930 research outputs found
Regularization, renormalization and "peratization" in effective field theory for two nucleons
We discuss conceptual aspects of renormalization in the context of effective
field theories for the two-nucleon system. It is shown that, contrary to
widespread belief, renormalization scheme dependence of the scattering
amplitude can only be eliminated up to the order the calculations are
performed. We further consider an effective theory for an exactly solvable
quantum mechanical model which possesses a long- and short-range interaction to
simulate pionful effective field theory. We discuss the meaning of low-energy
theorems in this model and demonstrate their validity in calculations with a
finite cutoff as long as it is chosen of the order of the hard scale
in the problem. Removing the cutoff by taking the limit
yields a finite result for the scattering amplitude but violates the low-energy
theorems and is, therefore, not compatible with the effective field theory
framework.Comment: 22 pages, 2 figures, to appear in Eur. Phys. J.
Wilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters
The Wilsonian renormalization group approach to the Lippmann-Schwinger
equation with a multitude of cutoff parameters is introduced. A system of
integro-differential equations for the cutoff-dependent potential is obtained.
As an illustration, a perturbative solution of these equations with two cutoff
parameters for a simple case of an S-wave low-energy potential in the form of a
Taylor series in momenta is obtained. The relevance of the obtained results for
the effective field theory approach to nucleon-nucleon scattering is discussed.Comment: 6 pages, no figure
Wilsonian renormalization group versus subtractive renormalization in effective field theories for nucleon--nucleon scattering
We compare the subtractive renormalization and the Wilsonian renormalization
group approaches in the context of an effective field theory for the
two-nucleon system. Based on an exactly solvable model of contact interactions,
we observe that the standard Wilsonian renormalization group approach with a
single cutoff parameter does not cover the whole space spanned by the
renormalization scale parameters of the subtractive formalism. In particular,
renormalization schemes corresponding to Weinberg's power counting in the case
of an unnaturally large scattering length are beyond the region covered by the
Wilsonian renormalization group approach. In the framework of pionless
effective field theory, also extended by the inclusion of a long-range
interaction of separable type, we demonstrate that Weinberg's power counting
scheme is consistent in the sense that it leads to a systematic order-by-order
expansion of the scattering amplitude.Comment: 23 pages, 2 figure
Two-Pion Exchange Currents in Photodisintegration of the Deuteron
Chiral effective field theory (ChEFT) is a modern framework to analyze the
properties of few-nucleon systems at low energies. It is based on the most
general effective Lagrangian for pions and nucleons consistent with the chiral
symmetry of QCD. For energies below the pion-production threshold it is
possible to eliminate the pionic degrees of freedom and derive nuclear
potentials and nuclear current operators solely in terms of the nucleonic
degrees of freedom. This is very important because, despite a lot of experience
gained in the past, the consistency between two-nucleon forces, many-nucleon
forces and the corresponding current operators has not been achieved yet. In
this presentation we consider the recently derived long-range two-pion exchange
(TPE) contributions to the nuclear current operator which appear at next-to
leading order of the chiral expansion. These operators do not contain any free
parameters. We study their role in the deuteron photodisintegration reaction
and compare our predictions with experimental data. The bound and scattering
states are calculated using five different chiral N2LO nucleon-nucleon (NN)
potentials which allows to estimate the theoretical uncertainty at a given
order in the chiral expansion. For some observables the results are very close
to the reference predictions based on the AV18 NN potential and the current
operator (partly) consistent with this force.Comment: Contribution to the 12th International Conference on Meson-Nucleon
Physics and the Structure of the Nucleon (MENU2010), Williamsburg, USA, May
31-June 4, 201
The magnetic moment of the \rho-meson
The magnetic moment of the \rho-meson is calculated in the framework of a
low-energy effective field theory of the strong interactions. We find that the
complex-valued strong interaction corrections to the gyromagnetic ratio are
small leading to a value close to the real leading tree level result, g_\rho =
2. This is in a reasonably good agreement with the available lattice QCD
calculations for this quantity.Comment: 10 pages, 4 figure
Efficient calculation of chiral three-nucleon forces up to N3LO for ab initio studies
We present a novel framework to decompose three-nucleon forces in a momentum
space partial-wave basis. The new approach is computationally much more
efficient than previous methods and opens the way to ab initio studies of
few-nucleon scattering processes, nuclei and nuclear matter based on
higher-order chiral 3N forces. We use the new framework to calculate matrix
elements of chiral three-nucleon forces at N2LO and N3LO in large basis spaces
and carry out benchmark calculations for neutron matter and symmetric nuclear
matter. We also study the size of the individual three-nucleon force
contributions for H. For nonlocal regulators, we find that the sub-leading
terms, which have been neglected in most calculations so far, provide important
contributions. All matrix elements are calculated and stored in a user-friendly
way, such that values of low-energy constants as well as the form of regulator
functions can be chosen freely.Comment: 10 pages, 4 figure
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