11,311 research outputs found

    Geometrical hierarchies in classical supergravity

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    We introduce a N=1N=1 supergravity model with a very simple hidden sector coupled to the electroweak gauge and Higgs sectors of the MSSM. At the classical level, supersymmetry and SU(2)×U(1)SU(2)\times U(1) are both spontaneously broken, with vanishing vacuum energy. Two real flat directions control the two symmetry-breaking scales m3/2m_{3/2} and mZm_Z. The two massless scalars are a gauge singlet and the standard Higgs boson. All other unobserved particles have masses of order m3/2m_{3/2}. This may be a new starting point for studying the compatibility of naturalness with the observed mass hierarchies.Comment: 5 pages, no figure

    A minimal approach to the scattering of physical massless bosons

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    Tree and loop level scattering amplitudes which involve physical massless bosons are derived directly from physical constraints such as locality, symmetry and unitarity, bypassing path integral constructions. Amplitudes can be projected onto a minimal basis of kinematic factors through linear algebra, by employing four dimensional spinor helicity methods or at its most general using projection techniques. The linear algebra analysis is closely related to amplitude relations, especially the Bern-Carrasco-Johansson relations for gluon amplitudes and the Kawai-Lewellen-Tye relations between gluons and graviton amplitudes. Projection techniques are known to reduce the computation of loop amplitudes with spinning particles to scalar integrals. Unitarity, locality and integration-by-parts identities can then be used to fix complete tree and loop amplitudes efficiently. The loop amplitudes follow algorithmically from the trees. A range of proof-of-concept examples is presented. These include the planar four point two-loop amplitude in pure Yang-Mills theory as well as a range of one loop amplitudes with internal and external scalars, gluons and gravitons. Several interesting features of the results are highlighted, such as the vanishing of certain basis coefficients for gluon and graviton amplitudes. Effective field theories are naturally and efficiently included into the framework. The presented methods appear most powerful in non-supersymmetric theories in cases with relatively few legs, but with potentially many loops. For instance, iterated unitarity cuts of four point amplitudes for non-supersymmetric gauge and gravity theories can be computed by matrix multiplication, generalising the so-called rung-rule of maximally supersymmetric theories. The philosophy of the approach to kinematics also leads to a technique to control color quantum numbers of scattering amplitudes with matter.Comment: 65 pages, exposition improved, typos correcte

    Revisit to Non-decoupling MSSM

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    Dipole operator sˉσμνFμνb\bar{s}\sigma_{\mu\nu}F^{\mu\nu}b requires the helicity flip in the involving quark states thus the breaking of chiral U(3)Q×U(3)dU(3)_{Q}\times U(3)_{d}. On the other hand, the bb-quark mass generation is also a consequence of chiral U(3)Q×U(3)dU(3)_{Q}\times U(3)_{d} symmetry breaking. Therefore, in many models, there might be strong correlation between the bsγb\to s\gamma and bb quark Yukawa coupling. We use non-decoupling MSSM model to illustrate this feature. The light Higgs boson may evade the direct search experiments at LEPII or Tevatron while the 125 GeV Higgs-like boson is identified as the heavy Higgs boson in the spectrum. A light charged Higgs is close to the heavy Higgs boson which is of 125 GeV and its contribution to bsγb\to s \gamma requires large supersymmetric correction with large PQ and RR symmetry breaking. The large supersymmetric contribution at the same time significantly modifies the bb quark Yukawa co upling. With combined flavor constraints BXsγB\to X_{s}\gamma and Bsμ+μB_{s}\to \mu^{+}\mu^{-} and direct constraints on Higgs properties, we find best fit scenarios with light stop of O\cal O(500 GeV), negative AtA_{t} around -750 GeV and large μ\mu-term of 2-3 TeV. In addition, reduction in bbˉb\bar{b} partial width may also result in large enhancement of ττ\tau\tau decay branching fraction. Large parameter region in the survival space under all bounds may be further constrained by HττH\to \tau\tau if no excess of ττ\tau\tau is confirmed at LHC. We only identify a small parameter region with significant HhhH\to hh decay that is consistent with all bounds and reduced ττ\tau\tau decay branching fraction.Comment: 18pages, 6 figure

    Population Modeling by Differential Equations

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    A general model for the population of Tibetan antelope is constructed. The present model shows that the given data is reasonably logistic. From this model the extinction of antelopes in China is predicted if we don’t consider the effects of humans on the population. Moreover, this model shows that the population is limited. A projected limiting number is given by this model. Some typical mathematical models are introduced such as exponential model and logistic model. The solutions of those models are analyzed

    The Goldstino Field in Linear and Nonlinear Realizations of Supersymmetry

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    A Goldstino field in the nonlinear realization of supersymmetry is constructed from an appropriate chiral super-multiplet of the linear theory, in general O'Raifeataigh-like models. The linear theories can thus be reformulated into their nonlinear versions, via the standard procedure. The Goldstino field disappears totally from the original Lagrangian in the process, but reemerges in the Jacobian of the transformation and covariant derivatives. Vertices with Goldstino fields carry at least one space-time derivative, as one would have expected.Comment: 7+1 pages, Late