A renormalized equation for the three-body system with short-range interactions

We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of the three-body scattering length on the two-body scattering length can be obtained analytically using the asymptotic solution to the integral equation. An analogous formula for the three-body recombination coefficient is also obtained.     

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, the 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 \( \Lambda\) as long as it is chosen of the order of the hard scale in the problem. Removing the cutoff by taking the limit \( \Lambda\) \( \rightarrow\) ∞ 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.     

High-energy scattering in QCD and cross singularities of Wilson loops

We consider elastic quark-quark scattering at high energy and fixed transferred momentum. Performing factorization of soft-gluon exchanges into the Wilson-line expectation value we find that there is one-to-one correspondence between high-energy asymptotics in QCD and renormalization properties of the so-called cross singularities of the Wilson lines. Using this relation we show that the asymptotic behavior of the quark-quark scattering amplitude is controlled by a 2 × 2 matrix of the cross anomalous dimensions. We evaluate the matrix of the cross anomalous dimension to two-loop order and study the properties of the obtained expressions to higher loop order.     

Surface-integral formulation of scattering theory

We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surface-integrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.     

Second-order effects in chiral-invariant pion Lagrangians and the use of superpropagators

We examine the second-order corrections to the scattering amplitude and to the vector currents for chiral-invariant Lagrangians of massless pions. Standard renormalization theory leads to three undetermined parameters. We discuss the possibility of choosing definite values for these parameters by applying the technique of superpropagators. In an appendix we investigate the restrictions which follow if localizability of the perturbation expansion in powers of the interaction Lagrangian is required. It is shown that this condition determines the pion-field coordinates uniquely.     

Coulomb scattering in a 2D interacting electron gas and production of EPR pairs

We propose a setup to generate nonlocal spin Einstein-Podolsky-Rosen pairs via pair collisions in a 2D interacting electron gas, based on constructive two-particle interference in the spin-singlet channel at the pi/2 scattering angle. We calculate the scattering amplitude via the Bethe-Salpeter equation in the ladder approximation and small r(s) limit and find that the Fermi sea leads to a substantial renormalization of the bare scattering process. From the scattering length, we estimate the current of spin-entangled electrons and show that it is within experimental reach.     

Calculation of the pion-nucleon σ term value from the experimental data on pionic atoms

The pion-nucleonσ term value is calculated using pion-nuclear scattering lengths extracted from the data on pionic atoms withA≦24 and isospinI = 0. The renormalization of the soft-pionπN amplitude in nuclear matter is taken into account. TheA-dependence of the pion-nuclear scattering lengths is studied. Comparison with other results forσ term leads to the conclusion that the most probable interval for it is 30–50 MeV. The dispersive part of theS-wave pion-nuclear potential is discussed.     

Exact results in QED

We consider several applications of the simplest nonlinear QED phenomena described by the light-by-light (LBL) scattering tensor. Among the relevant processes we present the splitting of high energy photon in a Coulomb field, calculate the asymptotics of differential photon photon elastic scattering. We show that LBL mechanism of the four photon mode of neutral pion decay have a dominant role compared, for instance, with the quark loop Feynman amplitude contribution. The mechanisms of creation of two and three gluon jets at colliding electro-positron beams is analyzed. We calculate also the contribution of LBL mechanism to the ortho-positronium decay width. One Of the important application is the analytic calculation of the QED contribution to the anomalous magnetic moment of the muon arising from LBL mechanism realized through electron positron loops, which is enhanced by the logarithm of the ratio of muon to electron masses. The modification of the QED kernel, which takes into account the QED polarization operator is used to extract the pure strong interaction contribution. We consider as well the problem of the Coulomb law modification. At second part of review we consider Moeller scattering process and RC to it. We show that RC are in agreement with renormalization group approach and could be taken into account in form of Drell-Yan process cross-section.     

Counting limit cycles with the help of the renormalization group

We use the renormalization group to set up an easy algorithm for finding the amplitude equation for an arbitrary two dimensional dynamical system of the Liénard type. This allows us to address the second part of Hilbert’s sixteenth problem, at least in the weak damping limit.     

Some QED processes: Light-by-light and moeller scattering

We consider several applications of the simplest nonlinear QED phenomena described by the light-by-light (LBL) scattering tensor. Among the relevant processes we present the splitting of high energy photon in a Coulomb field, calculate the asymptotics of differential photon photon elastic scattering. We show that LBL mechanism of the four photon mode of neutral pion decay have a dominant role compared, for instance, with the quark loop Feynman amplitude contribution. The mechanisms of creation of two and three gluon jets at colliding electro-positron beams is analyzed. We calculate also the contribution of LBL mechanism to the ortho-positronium decay width. One Of the important application is the analytic calculation of the QED contribution to the anomalous magnetic moment of the muon arising from LBL mechanism realized through electron positron loops, which is enhanced by the logarithm of the ratio of muon to electron masses. The modification of the QED kernel, which takes into account the QED polarization operator is used to extract the pure strong interaction contribution. We consider as well the problem of the Coulomb law modification. At second part of review we consider Moeller scattering process and RC to it. We show that RC are in agreement with renormalization group approach and could be taken into account in form of Drell-Yan process cross-section.     

利用色散关系计算单个粒子的格林函数

本文利用核子与反核子散射振幅的解析性和么正性导出单个虚介子的格林函数。在计算中不需要进行重正化手续     

Wilsonian RG and redundant operators in nonrelativistic effective field theory

In a Wilsonian renormalization group (RG) analysis, redundant operators, which may be eliminated by using field redefinitions, emerge naturally. It is therefore important to include them. We consider a nonrelativistic effective theory (the so-called “pionless” nuclear effective field theory) as a concrete example and show that the off-shell amplitudes cannot be renormalized if the redundant operators are not included. The relation between the theories with and without such redundant operators is established in the low-energy expansion. We perform a Wilsonian RG analysis for the off-shell scattering amplitude in the theory with the redundant operator.     

Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, a, which is large compared to the range of the interaction, ?. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N²LO) in the ?/a expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N²LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N²LO phase- shift predictions will receive higher-order corrections of < 0.2 %. In contrast, the prediction of SREFT for the binding energy of the “deep” trimer of Helium-4 atoms displays poor convergence.     

Origin of Dynamically Generated Baryon Rsonances

We study the origin of baryon resonances which are dynamically generated in the chiral unitary approach.We propose a natural renormalization scheme for the dynamical generation of resonances using the low energy chiral interaction and a general feature of the scattering theory.A deviation of a phenomenological scattering amplitude from the natural one is interpreted by an effective pole term interaction of genuine nature which can not be described by the meson-baryon dynamics,reminiscent of the CDD pole.Applying the present method to physical meson-baryon scatterings,we find that the ∧(1405) resonance is dominated by a meson-baryon component forming a (K)N-π∑ molecular-like structure,while the N(1535) resonance requires some pole contribution.     

A multiperipheral model with continued cross channel unitarity

We derive, by using a spectral representation in momentum transfer, t, an integral equation, similar in structure to a multipheral equation, with continued cross channel unitarity, for the absorptive part for a composite particle scattering amplitude from a Bethe-Salpeter equation describing composite particle scattering in the s channel. At high energy in the t channel, the equation becomes homogeneous and has a Reggeized solution. We indicate how this equation may be solved using determinental techniques. We also show how the composite particle amplitude resulting from the original equation may be used to construct production and three body amplitudes. We also infer the possibility of studying, using the amplitude from the cross channel problem, the effect of extra unitarity on Reggeon-Reggeon-particle vertices.     

TheO(ɛ2) scaling law fordσ/dt in the Reggeon Field Theory

We calculate the two loop contributions within the ε-expansion to the Reggeon Field Theory scaling law fordσ/dt, derived using the renormalization group and a general renormalization point for the Pomeron propagator. This generalizes theO(ε) work of Abarbanel, Bartels, Bronzan, and Sidhu. The invariance of the results under certain coupling constant rescalings is demonstrated. We also make some qualitative comments regarding phenomenological applications. Our amplitude in a certain limit approximates the form of the low energy diffractive amplitude advocated by Kane.     

Renormalization Group Invariance in Pionless Effective Field Theory for the NN System

We consider the NN interaction in pionless effective field theory (EFT) up to next-to-next-to-leading order (NNLO) and use a recursive subtractive renormalization scheme to describe NN scattering in the ¹ S ₀ channel. We fix the strengths of the contact interactions at a reference scale, chosen to be the one that provides the best fit for the phase-shifts, and then slide the renormalization scale by evolving the driving terms of the subtracted Lippmann?CSchwinger equation through a non-relativistic Callan?CSymanzik equation. The results show that such a systematic renormalization scheme with multiple subtractions is fully renormalization group invariant.