990 research outputs found
Stability for Borell-Brascamp-Lieb inequalities
We study stability issues for the so-called Borell-Brascamp-Lieb
inequalities, proving that when near equality is realized, the involved
functions must be -close to be -concave and to coincide up to
homotheties of their graphs.Comment: to appear in GAFA Seminar Note
The , , and electromagnetic form factors
The rainbow truncation of the quark Dyson-Schwinger equation is combined with
the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed
quark-photon vertex in a self-consistent Poincar\'e-invariant study of the pion
and kaon electromagnetic form factors in impulse approximation. We demonstrate
explicitly that the current is conserved in this approach and that the obtained
results are independent of the momentum partitioning in the Bethe-Salpeter
amplitudes. With model gluon parameters previously fixed by the condensate, the
pion mass and decay constant, and the kaon mass, the charge radii and spacelike
form factors are found to be in good agreement with the experimental data.Comment: 8 pages, 6 figures, Revte
mixing and the next-to-leading-order power correction
The next-to-leading-order power correction for and
form factors are evaluated and employed to explore the
mixing. The parameters of the two mixing angle scheme are
extracted from the data for form factors, two photon decay widths and radiative
decays. The analysis gives the result:
, where
and are the decay constants and the mixing
angles for the singlet (octet) state. In addition, we arrive at a stringent
range for MeV MeV.Comment: 23 pages, 9 figures, To be publshied in Phys. Rev.
Final-State Phases in , and Decays
The final-state phases in , and decays
appear to follow a pattern similar to those in , , and decays. Each set of processes is characterized by
three charge states but only two independent amplitudes, so the amplitudes form
triangles in the complex plane. For the first two sets the triangles appear to
have non-zero area, while for the or decays the areas
of the triangles are consistent with zero. Following an earlier discussion of
this behavior for decays, a similar analysis is performed for B decays, and
the relative phases and magnitudes of contributing amplitudes are determined.
The significance of recent results on \ob \to D^{(*)0} \bar{K}^{(*)0} is
noted. Open theoretical and experimental questions are indicated.Comment: 16 pages, LaTeX, 3 figures, to be submitted to Phys. Rev. D.
References added; comments on new experimental results and analysi
Composition of the Pseudoscalar Eta and Eta' Mesons
The composition of the eta and eta' mesons has long been a source of
discussion and is of current interest with new experimental results appearing.
We investigate what can be learnt from a number of different processes: V to P
gamma and P to V gamma (V and P are light vector and pseudoscalar mesons
respectively), P to gamma gamma, J/psi,psi' to P gamma, J/psi,psi' to P V, and
chi_{c0,2} to PP. These constrain the eta-eta' mixing angle to a consistent
value, phi approx 42 degrees; we find that the c cbar components are lesssim 5%
in amplitude. We also find that, while the data hint at a small gluonic
component in the eta', the conclusions depend sensitively on unknown form
factors associated with exclusive dynamics. In addition, we predict BR(psi' to
eta' gamma) approx 1 10^{-5} and BR(chi_{c0} to eta eta') approx 2 10^{-5} - 1
10^{-4}. We provide a method to test the mixing using chi_{c2} to eta eta, eta'
eta', and eta eta' modes and make some general observations on chi_{c0,2}
decays. We also survey the semileptonic and hadronic decays of bottom and
charmed mesons and find some modes where the mixing angle can be extracted
cleanly with the current experimental data, some where more data will allow
this, and some where a more detailed knowledge of the different amplitudes is
required.Comment: 34 pages, 11 figures. v2: version published in JHEP, added
substantial section on B and D meson electroweak decays, added comment on
psi' to eta(')/eta_c gamma, Figs 5 and 6 split and made clearer, added
references, other minor revisions which don't change conclusion
Final-State Phases in Charmed Meson Two-Body Nonleptonic Decays
Observed decay rates indicate large phase differences among the amplitudes
for the charge states in and but
relatively real amplitudes in the charge states for . This
feature is traced using an SU(3) flavor analysis to a sign flip in the
contribution of one of the amplitudes contributing to the latter processes in
comparison with its contribution to the other two sets. This amplitude may be
regarded as an effect of rescattering and is found to be of magnitude
comparable to others contributing to charmed particle two-body nonleptonic
decays.Comment: 19 pages, latex, 4 figures, to be submitted to Phys. Rev.
14Be(p,n)14B reaction at 69 MeV in inverse kinematics
A Gamow-Teller (GT) transition from the drip-line nucleus 14Be to 14B was
studied via the (p,n) reaction in inverse kinematics using a secondary 14Be
beam at 69 MeV/nucleon. The invariant mass method is employed to reconstruct
the energy spectrum. A peak is observed at an excitation energy of 1.27(2) MeV
in 14B, together with bumps at 2.08 and 4.06(5) MeV. The observed forward
peaking of the state at 1.27 MeV and a good description for the differential
cross section, obtained with a DWBA calculation provide support for the 1+
assignment to this state. By extrapolating the cross section to zero momentum
transfer the GT-transition strength is deduced. The value is found to compare
well with that reported in a beta-delayed neutron emission study.Comment: 5 pages, 2 figure
Closure properties of solutions to heat inequalities
We prove that if are
sufficiently well-behaved solutions to certain heat inequalities on then
the function given by
also satisfies a heat inequality of a
similar type provided . On
iterating, this result leads to an analogous statement concerning -fold
convolutions. As a corollary, we give a direct heat-flow proof of the sharp
-fold Young convolution inequality and its reverse form.Comment: 12 page
Scale setting for alpha_s beyond leading order
We present a general procedure for incorporating higher-order information
into the scale-setting prescription of Brodsky, Lepage and Mackenzie. In
particular, we show how to apply this prescription when the leading coefficient
or coefficients in a series in the strong coupling alpha_s are anomalously
small and the original prescription can give an unphysical scale. We give a
general method for computing an optimum scale numerically, within dimensional
regularization, and in cases when the coefficients of a series are known. We
apply it to the heavy quark mass and energy renormalization in lattice NRQCD,
and to a variety of known series. Among the latter, we find significant
corrections to the scales for the ratio of e+e- to hadrons over muons, the
ratio of the quark pole to MSbar mass, the semi-leptonic B-meson decay width,
and the top decay width. Scales for the latter two decay widths, expressed in
terms of MSbar masses, increase by factors of five and thirteen, respectively,
substantially reducing the size of radiative corrections.Comment: 39 pages, 15 figures, 5 tables, LaTeX2
Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation
We compute the axial and pseudoscalar form factors of the nucleon in the
Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev
equation for the nucleon wave function and determine the matrix elements of the
axialvector and pseudoscalar isotriplet currents. Our only input is a
well-established and phenomenologically successful ansatz for the
nonperturbative quark-gluon interaction. As a consequence of the axial
Ward-Takahashi identity that is respected at the quark level, the
Goldberger-Treiman relation is reproduced for all current-quark masses. We
discuss the timelike pole structure of the quark-antiquark vertices that enters
the nucleon matrix elements and determines the momentum dependence of the form
factors. Our result for the axial charge underestimates the experimental value
by 20-25% which might be a signal of missing pion-cloud contributions. The
axial and pseudoscalar form factors agree with phenomenological and lattice
data in the momentum range above Q^2 ~ 1...2 GeV^2.Comment: 17 pages, 7 figures, 1 tabl
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