126 research outputs found
On the controversy concerning the definition of quark and gluon angular momentum
A major controversy has arisen in QCD as to how to split the total angular
momentum into separate quark and gluon contributions, and as to whether the
gluon angular momentum can itself be split, in a gauge invariant way, into a
spin and orbital part. Several authors have proposed various answers to these
questions and offered a variety of different expressions for the relevant
operators. I argue that none of these is acceptable and suggest that the
canonical expression for the momentum and angular momentum operators is the
correct and physically meaningful one. It is then an inescapable fact that the
gluon angular momentum operator cannot, in general, be split in a gauge
invariant way into a spin and orbital part. However, the projection of the
gluon spin onto its direction of motion i.e. its helicity is gauge invariant
and is measured in deep inelastic scattering on nucleons. The Ji sum rule,
relating the quark angular momentum to generalized parton distributions, though
not based on the canonical operators, is shown to be correct, if interpreted
with due care. I also draw attention to several interesting aspects of QED and
QCD, which, to the best of my knowledge, are not commented upon in the standard
textbooks on Field Theory.Comment: 41 pages; Some incorrect statements have been rectified and a
detailed discussion has been added concerning the momentum carried by quarks
and the Ji sum rule for the angular momentu
Control of edge bulge evolution during photoresist reflow and its application to diamond microlens fabrication
Two-Loop Bethe Logarithms for Higher Excited S Levels
Processes mediated by two virtual low-energy photons contribute quite
significantly to the energy of hydrogenic S states. The corresponding level
shift is of the order of (alpha/pi)^2 (Zalpha)^6 m_e c^2 and may be ascribed to
a two-loop generalization of the Bethe logarithm. For 1S and 2S states, the
correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev.
Lett. vol. 91, 113005 (2003)]. Here, we generalize the approach to higher
excited S states, which in contrast to the 1S and 2S states can decay to P
states via the electric-dipole (E1) channel. The more complex structure of the
excited-state wave functions and the necessity to subtract P-state poles lead
to additional calculational problems. In addition to the calculation of the
excited-state two-loop energy shift, we investigate the ambiguity in the energy
level definition due to squared decay rates.Comment: 14 pages, RevTeX, to appear in Phys. Rev.
Multiplying unitary random matrices - universality and spectral properties
In this paper we calculate, in the large N limit, the eigenvalue density of
an infinite product of random unitary matrices, each of them generated by a
random hermitian matrix. This is equivalent to solving unitary diffusion
generated by a hamiltonian random in time. We find that the result is universal
and depends only on the second moment of the generator of the stochastic
evolution. We find indications of critical behavior (eigenvalue spacing scaling
like ) close to for a specific critical evolution time
.Comment: 12 pages, 2 figure
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
Constraints on the mass of the superlight gravitino from the muon anomaly
We reexamine the limits on the gravitino mass supplied by the muon anomaly in
the frame of supergravity models with a superlight gravitino and a superlight
scalar S and a superlight pseudoscalar P.Comment: 7 pages, REVTeX with 5 figures. Uses epsfi
Hadronic Contributions to the Muon Anomaly in the Constituent Chiral Quark Model
The hadronic contributions to the anomalous magnetic moment of the muon which
are relevant for the confrontation between theory and experiment at the present
level of accuracy, are evaluated within the same framework: the constituent
chiral quark model. This includes the contributions from the dominant hadronic
vacuum polarization as well as from the next--to--leading order hadronic vacuum
polarization, the contributions from the hadronic light-by-light scattering,
and the contributions from the electroweak hadronic vertex.
They are all evaluated as a function of only one free parameter: the
constituent quark mass. We also comment on the comparison between our results
and other phenomenological evaluations.Comment: Several misprints corrected and a clarifying sentence added. Three
figures superposed and two references added. Version to appear in JHE
Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge theory on the lattice
The line of phase transitions, separating the confinement and the Coulomb
phases in the four-dimensional pure compact U(1) gauge theory with extended
Wilson action, is reconsidered. We present new numerical evidence that a part
of this line, including the original Wilson action, is of second order. By
means of a high precision simulation on homogeneous lattices on a sphere we
find that along this line the scaling behavior is determined by one fixed point
with distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the
existence of a nontrivial and nonasymptotically free four-dimensional pure U(1)
gauge theory in the continuum very probable. The universality and duality
arguments suggest that this conclusion holds also for the monopole loop gas,
for the noncompact abelian Higgs model at large negative squared bare mass, and
for the corresponding effective string theory.Comment: 11 pages, LaTeX, 2 figure
High-statistics finite size scaling analysis of U(1) lattice gauge theory with Wilson action
We describe the results of a systematic high-statistics Monte-Carlo study of
finite-size effects at the phase transition of compact U(1) lattice gauge
theory with Wilson action on a hypercubic lattice with periodic boundary
conditions. We find unambiguously that the critical exponent nu is lattice-size
dependent for volumes ranging from 4^4 to 12^4. Asymptotic scaling formulas
yield values decreasing from nu(L >= 4) = 0.33 to nu(L >= 9) = 0.29. Our
statistics are sufficient to allow the study of different phenomenological
scenarios for the corrections to asymptotic scaling. We find evidence that
corrections to a first-order transition with nu=0.25 provide the most accurate
description of the data. However the corrections do not follow always the
expected first-order pattern of a series expansion in the inverse lattice
volume V^{-1}. Reaching the asymptotic regime will require lattice sizes
greater than L=12. Our conclusions are supported by the study of many cumulants
which all yield consistent results after proper interpretation.Comment: revtex, 12 pages, 9 figure
The Pole Mass of The Heavy Quark. Perturbation Theory and Beyond
The key quantity of the heavy quark theory is the quark mass . Since
quarks are unobservable one can suggest different definitions of . One of
the most popular choices is the pole quark mass routinely used in perturbative
calculations and in some analyses based on heavy quark expansions. We show that
no precise definition of the pole mass can be given in the full theory once
non-perturbative effects are included. Any definition of this quantity suffers
from an intrinsic uncertainty of order \Lam /m_Q. This fact is succinctly
described by the existence of an infrared renormalon generating a factorial
divergence in the high-order coefficients of the series; the
corresponding singularity in the Borel plane is situated at . A
peculiar feature is that this renormalon is not associated with the matrix
element of a local operator. The difference \La \equiv M_{H_Q}-m_Q^{pole} can
still be defined in Heavy Quark Effective Theory, but only at the price of
introducing an explicit dependence on a normalization point : \La (\mu
). Fortunately the pole mass {\em per se} does not appear in
calculable observable quantities.Comment: 22 pages, Latex, 6 figures (available upon request), TPI-MINN-94/4-T,
CERN-TH.7171/94, UND-HEP-94-BI
- …