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## D-term Dynamical Supersymmetry Breaking

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**D-term Dynamical Supersymmetry Breaking**• with N. Maru (Keio U.) • arXiv:1109.2276 • one in preparation K. Fujiwara and, H.I. andM. 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 cf. 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 nonrenormalizableD-gaugino-matter fermion • coupling and most natural in the context of SUSY gauge theory • spontaneous broken to alaAPT-FIS**II) Basic idea**• Start from a general lagrangian • bilinears: where . no bosonic counterpart assume is the 2nd derivative of a trace fn. : a Kähler potential : a gauge kinetic superfield of the chiral superfield in the adjoint representation : a superpotential. : holomorphic and nonvanishing part of the mass the gauginos receive masses of mixed Majorana-Dirac type and are split.**Determination of**stationary condition to where is the one-loop contribution and 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.**The rest of my talk**Contents I) Introduction II) Basic idea III) Illustrationby the Theory with vacuum at tree level IV) Mass spectrum at tree level and supercurrent V) Self-consistent HartreeFockapproximation 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)**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**Off-shell component lagrangian**The off-shell component lagrangian is where is the Kähler metric and its derivatives are defined as and . The gauge part is, in components, Finally, the superpotential can be written as**Eq of motion for auxiliary fields**While, from the transformation laws,**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**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**the entire contribution to the 1PI vertex function**• : mass matrix (holomorphic and nonvanishing part) The eigenvalues are We obtain where**:**In order to trade A with in Vc.t. , impose, for instance, we obtain (some number),**is a stationary condition to**Aside from a trivial solution , a nontrivial transcendental solution gap eq. In the approximate form in general exists • gap equation: susy is broken to .**VI) Vacuum shift and metastability(qualitative)**• vacuum condition of vacuum computable • e.g.**obviously and**• the tree vacuum is not lifted. • So the vacuum is metastable. • Estimate of the decay rate: provided can be made long lived**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. VII) Our work in the context of MSSM**transmission of DDSB in to the rest of the**theory by higher order • loop-corrections the sfermion masses Fox, Nelson, Weiner, JHEP(2002) the gaugino masses of the quadratic Casimir of representation some function of , which is essentially**Demanding**• We obtain**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**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.**D-term Dynamical Supersymmetry Breaking**• with N. Maru (Keio U.) • arXiv:1109.2276 • one in preparation K. Fujiwara and, H.I. andM. 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 cf. Obserbale (SU(N)) sector mass mass massive fermion scalar gluon gluino gluon -1/2 0 1/2 -1 -1/2 0 1/2 1