10,930 research outputs found

### Geometrical hierarchies in classical supergravity

We introduce a $N=1$ 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 $SU(2)\times U(1)$ are both spontaneously
broken, with vanishing vacuum energy. Two real flat directions control the two
symmetry-breaking scales $m_{3/2}$ and $m_Z$. The two massless scalars are a
gauge singlet and the standard Higgs boson. All other unobserved particles have
masses of order $m_{3/2}$. 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

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

Dipole operator $\bar{s}\sigma_{\mu\nu}F^{\mu\nu}b$ requires the helicity
flip in the involving quark states thus the breaking of chiral $U(3)_{Q}\times
U(3)_{d}$. On the other hand, the $b$-quark mass generation is also a
consequence of chiral $U(3)_{Q}\times U(3)_{d}$ symmetry breaking. Therefore,
in many models, there might be strong correlation between the $b\to s\gamma$
and $b$ 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 $b\to s \gamma$ requires
large supersymmetric correction with large PQ and $R$ symmetry breaking. The
large supersymmetric contribution at the same time significantly modifies the
$b$ quark Yukawa co upling. With combined flavor constraints $B\to X_{s}\gamma$
and $B_{s}\to \mu^{+}\mu^{-}$ and direct constraints on Higgs properties, we
find best fit scenarios with light stop of $\cal O$(500 GeV), negative $A_{t}$
around -750 GeV and large $\mu$-term of 2-3 TeV. In addition, reduction in
$b\bar{b}$ partial width may also result in large enhancement of $\tau\tau$
decay branching fraction. Large parameter region in the survival space under
all bounds may be further constrained by $H\to \tau\tau$ if no excess of
$\tau\tau$ is confirmed at LHC. We only identify a small parameter region with
significant $H\to hh$ decay that is consistent with all bounds and reduced
$\tau\tau$ decay branching fraction.Comment: 18pages, 6 figure

### Population Modeling by Differential Equations

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 donâ€™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

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

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