On the S-matrix renormalization in effective theories

This is the 5-th paper in the series devoted to explicit formulating of the rules needed to manage an effective field theory of strong interactions in S-matrix sector. We discuss the principles of constructing the meaningful perturbation series and formulate two basic ones: uniformity and summability. Relying on these principles one obtains the bootstrap conditions which restrict the allowed values of the physical (observable) parameters appearing in the extended perturbation scheme built for a given localizable effective theory. The renormalization prescriptions needed to fix the finite parts of counterterms in such a scheme can be divided into two subsets: minimal -- needed to fix the S-matrix, and non-minimal -- for eventual calculation of Green functions; in this paper we consider only the minimal one. In particular, it is shown that in theories with the amplitudes which asymptotic behavior is governed by known Regge intercepts, the system of independent renormalization conditions only contains those fixing the counterterm vertices with $n \leq 3$ lines, while other prescriptions are determined by self-consistency requirements. Moreover, the prescriptions for $n \leq 3$ cannot be taken arbitrary: an infinite number of bootstrap conditions should be respected. The concept of localizability, introduced and explained in this article, is closely connected with the notion of resonance in the framework of perturbative QFT. We discuss this point and, finally, compare the corner stones of our approach with the philosophy known as ``analytic S-matrix''.Comment: 28 pages, 10 Postscript figures, REVTeX4, submitted to Phys. Rev.

Large Nc and Chiral Dynamics

We study the dependence on the number of colors of the leading pi pi scattering amplitude in chiral dynamics. We demonstrate the existence of a critical number of colors for and above which the low energy pi pi scattering amplitude computed from the simple sum of the current algebra and vector meson terms is crossing symmetric and unitary at leading order in a truncated and regularized 1/Nc expansion. The critical number of colors turns out to be Nc=6 and is insensitive to the explicit breaking of chiral symmetry. Below this critical value, an additional state is needed to enforce the unitarity bound; it is a broad one, most likely of "four quark" nature.Comment: RevTeX4, 6 fig., 5 page

Tree-level (pi, K)-amplitude and analyticity

We consider the tree-level amplitude, describing all 3 channels of the binary (pi ,K)-reaction, as a meromorphic polynomially bounded function of 3 dependent complex variables. Relying systematically on the Mittag-Leffler theorem, we construct 3 convergent partial fraction expansions, each one being applied in the corresponding domain. Noting, that the mutual intersections of those domains are nonempty, we realize the analytical continuation. It is shown that the necessary conditions to make such a continuation feasible, are the following: 1) The only parameters completely determining the amplitude are the on-shell couplings and masses; 2) These parameters are restricted by a certain (infinite) system of bootstrap equations; 3) The full cross-symmetric amplitude takes the typically dual form, the Pomeron contribution being taken into account; 4)This latter contribution corresponds to a nonresonant background, which, in turn, is expressed in terms of cross-channel resonances parameters. It is demonstrated also, that the Chiral Symmetry provides a unique scale for the mentioned parameters, the resonance saturation effect appearing as a direct consequence of the above results

Mechanism for a next-to-lowest lying scalar meson nonet

Recent work suggests the existence of a non-conventional lowest-lying scalar nonet containing the a0(980). Then the a0(1450) and also the K0*(1430) are likely candidates to belong to a conventional p-wave $q \bar q$ nonet. However a comparison of their properties with those expected on this basis reveals a number of puzzling features. It is pointed out that these puzzles can be resolved in a natural and robust way by assuming a ``bare'' conventional p-wave scalar $q \bar q$ nonet to mix with a lighter four quark $qq \bar q \bar q$ scalar nonet to form new ``physical'' states. The essential mechanism is driven by the fact that the isospinor is lighter than the isovector in the unmixed $qq \bar q \bar q$ multiplet.Comment: 22 pages, 6 figure

Таутакс (доцетаксел) в лечении гормонорефрактерного рака предстательной железы

Purpose. Evaluate efficacy and portability of the combination of the drugs Tautax (docetaxel) with a dose of 75mg/m2 1 time per 21 days and prednisolone — 10 mg per 24 h in hormone-refractory prostate cancer (HRPC) patients. Methods. Patients with verified HRPC were included in the study. Patients without being performed orchofuniculectomy were given LHRH analogues during the entire study. The treatment scheme was: tautax 75 mg/m2 1 time per 21 days as 1,5 h infusion + prednisolone — 10 mg per 24 h per os. Dexamethasone 8 mg was introduced intramuscularly as a premedication before tautax infusion prior to 12, 6 and 1 h. Patients with the revealed bone metastases were given zoledronic acid 4 mg 1 time per 28 days. The therapy was has been being performed for 6 months or till disease progression revelation. In case of regression or stabilization of the disease, up to 10 chemotherapy courses were performed. Results. 29 HRPC patients are examined. 178 chemotherapy courses are performed. Partial regression is noted in 8 (28%) patients, stabilization — in 9 (31%), progression - in 8 (28%) patients. PSA level decrease >50% has been observed in 19 (65,5%) patients. Improvement of the life quality was reached in 11 (38%) patients. The decrease in hyperfixation of radiopharmaceutical by osteoscintigraphy ocurred in 14 (48%) patients. Conclusion. Combination of Tautax and prednisolone is an effective treatment regimen of the HRPC patients.

Working group on ππ\pi\pi and π\piN interactions - Summary

This is the summary of the working group on $\pi\pi$ and $\pi$N interactions of the Chiral Dynamics Workshop in Mainz, September 1-5, 1997. Each talk is represented by an extended one page abstract. Some additional remarks by the convenors are addedComment: 20 pp, LaTeX2e, uses epsf, 1 fi

Effective Chiral Lagrangian from Dual Resonance Models

Parameters of the effective chiral lagrangian (EChL) of orders $O(p^4)$ and $O(p^6)$ are extracted from low--energy behaviour of dual resonance models for $\pi\pi$ and $\pi K$ scattering amplitudes. Dual resonance models are considered to be good candidates for the resonance spectrum and for hadronic scattering amplitudes in the large $N_c$ limit of QCD. We discuss dual resonance models in the presence of spontaneous and explicit chiral symmetry breaking. Obtained parameters of the EChL are used to estimate chiral corrections up to the sixth order to various low--energy characteristics of $\pi\pi$ and $\pi K$ scattering amplitudes.Comment: 32 pages, the references list is updated, comparison with chiral quark model is done in more detail

Pion-Pion Scattering in Two Dimensions

Massive two-flavor QED_2 is known to have many similarities to the two-flavor QCD_4. Here we compare the \pi-\pi scattering amplitudes (actually an analog process in QED_2) of the two theories. The QED_2 amplitude is computed from the bosonized version of the model while the QCD_4 amplitude is computed from an effective low energy chiral Lagrangian. A number of interesting features are noted. For example, the contribution of the two-dimensional Wess-Zumino-Witten (WZW) term in QED_2 is structurally identical to the vector meson exchange contribution in QCD_4. Also it is shown that the QED_2 amplitude computed at tree level is a reasonable approximation to the known exact strong coupling solution.Comment: 17 pages, 1 figure, LaTex. Typos and references corrected. Discussion of KSRF formula change

Putative Light Scalar Nonet

We investigate the "family" relationship of a possible scalar nonet composed of the a_0(980), the f_0(980) and the \sigma and \kappa type states found in recent treatments of \pi\pi and \pi K scattering. We work in the effective Lagrangian framework, starting from terms which yield "ideal mixing" according to Okubo's original formulation. It is noted that there is another solution corresponding to dual ideal mixing which agrees with Jaffe's picture of scalars as qq\bar q \bar q states rather than as q\bar q states. At the Lagrangian level there is no difference in the formulation of the two cases (other than the numerical values of the coefficients). In order to agree with experiment, additional mass and coupling terms which break ideal mixing are included. The resulting model turns out to be closer to dual ideal mixing than to conventional ideal mixing; the scalar mixing angle is roughly -17 degrees in a convention where dual ideal mixing is 0 degrees.Comment: 24 pages, 3 figure

eta' to eta pi pi Decay as a Probe of a Possible Lowest-Lying Scalar Nonet

We study the eta' to eta pi pi decay within an effective chiral Lagrangian approach in which the lowest lying scalar meson candidates sigma(560) and kappa(900) together with the f0(980) and a0(980) are combined into a possible nonet. We show that there exists a unique choice of the free parameters of this model which, in addition to fitting the pi pi and pi K scattering amplitudes, well describes the experimental measurements for the partial decay width of eta' to eta pi pi and the energy dependence of this decay. As a by-product, we estimate the a0(980) width to be 70 MeV, in agreement with a new experimental analysis.Comment: 25 pages, 11 figure