312 research outputs found
ϱ → 4π in chirally symmetric models
The decays rho0 → 2π+2π− and rho0 → 2π0π+π− are studied using various effective Lagrangians for π and rho (and in some case a1) mesons, all of which respect the approximate chiral symmetry of the strong interaction. Partial widths of the order of 1 keV or less are found in all cases. These are an order of magnitude smaller than recent predictions based on non-chiral models
Deconstructing triplet nucleon-nucleon scattering
Nucleon-nucleon scattering in spin-triplet channels is analysed within an
effective field theory where one-pion exchange is treated nonperturbatively.
Justifying this requires the identification of an additional low-energy scale
in the strength of that potential. Short-range interactions are organised
according to the resulting power counting, in which the leading term is
promoted to significantly lower order than in the usual perturbative counting.
In each channel there is a critical momentum above which the waves probe the
singular core of the tensor potential and the new counting is necessary. When
the effects of one- and two-pion exchange have been removed using a
distorted-wave Born approximation, the residual scattering in waves with L<=2
is well described by the first three terms in the new counting. In contrast,
the scattering in waves with L>=3 is consistent with the perturbative counting,
at least for energies up to 300 MeV. This pattern is in agreement with
estimates of the critical momenta in these channels.Comment: 13 pages, RevTeX, 8 figures, minor clarifications adde
Comment on soft-pion emission in DVCS
The soft-pion theorem for pion production in deeply virtual Compton
scattering, derived by Guichon, Mosse and Vanderhaegen, is shown to be
consistent with chiral perturbation theory. Chiral symmetry requires that the
nonsinglet operators corresponding to spin-independent and spin-dependent
parton distributions have the same anomalous dimensions in cases where those
operators are related by chiral transformations. In chiral perturbation theory,
their scale-dependences can thus be absorbed in the coefficents of the
corresponding effective operators, without affecting their chiral structures.Comment: 2 pages, RevTe
Effective short-range interaction for spin-singlet P-wave nucleon-nucleon scattering
Distorted-wave methods are used to remove the effects of one- and two-pion
exchange up to order Q^3 from the empirical 1P1 phase shift. The one divergence
that arises can be renormalised using an order-Q^2 counterterm which is
provided by the (Weinberg) power counting appropriate to the effective field
theory for this channel. The residual interaction is used to estimate the scale
of the underlying physics.Comment: 4 pages, 3 figures (pdf
Low-energy interaction of composite spin-half systems with scalar and vector fields
We consider a composite spin-half particle moving in spatially-varying scalar
and vector fields. The vector field is assumed to couple to a conserved charge,
but no assumption is made about either the structure of the composite or its
coupling to the scalar field. A general form for the piece of the spin-orbit
interaction of the composite with the scalar and vector fields which is
first-order in momentum transfer and second-order in the fields is
derived.Comment: 10 pages, RevTe
Renormalisation-group analysis of repulsive three-body systems
A coordinate space approach, based on that used by Efimov, is applied to
three-body systems with contact interactions between pairs of particles. In
systems with nonzero orbital angular momentum or with asymmetric spatial wave
functions, the hyperradial equation contains a repulsive 1/r^2 potential. The
resulting wave functions are used in a renormalisation group analysis. This
confirms Griesshammer's power counting for short-range three-body forces in
these systems. The only exceptions are ones like the 4S channel for three
nucleons, where any derivatives needed in the interaction are found to be
already counted by the scaling with the cut-off.Comment: 5 pages, RevTe
Power counting with one-pion exchange
Techniques developed for handing inverse-power-law potentials in atomic
physics are applied to the tensor one-pion exchange potential to determine the
regions in which it can be treated perturbatively. In S-, P- and D-waves the
critical values of the relative momentum are less than or of the order of 400
MeV. The RG is then used to determine the power counting for short-range
interaction in the presence of this potential. In the P-and D-waves, where
there are no low-energy bound or virtual states, these interactions have
half-integer RG eigenvalues and are substantially promoted relative to naive
expectations. These results are independent of whether the tensor force is
attractive or repulsive. In the 3S1 channel the leading term is relevant, but
it is demoted by half an order compared to the counting for the effective-range
expansion with only a short-range potential. The tensor force can be treated
perturbatively in those F-waves and above that do not couple to P- or D-waves.
The corresponding power counting is the usual one given by naive dimensional
analysis.Comment: 18 pages, RevTeX (further details, explanation added
Vacuum Properties of Mesons in a Linear Sigma Model with Vector Mesons and Global Chiral Invariance
We present a two-flavour linear sigma model with global chiral symmetry and
vector and axial-vector mesons. We calculate pion-pion scattering lengths and
the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated
that vector and axial-vector meson degrees of freedom play an important role in
these low-energy processes and that a reasonable theoretical description
requires globally chirally invariant terms other than the vector meson mass
term. An important question for meson vacuum phenomenology is the quark content
of the physical scalar f0(600) and a0(980) mesons. We investigate this question
by assigning the quark-antiquark sigma and a0 states of our model with these
physical mesons. We show via a detailed comparison with experimental data that
this scenario can describe all vacuum properties studied here except for the
decay width of the sigma, which turns out to be too small. We also study the
alternative assignment f0(1370) and a0(1450) for the scalar mesons. In this
case the decay width agrees with the experimental value, but the pion-pion
scattering length is too small. This indicates the necessity to
extend our model by additional scalar degrees of freedom.Comment: 22 pages, 6 figure
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