47 research outputs found
Polarized photons in radiative muon capture
We discuss the measurement of polarized photons arising from radiative muon
capture. The spectrum of left circularly polarized photons or equivalently the
circular polarization of the photons emitted in radiative muon capture on
hydrogen is quite sensitive to the strength of the induced pseudoscalar
coupling constant . A measurement of either of these quantities, although
very difficult, might be sufficient to resolve the present puzzle resulting
from the disagreement between the theoretical prediction for and the
results of a recent experiment. This sensitivity results from the absence of
left-handed radiation from the muon line and from the fact that the leading
parts of the radiation from the hadronic lines, as determined from the chiral
power counting rules of heavy-baryon chiral perturbation theory, all contain
pion poles.Comment: 10 pages, 6 figure
The effect of vacuum polarisation on muon-proton scattering at small energies and angles
We give a compact expression for the unpolarised differential cross section
for muon-proton scattering in the one photon exchange approximation. The effect
of adding the vacuum polarisation amplitude to the no-spin-flip amplitude for
one photon exchange is calculated at small energies and scattering angles and
is found to be negligible for present experiments.Comment: 6 pages, one figur
The equivalence theorem and the Bethe-Salpeter equation
We solve the Bethe-Salpeter equation for two-particle scattering in a
field-theoretical model using two lagrangians related by a field
transformation. The kernel of the equation consists of the sum of all
tree-level diagrams for each lagrangian. The solutions differ even if all four
external particles are put on the mass shell, which implies that observables
calculated by solving the Bethe-Salpeter equation depend on the representation
of the theory. We point out that this violation of the equivalence theorem has
a simple explanation and should be expected for any Bethe-Salpeter equation
with a tree-level kernel. Implications for dynamical models of hadronic
interactions are discussed.Comment: 10 pages, 4 figures, using REVTeX. Fig. 2 corrected, results
unchanged, to be published in Phys. Lett.
Effective Hamiltonians with Relativistic Corrections I: The Foldy--Wouthuysen transformation versus the direct Pauli reduction
Two different methods of obtaining ``effective Hamiltonians''
which include relativistic corrections to nonrelativistic calculations are
discussed, the standard Foldy--Wouthuysen transformation and what we call the
``direct Pauli reduction''. We wish to investigate under which circumstances
the two approaches yield the same result. Using a generic interaction with
harmonic time dependence we show that differences in the corresponding
effective S--matrices do arise beyond first--order perturbation theory. We
attribute them to the fact that the use of the direct reduction effective
Hamiltonian involves the additional approximation of neglecting contributions
from the negative--energy intermediate states, an approximation which is
unnecessary in the Foldy--Wouthuysen case as there the Hamiltonian
does not connect positive-- and negative--energy states. We conclude that at
least in the cases where the relativistic Hamiltonian is known, using the
direct Pauli reduction effective Hamiltonian introduces spurious relativistic
effects and therefore the Foldy--Wouthuysen reduction should be preferred.Comment: TRIUMF preprint TRI-PP-93-1
Aspects of radiative K^+_e3 decays
We re-investigate the radiative charged kaon decay K+- --> pi0 e+- nu_e gamma
in chiral perturbation theory, merging the chiral expansion with Low's theorem.
We thoroughly analyze the precision of the predicted branching ratio relative
to the non-radiative decay channel. Structure dependent terms and their impact
on differential decay distributions are investigated in detail, and the
possibility to see effects of the chiral anomaly in this decay channel is
emphasized.Comment: 15 pages, 6 figure
Neutron beta decay in effective field theory
Radiative corrections to the lifetime and angular correlation coefficients of
neutron beta-decay are evaluated in effecitive field theory. We also evaluate
the lowest order nucleon recoil corrections, including weak-magnetism. Our
results agree with those of the long-range and model-independent part of
previous calculations. In an effective theory the model-dependent radiative
corrections are replaced by well-defined low-energy constants. The effective
field theory allows a systematic evaluation of higher order corrections to our
results to the extent that the relevant low-energy constants are known.Comment: 13 pages, 1 figure; two references added, minor correctio
Unphysical Operators in Partially Quenched QCD
We point out that the chiral Lagrangian describing pseudo-Goldstone bosons in
partially quenched QCD has one more four-derivative operator than that for
unquenched QCD with three flavors. The new operator can be chosen to vanish in
the unquenched sector of the partially quenched theory. Its contributions begin
at next-to-leading order in the chiral expansion. At this order it contributes
only to unphysical scattering processes, and we work out some examples. Its
contributions to pseudo-Goldstone properties begin at next-to-next-to-leading
order, and we determine their form. We also determine all the zero and two
derivative operators in the partially quenched chiral Lagrangian,
finding three more than in unquenched QCD, and use these to give the general
form of the analytic next-to-next-to-leading order contributions to the
pseudo-Goldstone mass and decay constant. We discuss the general implications
of such additional operators for the utility of partially quenched simulationsComment: 13 pages, 11 figures Version 2: Additional footnote and parenthesis
in section
Nuclear Medium Effects in the Relativistic Treatment of Quasifree Electron Scattering
Non-relativistic reduction of the S-matrix for the quasifree electron
scattering process is studied in order to
understand the source of differences between non-relativistic and relativistic
models. We perform an effective Pauli reduction on the relativistic expression
for the S-matrix in the one-photon exchange approximation. The reduction is
applied to the nucleon current only; the electrons are treated fully
relativistically. An expansion of the amplitude results in a power series in
the nuclear potentials. The series is found to converge rapidly only if the
nuclear potentials are included in the nuclear current operator. The results
can be cast in a form which reproduces the non-relativistic amplitudes in the
limit that the potentials are removed from the nuclear current operator. Large
differences can be found between calculations which do and do not include the
nuclear potentials in the different orders of the nuclear current operator. In
the high missing momentum region we find that the non-relativistic calculations
with potentials included in the nuclear current up to second order give results
which are close to those of the fully relativistic calculation. This behavior
is an indication of the importance of the medium modifications of the nuclear
currents in this model, which are naturally built into the relativistic
treatment of the reaction.Comment: Latex, 26 pages including 5 uuencoded postscript figures. accepted
for publication in Phys. Rev. C
Meson resonances, large N_c and chiral symmetry
We investigate the implications of large N_c and chiral symmetry for the mass
spectra of meson resonances. Unlike for most other mesons, the mass matrix of
the light scalars deviates strongly from its large-N_c limit. We discuss the
possible assignments for the lightest scalar nonet that survives in the
large-N_c limit.Comment: 14 page
The decay pi0 to gamma gamma to next to leading order in Chiral Perturbation Theory
The two photon decay width of the neutral pion is analyzed within the
combined framework of Chiral Perturbation Theory and the 1/Nc expansion up to
order p^6 and p^4 times 1/Nc in the decay amplitude. The eta' is explicitly
included in the analysis. It is found that the decay width is enhanced by about
4.5% due to the isospin-breaking induced mixing of the pure U(3) states. This
effect, which is of leading order in the low energy expansion, is shown to
persist nearly unchanged at next to leading order. The chief prediction for the
width with its estimated uncertainty is 8.10+-0.08 eV. This prediction at the
1% level makes the upcomming precision measurement of the decay width even more
urgent.
Observations on the eta and eta' can also be made, especially about their
mixing, which is shown to be significantly affected by next to leading order
corrections.Comment: 21 pages, two figure