68 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
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
Deuteron electromagnetic form factors in a renormalizable formulation of chiral effective field theory
We calculate the deuteron electromagnetic form factors in a modified version
of Weinberg's chiral effective field theory approach to the two-nucleon system.
We derive renormalizable integral equations for the deuteron without partial
wave decomposition. Deuteron form factors are extracted by applying the
Lehmann-Symanzik-Zimmermann reduction formalism to the three-point correlation
function of deuteron interpolating fields and the electromagnetic current
operator. Numerical results of a leading-order calculation with removed cutoff
regularization agree well with experimental data.Comment: 9 pages, 2 figure
How (not) to renormalize integral equations with singular potentials in effective field theory
We discuss the connection between the perturbative and non-perturbative
renormalization and related conceptual issues in the few-nucleon sector of the
low-energy effective field theory of the strong interactions. General arguments
are supported by examples from effective theories with and without pions as
dynamical degrees of freedom. A quantum mechanical potential with explicitly
specified short- and long-range parts is considered as an "underlying
fundamental theory" and the corresponding effective field theory potential is
constructed. Further, the problem of the effective field theoretical
renormalization of the Skornyakov-Ter-Martyrosian equation is revisited.Comment: 12 pages, 5 figure
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