989 research outputs found
High Energy Theorems at Large-N
Sum rules for products of two, three and four QCD currents are derived using
chiral symmetry at infinite momentum in the large-N limit. These exact
relations among meson decay constants, axialvector couplings and masses
determine the asymptotic behavior of an infinite number of QCD correlators. The
familiar spectral function sum rules for products of two QCD currents are among
the relations derived. With this precise knowledge of asymptotic behavior, an
infinite number of large-N QCD correlators can be constructed using dispersion
relations. A detailed derivation is given of the exact large-N pion vector form
factor and forward pion-pion scattering amplitudes.Comment: 34 pages TeX and mtexsis.tex, 10 figures (uses epsf
Neutron matter on the lattice with pionless effective field theory
We study neutron matter by combining pionless effective field theory with
non-perturbative lattice methods. The neutron contact interaction is determined
by zero temperature scattering data. We simulate neutron matter on the lattice
at temperatures 4 and 8 MeV and densities below one-fifth normal nuclear matter
density. Our results at different lattice spacings agree with one another and
match bubble chain calculations at low densities. The equation of state of pure
neutron matter obtained from our simulations agrees quantitatively with
variational calculations based on realistic potentials.Comment: 28 pages, 13 figure
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
Bridging over p-wave pi-production and weak processes in few-nucleon systems with chiral perturbation theory
I study an aspect of chiral perturbation theory (\chi PT) which enables one
to ``bridge'' different reactions. That is, an operator fixed in one of the
reactions can then be used to predict the other. For this purpose, I calculate
the partial wave amplitude for the p-wave pion production (pp\to pn\pi^+) using
the pion production operator from the lowest and the next nonvanishing orders.
The operator includes a contact operator whose coupling has been fixed using a
matrix element of a low-energy weak process (pp\to de^+\nu_e). I find that this
operator does not reproduce the partial wave amplitude extracted from
experimental data, showing that the bridging over the reactions with
significantly different kinematics is not necessarily successful. I study the
dependence of the amplitude on the various inputs such as the NN potential, the
\pi N\Delta coupling, and the cutoff. I argue the importance of a higher order
calculation. In order to gain an insight into a higher order calculation, I add
a higher order counter term to the operator used above, and fit the couplings
to both the low-energy weak process and the pion production. The energy
dependence of the partial wave amplitude for the pion production is described
by the operator consistently with the data. However, I find a result which
tells us to be careful about the convergence of the chiral expansion for the
pp\to pn\pi^+ reaction.Comment: 30 pages, 13 figures, figures changed, compacted tex
I=2 pi pi S-wave scattering phase shift from lattice QCD
The pi(+)pi(+) s-wave scattering phase shift is determined below the inelastic threshold using lattice QCD. Calculations were performed at a pion mass of m(pi) similar to 390 MeV with an anisotropic n(f) = 2 _+ 1 clover fermion discretization in four lattice volumes, with spatial extent L similar to 2.0, 2.5, 3.0 and 3.9 fm, and with a lattice spacing of b(s) similar to 0.123 fm in the spatial direction and b(t) similar to b(s)/3. 5 in the time direction. The phase shift is determined from the energy eigenvalues of pi(+)pi(+) systems with both zero and nonzero total momentum in the lattice volume using Lu scher\u27s method. Our calculations are precise enough to allow for a determination of the threshold scattering parameters, the scattering length a, the effective range r, and the shape parameter P, in this channel and to examine the prediction of two- flavor chiral perturbation theory: m(pi)(2)ar = 3 + O(m(pi)(2)/=Lambda(2)(chi)). Chiral perturbation theory is used, with the lattice QCD results as input, to predict the scattering phase shift (and threshold parameters) at the physical pion mass. Our results are consistent with determinations from the Roy equations and with the existing experimental phase shift data
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