67,640 research outputs found
A Solution of the Strong CP Problem Transforming the theta-angle to the KM CP-violating Phase
It is shown that in the scheme with a rotating fermion mass matrix (i.e. one
with a scale-dependent orientation in generation space) suggested earlier for
explaining fermion mixing and mass hierarchy, the theta-angle term in the QCD
action of topological origin can be eliminated by chiral transformations, while
giving still nonzero masses to all quarks. Instead, the effects of such
transformations get transmitted by the rotation to the CKM matrix as the KM
phase giving, for of order unity, a Jarlskog invariant typically of
order as experimentally observed. Strong and weak CP violations
appear then as just two facets of the same phenomenon.Comment: 14 pages, 2 figure
Axiomatic Holonomy Maps and Generalized Yang-Mills Moduli Space
This article is a follow-up of ``Holonomy and Path Structures in General
Relativity and Yang-Mills Theory" by Barrett, J. W. (Int.J.Theor.Phys., vol.30,
No.9, 1991). Its main goal is to provide an alternative proof of this part of
the reconstruction theorem which concerns the existence of a connection. A
construction of connection 1-form is presented. The formula expressing the
local coefficients of connection in terms of the holonomy map is obtained as an
immediate consequence of that construction. Thus the derived formula coincides
with that used in "On Loop Space Formulation of Gauge Theories" by Chan, H.-M.,
Scharbach, P. and Tsou S.T. (Ann.Phys., vol.167, 454-472, 1986). The
reconstruction and representation theorems form a generalization of the fact
that the pointed configuration space of the classical Yang-Mills theory is
equivalent to the set of all holonomy maps. The point of this generalization is
that there is a one-to-one correspondence not only between the holonomy maps
and the orbits in the space of connections, but also between all maps from the
loop space on to group fulfilling some axioms and all possible
equivalence classes of bundles with connection, where the equivalence
relation is defined by bundle isomorphism in a natural way.Comment: amslatex, 7 pages, no figure
New Angle on the Strong CP and Chiral Symmetry Problems from a Rotating Mass Matrix
It is shown that when the mass matrix changes in orientation (rotates) in
generation space for changing energy scale, then the masses of the lower
generations are not given just by its eigenvalues. In particular, these masses
need not be zero even when the eigenvalues are zero. In that case, the strong
CP problem can be avoided by removing the unwanted term by a chiral
transformation in no contradiction with the nonvanishing quark masses
experimentally observed. Similarly, a rotating mass matrix may shed new light
on the problem of chiral symmetry breaking. That the fermion mass matrix may so
rotate with scale has been suggested before as a possible explanation for
up-down fermion mixing and fermion mass hierarchy, giving results in good
agreement with experiment.Comment: 14 page
A Consistent Histogram Estimator for Exchangeable Graph Models
Exchangeable graph models (ExGM) subsume a number of popular network models.
The mathematical object that characterizes an ExGM is termed a graphon. Finding
scalable estimators of graphons, provably consistent, remains an open issue. In
this paper, we propose a histogram estimator of a graphon that is provably
consistent and numerically efficient. The proposed estimator is based on a
sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree
of a graph, then smooths the sorted graph using total variation minimization.
The consistency of the SAS algorithm is proved by leveraging sparsity concepts
from compressed sensing.Comment: 28 pages, 5 figure
Evidence of spin liquid with hard-core bosons in a square lattice
We show that laser assisted hopping of hard core bosons in a square optical
lattice can be described by an antiferromagnetic - XY model with
tunable ratio of . We numerically investigate the phase diagram of
the - XY model using both the tensor network algorithm for
infinite systems and the exact diagonalization for small clusters and find
strong evidence that in the intermediate region around ,
there is a spin liquid phase with vanishing magnetization and valence bond
orders, which interconnects the Neel state on the side and the
stripe antiferromagnetic phase on the side. This finding
opens up the possibility of studying the exotic spin liquid phase in a
realistic experimental system using ultracold atoms in an optical lattice.Comment: 5 pages, 5 figure
ENO-wavelet transforms for piecewise smooth functions
We have designed an adaptive essentially nonoscillatory (ENO)-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the main idea from ENO schemes for numerical shock capturing to standard wavelet transforms. The crucial point is that the wavelet coefficients are computed without differencing function values across jumps. However, we accomplish this in a different way than in the standard ENO schemes. Whereas in the standard ENO schemes the stencils are adaptively chosen, in the ENO-wavelet transforms we adaptively change the function and use the same uniform stencils. The ENO-wavelet transform retains the essential properties and advantages of standard wavelet transforms such as concentrating the energy to the low frequencies, obtaining maximum accuracy, maintained up to the discontinuities, and having a multiresolution framework and fast algorithms, all without any edge artifacts. We have obtained a rigorous approximation error bound which shows that the error in the ENO-wavelet approximation depends only on the size of the derivative of the function away from the discontinuities. We will show some numerical examples to illustrate this error estimate
Fermion Generations and Mixing from Dualized Standard Model
We review a possible solution to the fermion generation puzzle based on a
nonabelian generalization of electric--magnetic duality derived some years ago.
This nonabelian duality implies the existence of another SU(3) symmetry dual to
colour, which is necessarily broken when colour is confined and so can play the
role of the ``horizontal'' symmetry for fermion generations. When thus
identified, dual colour then predicts 3 and only 3 fermion generations, besides
suggesting a special Higgs mechanism for breaking the generation symmetry. A
phenomenological model with a Higgs potential and a Yukawa coupling constructed
on these premises is shown to explain immediately all the salient qualitative
features of the fermion mass hierarchy and mixing pattern, excepting for the
moment CP-violation. Calculations already carried out to 1-loop order is shown
to give with only 3 adjustable parameters the following quantities all to
within present experimental error: all 9 CKM matrix elements for
quarks, the neutrino oscillation angles or the MNS lepton mixing matrix
elements , and the mass ratios . The special feature of this model crucial for deriving the above
results is a fermion mass matrix which changes its orientation (rotates) in
generation space with changing energy scale, a feature which is shown to have
direct empirical support.Comment: updated version of course of lectures given at the 42nd Cracow School
of Theoretical Physics, 2002, Polan
Modeling of secondary organic aerosol yields from laboratory chamber data
Laboratory chamber data serve as the basis for constraining models of secondary organic aerosol (SOA) formation. Current models fall into three categories: empirical two-product (Odum), product-specific, and volatility basis set. The product-specific and volatility basis set models are applied here to represent laboratory data on the ozonolysis of α-pinene under dry, dark, and low-NOx conditions in the presence of ammonium sulfate seed aerosol. Using five major identified products, the model is fit to the chamber data. From the optimal fitting, SOA oxygen-to-carbon (O/C) and hydrogen-to-carbon (H/C) ratios are modeled. The discrepancy between measured H/C ratios and those based on the oxidation products used in the model fitting suggests the potential importance of particle-phase reactions. Data fitting is also carried out using the volatility basis set, wherein oxidation products are parsed into volatility bins. The product-specific model is most likely hindered by lack of explicit inclusion of particle-phase accretion compounds. While prospects for identification of the majority of SOA products for major volatile organic compounds (VOCs) classes remain promising, for the near future empirical product or volatility basis set models remain the approaches of choice
A Model Behind the Standard Model
In spite of its many successes, the Standard Model makes many empirical
assumptions in the Higgs and fermion sectors for which a deeper theoretical
basis is sought. Starting from the usual gauge symmetry plus the 3 assumptions: (A) scalar fields as vielbeins in
internal symmetry space \cite{framevec}, (B) the ``confinement picture'' of
symmetry breaking \cite{tHooft,Banovici}, (C) generations as ``dual'' to colour
\cite{genmixdsm}, we are led to a scheme which offers: (I) a geometrical
significance to scalar fields, (II) a theoretical criterion on what scalar
fields are to be introduced, (III) a partial explanation of why appears
broken while confines, (IV) baryon-lepton number (B - L) conservation,
(V) the standard electroweak structure, (VI) a 3-valued generation index for
leptons and quarks, and (VII) a dynamical system with all the essential
features of an earlier phenomenological model \cite{genmixdsm} which gave a
good description of the known mass and mixing patterns of quarks and leptons
including neutrino oscillations. There are other implications the consistency
of which with experiment, however, has not yet been systematically explored. A
possible outcome is a whole new branch of particle spectroscopy from
confinement, potentially as rich in details as that of hadrons from colour
confinement, which will be accessible to experiment at high energy.Comment: 66 pages, added new material on phenomenology, and some new
reference
- …