4,498 research outputs found
Collinearity, convergence and cancelling infrared divergences
The Lee-Nauenberg theorem is a fundamental quantum mechanical result which
provides the standard theoretical response to the problem of collinear and
infrared divergences. Its argument, that the divergences due to massless
charged particles can be removed by summing over degenerate states, has been
successfully applied to systems with final state degeneracies such as LEP
processes. If there are massless particles in both the initial and final
states, as will be the case at the LHC, the theorem requires the incorporation
of disconnected diagrams which produce connected interference effects at the
level of the cross-section. However, this aspect of the theory has never been
fully tested in the calculation of a cross-section. We show through explicit
examples that in such cases the theorem introduces a divergent series of
diagrams and hence fails to cancel the infrared divergences. It is also
demonstrated that the widespread practice of treating soft infrared divergences
by the Bloch-Nordsieck method and handling collinear divergences by the
Lee-Nauenberg method is not consistent in such cases.Comment: 29 pages, 17 figure
A Magellanic Origin for the Warp of the Galaxy
We show that a Magellanic Cloud origin for the warp of the Milky Way can
explain most quantitative features of the outer HI layer recently identified by
Levine, Blitz & Heiles (2005). We construct a model similar to that of Weinberg
(1998) that produces distortions in the dark matter halo, and we calculate the
combined effect of these dark-halo distortions and the direct tidal forcing by
the Magellanic Clouds on the disk warp in the linear regime. The interaction of
the dark matter halo with the disk and resonances between the orbit of the
Clouds and the disk account for the large amplitudes observed for the vertical
m=0,1,2 harmonics. The observations lead to six constraints on warp forcing
mechanisms and our model reasonably approximates all six. The disk is shown to
be very dynamic, constantly changing its shape as the Clouds proceed along
their orbit. We discuss the challenges to MOND placed by the observations.Comment: 4 pages, 3 figures, submitted to ApJ Letters. Additional graphics, 3d
visualizations and movies available at
http://www.astro.umass.edu/~weinberg/lm
Isospin breaking in the nucleon mass and the sensitivity of β decays to new physics
We discuss the consequences of the approximate conservation of the vector and axial currents for the hadronic matrix elements appearing in β decay if nonstandard interactions are present. In particular, the isovector (pseudo)scalar charge gS(P) of the nucleon can be related to the difference (sum) of the nucleon masses in the absence of electromagnetic effects. Using recent determinations of these quantities from phenomenological and lattice QCD studies we obtain the accurate values gS=1.02(11) and gP=349(9) in the modified minimal subtraction scheme at μ=2  GeV. The consequences for searches of nonstandard scalar interactions in nuclear β decays are studied, finding for the corresponding Wilson coefficient εS=0.0012(24) at 90% C.L., which is significantly more stringent than current LHC bounds and previous low-energy bounds using less precise gS values. We argue that our results could be rapidly improved with updated computations and the direct calculation of certain ratios in lattice QCD. Finally, we discuss the pion-pole enhancement of gP, which makes β decays much more sensitive to nonstandard pseudoscalar interactions than previously thought
Low Energy Constants from High Energy Theorems
New constraints on resonance saturation in chiral perturbation theory are
investigated. These constraints arise because each consistent saturation scheme
must map to a representation of the full QCD chiral symmetry group. The
low-energy constants of chiral perturbation theory are then related by a set of
mixing angles. It is shown that vector meson dominance is a consequence of the
fact that nature has chosen the lowest-dimensional nontrivial chiral
representation. It is further shown that chiral symmetry places an upper bound
on the mass of the lightest scalar in the hadron spectrum.Comment: 11 pages TeX and mtexsis.te
The gravitational analogue to the hydrogen atom (A summer study at the borders of quantum mechanics and general relativity)
This article reports on a student summer project performed in 2006 at the
University of Frankfurt. It is addressed to undergraduate students familiar
with the basic principles of relativistic quantum mechanics and general
relativity. The aim of the project was to study the Dirac equation in curved
space time. To obtain the general relativistic Dirac equation we use the
formulation of gravity as a gauge theory in the first part. After these general
considerations we restrict the further discussion to the special case of the
Schwarzschild metric. This setting corresponds to the hydrogen atom, with the
electromagnetic field replaced by gravity. Although there is a singularity at
the event horizon it turns out that a regular solution of the time independent
Dirac equation exists. Finally the Dirac equation is solved numerically using
suitable boundary conditions.Comment: 19 pages, 3 figure
New GUT predictions for quark and lepton mass ratios confronted with phenomenology
Group theoretical factors from GUT symmetry breaking can lead to predictions
for the ratios of quark and lepton masses (or Yukawa couplings) at the
unification scale. Due to supersymmetric (SUSY) threshold corrections the
viability of such predictions can depend strongly on the SUSY parameters. For
three common minimal SUSY breaking scenarios with anomaly, gauge and gravity
mediation we investigate which GUT scale ratios , ,
and are allowed when phenomenological constraints from
electroweak precision observables, physics, , mass-limits on
sparticles from direct searches as well as, optionally, constraints from the
observed dark matter density are taken into account. We derive possible new
predictions for the GUT scale mass ratios and compare them with the
phenomenologically allowed ranges. We find that new GUT scale predictions such
as or 6 and or 2 are often favoured
compared to the ubiquitous relations or . They
are viable for characteristic SUSY scenarios, testable at the CERN LHC and
future colliders.Comment: 33 pages, 5 figures; references added; version to appear in Phys.
Rev.
Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity
An analysis of insular solutions of Einstein's field equations for static,
spherically symmetric, source mass, on the basis of exterior Schwarzschild
solution is presented. Following the analysis, we demonstrate that the {\em
regular} solutions governed by a self-bound (that is, the surface density does
not vanish together with pressure) equation of state (EOS) or density variation
can not exist in the state of hydrostatic equilibrium, because the source mass
which belongs to them, does not represent the `actual mass' appears in the
exterior Schwarzschild solution. The only configuration which could exist in
this regard is governed by the homogeneous density distribution (that is, the
interior Schwarzschild solution). Other structures which naturally fulfill the
requirement of the source mass, set up by exterior Schwarzschild solution (and,
therefore, can exist in hydrostatic equilibrium) are either governed by
gravitationally-bound regular solutions (that is, the surface density also
vanishes together with pressure), or self-bound singular solutions (that is,
the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for
publication in Modern Physics Letters
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