY
is much less frequent compared with that of internal symmetry
• most desirable to break
SUSY dynamically (DSB)
• F term DSB has been popular since mid 80’s, in particular,
in the context of instanton generated superpotential
• In this talk, we will accomplish D term DSB, DDSB, for short
• based on the nonrenormalizable D-gaugino-matter fermion
coupling and most natural in the context of
SUSY gauge theory
spontaneous broken to
ala APT-FIS
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II) Basic idea
• Start from a general lagrangian
: a Kähler potential
: a gauge kinetic superfield of the chiral superfield
: a superpotential.
•
in the adjoint representation
bilinears:
where
.
no bosonic counterpart
assume
is the 2nd derivative of a trace fn.
: holomorphic and nonvanishing part of the mass
the
gauginos receive masses of mixed
Majorana-Dirac type and are split.
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• Determination of
stationary condition to
where
and
is the one-loop contribution
is a counterterm.
condensation of the Dirac bilinear is responsible for
In fact, the stationary condition is nothing but the well-known gap equation of
the theory on-shell which contains four-fermi interactions.
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The rest of my talk
Contents
I)
Introduction
II)
Basic idea
III) Illustration by the Theory with
vacuum
at tree level
IV) Mass spectrum at tree level and supercurrent
V)
Self-consistent Hartree Fock approximation
VI) Vacuum shift and metastability (qualitative)
VII) Our work in the context of MSSM
VIII) More on the fermion masses in the H. F. (qualitative)
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III) Theory with
vacuum at tree level
Action to work with
•
•
U(N) gauge group assumed for definiteness (product gauge group O.K.)
: prepotential, input function
• superpotential W supplied by the electric and magnetic FI terms,
made possible by a particular fixing of rigid SU(2)R symmetry
• should contrast with
•
Later, will work with
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Off-shell component lagrangian
The off-shell component lagrangian is
where
and
is the Kähler metric and its derivatives are defined as
.
The gauge part
is, in components,
Finally, the superpotential can be written as
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Eq of motion for auxiliary fields
While, from the transformation laws,
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susy of
• construction of 2nd susy
: Let
and tree vacua
be
so that
• the form of
and
follows from
are derived by imposing
•
where
•
; vacuum condition
•
2nd susy broken
• generic breaking pattern of gauge symmetry:
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IV) Mass spectrum at tree level and supercurrent
a
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vacuum condition
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V) Self-consistent Hartree-Fock approximation
For simplicity, consider the case U(N) unbroken
Recall we hunt for the possibility (up to one-loop):
Mixed Maj.-Dirac mass to
gaugino,
no such coupling to bosons present
DSB
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•
:
mass matrix (holomorphic and nonvanishing part)
The eigenvalues are
We obtain
where
the entire contribution to the 1PI vertex function
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•
:
In order to trade A with
in Vc.t. ,
impose, for instance,
(some number),
we obtain
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• gap equation:
is a stationary condition to
Aside from a trivial solution
, a nontrivial transcendental solution
in general exists
gap eq. In the approximate form
susy is broken to
.
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VI) Vacuum shift and metastability (qualitative)

vacuum condition of ∆ ≠
0 vacuum
computable
•
e.g.
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• obviously
and
the 𝐷 = 0 tree vacuum is not lifted.
So the 𝐷 ≠ 0 vacuum is metastable.
Estimate of the decay rate:
provided
∴ can be made long lived
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VII) Our work in the context of MSSM
Symbolically
•
vector superfields, chiral superfields,
their coupling
extend this to the type of actions with s-gluons and adjoint fermions
so as not to worry about mirror fermions e.t.s.
• gauge group
, the simplest case being
• Due to the non-Lie algebraic nature of
the third prepotential derivatives,
or
,
we do not really need messenger superfields.
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• transmission of DDSB in
loop-corrections
the sfermion masses
to the rest of the theory by higher order
Fox, Nelson, Weiner, JHEP(2002)
the gaugino masses of
the quadratic Casimir of representation
some function of
, which is essentially
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• Demanding
We obtain
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VIII) More on the fermion masses in the H. F. (qualitative)
• Back to the general theory with 3 input functions
• H. F. can be made into a systematic expansion by an index loop argument.
• Take
to be 𝑂(𝑁 2 ).
• In the unbroken 𝑈(𝑁) phase,
The gap eq. is
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• Two sources beyond tree but leading in H. F.
i) Due to the vacuum shift,
as well
ii) For U(1) sector, an index loop circulates
+
These contribute to the masses in the leading order in the H. F.
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D-term Dynamical Supersymmetry Breaking
with N. Maru (Keio U.)
• arXiv:1109.2276
• one in preparation
cf. K. Fujiwara and, H.I. and M. Sakaguchi
arXiv: hep-th/0409060, P. T. P. 113
arXiv: hep-th/0503113, N. P. B 723
H. I., K. Maruyoshi and S. Minato
arXiv:0909.5486, Nucl. Phys. B 830
Obserbale (SU(N)) sector
mass
mass
𝜓′
λ′
gluino
scalar gluon
ℎ
gluon
-1
-1/2
0
1/2
massive fermion
1
𝑆𝑧
-1/2
0
1/2
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