D-term Dynamical Supersymmetry Breaking K. Fujiwara and, H.I. and M. Sakaguchi arXiv:...
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Transcript of D-term Dynamical Supersymmetry Breaking K. Fujiwara and, H.I. and M. Sakaguchi arXiv:...
D-term Dynamical Supersymmetry Breaking
K. Fujiwara and, H.I. and M. SakaguchiarXiv: hep-th/0409060, P. T. P. 113arXiv: hep-th/0503113, N. P. B 723
H. I., K. Maruyoshi and S. MinatoarXiv:0909.5486, Nucl. Phys. B 830
cf.
1
with N. Maru (Keio U.)• arXiv:1109.2276 • one in preparation
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
II) Basic idea• Start from a general lagrangian
: a Kähler potential : a gauge kinetic superfield of the chiral superfield in the adjoint representation: a superpotential.
• bilinears:
where .
no bosonic counterpart
assume is the 2nd derivative of a trace fn.
the gauginos receive masses of mixed Majorana-Dirac type and are split.
: holomorphic and nonvanishing part of the mass
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• Determination of
stationary condition to
where is the one-loop contribution
and is a counterterm.
In fact, the stationary condition is nothing but the well-known gap equation of
the theory on-shell which contains four-fermi interactions.
condensation of the Dirac bilinear is responsible for
The rest of my talk
ContentsI) 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
• 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
Action to work with
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Off-shell component lagrangianThe off-shell component lagrangian is
where is the Kähler metric and its derivatives are defined asand .
The gauge part is, in components,
Finally, the superpotential can be written as
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susy of and tree vacua• construction of 2nd susy : Let be
• the form of and are derived by imposing
•
• ; vacuum condition
•
• generic breaking pattern of gauge symmetry:
so that follows from
where
2nd susy broken
V) Self-consistent Hartree-Fock approximation
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For simplicity, consider the case U(N) unbroken
Recall we hunt for the possibility (up to one-loop):
no such coupling to bosons present
Mixed Maj.-Dirac mass to gaugino,
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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• gap equation:
is a stationary condition to
susy is broken to .
Aside from a trivial solution , a nontrivial transcendental solution
gap eq. In the approximate form
in general exists
vacuum condition of vacuum
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VI) Vacuum shift and metastability (qualitative)
computable
•
e.g.
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• obviously and
the tree vacuum is not lifted.
So the vacuum is metastable.
Estimate of the decay rate:
provided
can be made long lived∴
VII) Our work in the context of MSSM
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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.
• transmission of DDSB in to the rest of the theory by higher order loop-corrections
the sfermion masses
the gaugino masses of
the quadratic Casimir of representation
some function of , which is essentially
Fox, Nelson, Weiner, JHEP(2002)
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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 .
• In the unbroken 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
K. Fujiwara and, H.I. and M. SakaguchiarXiv: hep-th/0409060, P. T. P. 113arXiv: hep-th/0503113, N. P. B 723
H. I., K. Maruyoshi and S. MinatoarXiv:0909.5486, Nucl. Phys. B 830
cf.with N. Maru (Keio U.)• arXiv:1109.2276 • one in preparation
gluino
gluon
𝜓 ′λ ′massive fermion
scalar gluon
-1 -1/2 0 1/2 1
mass
h-1/2 0 1/2
mass
𝑆𝑧
Obserbale (SU(N)) sector