145 research outputs found
Quantum Mechanics on Manifolds Embedded in Euclidean Space
Quantum particles confined to surfaces in higher dimensional spaces are acted
upon by forces that exist only as a result of the surface geometry and the
quantum mechanical nature of the system. The dynamics are particularly rich
when confinement is implemented by forces that act normal to the surface. We
review this confining potential formalism applied to the confinement of a
particle to an arbitrary manifold embedded in a higher dimensional Euclidean
space. We devote special attention to the geometrically induced gauge potential
that appears in the effective Hamiltonian for motion on the surface. We
emphasize that the gauge potential is only present when the space of states
describing the degrees of freedom normal to the surface is degenerate. We also
distinguish between the effects of the intrinsic and extrinsic geometry on the
effective Hamiltonian and provide simple expressions for the induced scalar
potential. We discuss examples including the case of a 3-dimensional manifold
embedded in a 5-dimensional Euclidean space.Comment: 12 pages, LaTe
An alternative NMSSM phenomenology with manifest perturbative unification
Can supersymmetric models with a moderate stop mass be made consistent with
the negative Higgs boson searches at LEP, while keeping perturbative
unification manifest? The NMSSM achieves this rather easily, but only if extra
matter multiplets filling complete SU(5) representations are present at
intermediate energies. As a concrete example which makes use of this feature,
we give an analytic description of the phenomenology of a constrained NMSSM
close to a Peccei-Quinn symmetry point. The related pseudo-Goldstone boson
appears in decays of the Higgs bosons and possibly of the lightest neutralino,
and itself decays into (b anti-b) and (tau anti-tau).Comment: 19 pages, 13 figures; v2: possibility of pseudo-Goldstone below 2m_b
threshold added, version published by JHE
Amplitudes and Spinor-Helicity in Six Dimensions
The spinor-helicity formalism has become an invaluable tool for understanding
the S-matrix of massless particles in four dimensions. In this paper we
construct a spinor-helicity formalism in six dimensions, and apply it to derive
compact expressions for the three, four and five point tree amplitudes of
Yang-Mills theory. Using the KLT relations, it is a straightforward process to
obtain amplitudes in linearized gravity from these Yang-Mills amplitudes; we
demonstrate this by writing down the gravitational three and four point
amplitudes. Because there is no conserved helicity in six dimensions, these
amplitudes describe the scattering of all possible polarization states (as well
as Kaluza-Klein excitations) in four dimensions upon dimensional reduction. We
also briefly discuss a convenient formulation of the BCFW recursion relations
in higher dimensions.Comment: 26 pages, 2 figures. Minor improvements of the discussio
Supersymmetry for Fermion Masses
It is proposed that supersymmetry (SUSY) maybe used to understand fermion
mass hierarchies. A family symmetry Z_{3L} is introduced, which is the cyclic
symmetry among the three generation SU(2) doublets. SUSY breaks at a high
energy scale ~ 10^{11} GeV. The electroweak energy scale ~ 100 GeV is
unnaturally small. No additional global symmetry, like the R-parity, is
imposed. The Yukawa couplings and R-parity violating couplings all take their
natural values which are about (10^0-10^{-2}). Under the family symmetry, only
the third generation charged fermions get their masses. This family symmetry is
broken in the soft SUSY breaking terms which result in a hierarchical pattern
of the fermion masses. It turns out that for the charged leptons, the tau mass
is from the Higgs vacuum expectation value (VEV) and the sneutrino VEVs, the
muon mass is due to the sneutrino VEVs, and the electron gains its mass due to
both Z_{3L} and SUSY breaking. The large neutrino mixing are produced with
neutralinos playing the partial role of right-handed neutrinos. |V_{e3}| which
is for nu_e-nu_{tau} mixing is expected to be about 0.1. For the quarks, the
third generation masses are from the Higgs VEVs, the second generation masses
are from quantum corrections, and the down quark mass due to the sneutrino
VEVs. It explains m_c/m_s, m_s/m_e, m_d > m_u and so on. Other aspects of the
model are discussed.Comment: 25 pages, 3 figures, revtex4; neutrino oscillation and many
discussions added, smallness of the electron mass due to supersymmetry
pointed out; v3: numerical errors correcte
The Minimally Tuned Minimal Supersymmetric Standard Model
The regions in the Minimal Supersymmetric Standard Model with the minimal
amount of fine-tuning of electroweak symmetry breaking are presented for
general messenger scale. No a priori relations among the soft supersymmetry
breaking parameters are assumed and fine-tuning is minimized with respect to
all the important parameters which affect electroweak symmetry breaking. The
superpartner spectra in the minimally tuned region of parameter space are quite
distinctive with large stop mixing at the low scale and negative squark soft
masses at the high scale. The minimal amount of tuning increases enormously for
a Higgs mass beyond roughly 120 GeV.Comment: 38 pages, including 2 appendices, 8 figure
Supersymmetry and the LHC Inverse Problem
Given experimental evidence at the LHC for physics beyond the standard model,
how can we determine the nature of the underlying theory? We initiate an
approach to studying the "inverse map" from the space of LHC signatures to the
parameter space of theoretical models within the context of low-energy
supersymmetry, using 1808 LHC observables including essentially all those
suggested in the literature and a 15 dimensional parametrization of the
supersymmetric standard model. We show that the inverse map of a point in
signature space consists of a number of isolated islands in parameter space,
indicating the existence of "degeneracies"--qualitatively different models with
the same LHC signatures. The degeneracies have simple physical
characterizations, largely reflecting discrete ambiguities in electroweak-ino
spectrum, accompanied by small adjustments for the remaining soft parameters.
The number of degeneracies falls in the range 1<d<100, depending on whether or
not sleptons are copiously produced in cascade decays. This number is large
enough to represent a clear challenge but small enough to encourage looking for
new observables that can further break the degeneracies and determine at the
LHC most of the SUSY physics we care about. Degeneracies occur because
signatures are not independent, and our approach allows testing of any new
signature for its independence. Our methods can also be applied to any other
theory of physics beyond the standard model, allowing one to study how model
footprints differ in signature space and to test ways of distinguishing
qualitatively different possibilities for new physics at the LHC.Comment: 55 pages, 30 figure
Localization of gravity in brane world with arbitrary extra dimensions
We study the induced 4-dimensional linearized Einstein field equations in an
m-dimensional bulk space by means of a confining potential. It is shown that in
this approach the mass of graviton is quantized. The cosmological constant
problem is also addressed within the context of this approach. We show that the
difference between the values of the cosmological constant in particle physics
and cosmology stems from our measurements in two different scales, small and
large.Comment: 8 pages. arXiv admin note: substantial text overlap with
arXiv:gr-qc/0408004, arXiv:gr-qc/0607067, arXiv:0704.1035, arXiv:0707.3558,
arXiv:0710.266
Schwinger-Keldysh Approach to Disordered and Interacting Electron Systems: Derivation of Finkelstein's Renormalization Group Equations
We develop a dynamical approach based on the Schwinger-Keldysh formalism to
derive a field-theoretic description of disordered and interacting electron
systems. We calculate within this formalism the perturbative RG equations for
interacting electrons expanded around a diffusive Fermi liquid fixed point, as
obtained originally by Finkelstein using replicas. The major simplifying
feature of this approach, as compared to Finkelstein's is that instead of replicas, we only need to consider N=2 species. We compare the dynamical
Schwinger-Keldysh approach and the replica methods, and we present a simple and
pedagogical RG procedure to obtain Finkelstein's RG equations.Comment: 22 pages, 14 figure
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