1,333 research outputs found
Renormalization : A number theoretical model
We analyse the Dirichlet convolution ring of arithmetic number theoretic
functions. It turns out to fail to be a Hopf algebra on the diagonal, due to
the lack of complete multiplicativity of the product and coproduct. A related
Hopf algebra can be established, which however overcounts the diagonal. We
argue that the mechanism of renormalization in quantum field theory is modelled
after the same principle. Singularities hence arise as a (now continuously
indexed) overcounting on the diagonals. Renormalization is given by the map
from the auxiliary Hopf algebra to the weaker multiplicative structure, called
Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep
2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200
Improved Term of the Electron Anomalous Magnetic Moment
We report a new value of electron , or , from 891 Feynman diagrams
of order . The FORTRAN codes of 373 diagrams containing closed
electron loops have been verified by at least two independent formulations. For
the remaining 518 diagrams, which have no closed lepton loop, verification by a
second formulation is not yet attempted because of the enormous amount of
additional work required. However, these integrals have structures that allow
extensive cross-checking as well as detailed comparison with lower-order
diagrams through the renormalization procedure. No algebraic error has been
uncovered for them. The numerical evaluation of the entire term by
the integration routine VEGAS gives , where the
uncertainty is obtained by careful examination of error estimates by VEGAS.
This leads to ,
where the uncertainties come from the term, the estimated
uncertainty of term, and the inverse fine structure constant,
, measured by atom interferometry combined
with a frequency comb technique, respectively. The inverse fine structure
constant derived from the theory and the Seattle
measurement of is .Comment: 64 pages and 10 figures. Eq.(16) is corrected. Comments are added
after Eq.(40
On the statistics of resonances and non-orthogonal eigenfunctions in a model for single-channel chaotic scattering
We describe analytical and numerical results on the statistical properties of
complex eigenvalues and the corresponding non-orthogonal eigenvectors for
non-Hermitian random matrices modeling one-channel quantum-chaotic scattering
in systems with broken time-reversal invariance.Comment: 4 pages, 2 figure
Testing new physics with the electron g-2
We argue that the anomalous magnetic moment of the electron (a_e) can be used
to probe new physics. We show that the present bound on new-physics
contributions to a_e is 8*10^-13, but the sensitivity can be improved by about
an order of magnitude with new measurements of a_e and more refined
determinations of alpha in atomic-physics experiments. Tests on new-physics
effects in a_e can play a crucial role in the interpretation of the observed
discrepancy in the anomalous magnetic moment of the muon (a_mu). In a large
class of models, new contributions to magnetic moments scale with the square of
lepton masses and thus the anomaly in a_mu suggests a new-physics effect in a_e
of (0.7 +- 0.2)*10^-13. We also present examples of new-physics theories in
which this scaling is violated and larger effects in a_e are expected. In such
models the value of a_e is correlated with specific predictions for processes
with violation of lepton number or lepton universality, and with the electric
dipole moment of the electron.Comment: 34 pages, 7 figures. Minor changes and references adde
On the Floquet Theory of Delay Differential Equations
We present an analytical approach to deal with nonlinear delay differential
equations close to instabilities of time periodic reference states. To this end
we start with approximately determining such reference states by extending the
Poincar'e Lindstedt and the Shohat expansions which were originally developed
for ordinary differential equations. Then we systematically elaborate a linear
stability analysis around a time periodic reference state. This allows to
approximately calculate the Floquet eigenvalues and their corresponding
eigensolutions by using matrix valued continued fractions
Hadronic Loop Corrections to the Muon Anomalous Magnetic Moment
The dominant theoretical uncertainties in both, the anomalous magnetic moment
of the muon and the value of the electromagnetic coupling at the Z scale arise
from their hadronic contributions. Since these will ultimately dominate the
experimental errors, we study the correlation between them, as well as with
other fundamental parameters. To this end we present analytical formulas for
the QCD contribution from higher energies and from heavy quarks. Including
these correlations affects the Higgs boson mass extracted from precision data.Comment: 4 page
RASSF1A–LATS1 signalling stabilizes replication forks by restricting CDK2-mediated phosphorylation of BRCA2
Genomic instability is a key hallmark of cancer leading to tumour heterogeneity and therapeutic resistance. BRCA2 has a fundamental role in error-free DNA repair but also sustains genome integrity by promoting RAD51 nucleofilament formation at stalled replication forks. CDK2 phosphorylates BRCA2 (pS3291-BRCA2) to limit stabilizing contacts with polymerized RAD51; however, how replication stress modulates CDK2 activity and whether loss of pS3291-BRCA2 regulation results in genomic instability of tumours are not known. Here we demonstrate that the Hippo pathway kinase LATS1 interacts with CDK2 in response to genotoxic stress to constrain pS3291-BRCA2 and support RAD51 nucleofilaments, thereby maintaining genomic fidelity during replication stalling. We also show that LATS1 forms part of an ATR-mediated response to replication stress that requires the tumour suppressor RASSF1A. Importantly, perturbation of the ATR–RASSF1A–LATS1 signalling axis leads to genomic defects associated with loss of BRCA2 function and contributes to genomic instability and ‘BRCA-ness’ in lung cancers
Random Matrices close to Hermitian or unitary: overview of methods and results
The paper discusses progress in understanding statistical properties of
complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and
non-Hermitian random matrices. Ensembles of this type emerge in various
physical contexts, most importantly in random matrix description of quantum
chaotic scattering as well as in the context of QCD-inspired random matrix
models.Comment: Published version, with a few more misprints correcte
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