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Register a new userWilsonian renormalization group and the Lippmann-Schwinger equation with a multitude of cutoff parameters
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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.
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We propose a new method to describe three-body breakups of nuclei, in which the Lippmann-Schwinger equation is solved combining with the complex scaling method. The complex-scaled solutions of the Lippmann-Schwinger equation (CSLS) enables us to treat boundary conditions of many-body open channels correctly and to describe a many-body breakup amplitude from the ground state. The Coulomb breakup cross section from the 6He ground state into 4He+n+n three-body decaying states as a function of the total excitation energy is calculated by using CSLS, and the result well reproduces the experimental data. Furthermore, the two-dimensional energy distribution of the E1 transition strength is obtained and an importance of the 5He(3/2-) resonance is confirmed. It is shown that CSLS is a promising method to investigate correlations of subsystems in three-body breakup reactions of the weakly-bound nuclei.
We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the mathematical literature, which describes a function with an infinite number of singularities in the positive axis of the Borel plane. Consistency requires a one-to-one correspondence between the existence of such kind of equation and the actual (generalized) Borel resummation of the renormalons through a one-parameter transseries. Our finding suggests how non-perturbative contributions can affect the running couplings. We also discuss these concepts within the context of gauge theories, making use of the large number of flavor expansion.
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 Weinbergs 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 Weinbergs power counting scheme is consistent in the sense that it leads to a systematic order-by-order expansion of the scattering amplitude.
We formulate a Lippmann-Schwinger-type resonating-group equation to calculate invariant amplitudes of the quark-model baryon-baryon interaction. When applied to our recent SU6 quark model for the nucleon-nucleon and hyperon-nucleon interactions, this technique yields very accurate phase-shift parameters for all partial waves up to the energies of several GeV. The technique also has a merit of a straightforward extension to the G-matrix equation. A new analytic method is proposed to calculate the quark-exchange Born kernel for the momentum-dependent two-body interaction. The partial-wave decomposition in the momentum representation is carried out numerically. The invariant amplitudes are then used to calculate single-nucleon potentials in normal nuclear matter for high incident momenta q_1 > 3 (1/fm), in which the so-called t^eff-rho prescription is found to be a good approximation to the single-particle potentials directly calculated in the lowest-order Brueckner theory.
With the introduction of a spectral representation, the Schwinger-Dyson equation (SDE) for the fermion propagator is formulated in Minkowski space in QED. After imposing the on-shell renormalization conditions, analytic solutions for the fermion propagator spectral functions are obtained in four dimensions with a renormalizable version of the Gauge Technique anzatz for the fermion-photon vertex in the quenched approximation in the Landau gauge. Despite the limitations of this model, having an explicit solution provides a guiding example of the fermion propagator with the correct analytic structure. The Pad{e} approximation for the spectral functions is also investigated.
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