The 1/N Expansion of Tensor Models Beyond Perturbation Theory

We analyze in full mathematical rigor the most general quartically perturbed invariant probability measure for a random tensor. Using a version of the Loop Vertex Expansion (which we call the mixed expansion) we show that the cumulants write as explicit series in 1/N plus bounded rest terms. The mixed expansion recasts the problem of determining the subleading corrections in 1/N into a simple combinatorial problem of counting trees decorated by a finite number of loop edges. As an aside, we use the mixed expansion to show that the (divergent) perturbative expansion of the tensor models is Borel summable and to prove that the cumulants respect an uniform scaling bound. In particular the quartically perturbed measures fall, in the N→ ∞ limit, in the universality class of Gaussian tensor models.     

decays in Chiral Perturbation Theory

We study the decays K→ππ in one-loop two-flavour Chiral Perturbation Theory. We provide arguments why the calculation of the coefficient of the pionic chiral logarithm ℓ_M=M²logM² is unique and then perform the calculation. As a check we perform the reduction of the known three-flavour result. Our result can be used to perform the extrapolation to the physical pion mass of direct lattice QCD calculations of K→ππ at fixed m_s or . The underlying arguments are expected to be valid for heavier particles and other processes as well.     

Experimental tests of Chiral Perturbation Theory

In this paper the current status of the threshold photo- and electroproduction of neutral pions as test of Chiral Perturbation Theory is summarized. The combination of differential cross-section data with polarized photon asymmetries allows to determine a complete set of s- and p-wave amplitudes at threshold for the photoproduction case. These extracted amplitudes are in good agreement with predictions and fits of Heavy Baryon Chiral Perturbation Theory. On the other hand, new data on pion electroproduction shows a significant deviation from the predicted cross-sections at a four-momentum transfer of Q ² = 0.05GeV²/c ². For the coherent pion production from the deuteron the photoproduction data agree with Chiral Perturbation Theory. The former reported severe disagreement between the electroproduction s-wave amplitude at a four-momentum transfer of Q ² = 0.1GeV²/c ² and first calculations seems to be resolved now.Received: 12 August 2002, Published online: 22 October 2003PACS: 25.30.Rw Electroproduction reactions - 13.60.Le Meson production - 12.39.Fe Chiral LagrangiansH. Merkel: For the MAMI A1 Collaboration     

核物理中的手征微扰论

手征微扰论是基于量子色动力学的低能有效理论 ,已成为核物理和低能粒子物理研究的有力方法 .简单介绍了手征微扰论的基本概念、方法和应用 ,特别是近年来重子手征微扰论的形式发展和一些应用中的前沿问题. Chiral Perturbation Theory (CHPT), as a low-energy effective field theory based on QCD, is a powerful tool in the investigation of the nuclear and particle physics. We present an introduction to the basic idea, the method and the application of CHPT, and emphasize the recent development in the formalism and the application of baryon CHPT.     

Transport coefficients in Chiral Perturbation Theory

We present recent results on the calculation of transport coefficients for a pion gas at zero chemical potential in Chiral Perturbation Theory (ChPT) using the Linear Response Theory (LRT). More precisely, we show the behavior of DC conductivity and shear viscosity at low temperatures. To compute transport coefficients, the standard power counting of ChPT has to be modified. The effects derived from imposing unitarity are also analyzed. As physical applications in relativistic heavy-ion collisions, we show the relation of the DC conductivity to soft-photon production and phenomenological effects related to a non-zero shear viscosity. In addition, our values for the shear viscosity to entropy ratio satisfy the KSS bound.     

Chiral Charged Fermions,One-Dimensional Quantum Field Theory and Vertex Algebras

We give an explicit L ²-representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the pure case such a representation has already been used by M. Sato in holonomic field theory. We study both pure and mixed cases. In the compact case, we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions, we orient our findings towards a functional analytic study of vertex algebras as one-dimensional quantum field theory.     

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

The positive-parity yrast bands of ^{79, 81, 83, 85, 87, 89}Y isotopes have been studied using the projected shell model (PSM). Nuclear-structure properties like yrast spectra, transition energies, band diagrams, kinetic moment of inertia, rotational frequencies and reduced transition probabilities (B(M1) and B(E2) are calculated. The results obtained from the PSM calculations are also compared with the available experimental as well as theoretical data and, in general, a reasonable agreement is obtained between them. Calculations in the present work also predict that these isotopes have multi-quasiparticle structure.     

Pion Loops in Chiral Perturbation Theory and Light-Front Dynamics

From the approximate chiral symmetry of QCD, it is known that the pion loops in chiral perturbation theory play a vital role in understanding the nucleon’s long-range structure. We demonstrate the equivalence of the light-front, equal-time and covariant formulations for the interactions of nucleons with pions in chiral perturbation theory. In particular, we discuss the self-energy Σ of a nucleon dressed by pion loops with the pseudovector πNN coupling. It is shown that the leading nonanalytic behavior of Σ is equivalent whichever formulations are used for the derivation. We also discuss the relation between the mass shift and the wavefunction renormalization as well as the difference between the pseudovector and pseudoscalar theories.     

Resumming QCD vacuum fluctuations in three-flavor Chiral Perturbation Theory

Due to its light mass, of order , the strange quark can play a special role in chiral symmetry breaking ( SB): differences in the pattern of SB in the limits N_f = 2 ( , m_s physical) and N_f = 3 ( ) may arise due to vacuum fluctuations of pairs, related to the violation of the Zweig rule in the scalar sector and encoded in particular in the O(p⁴) low-energy constants L₄ and L₆. In case of large fluctuations, we show that the customary treatment of SU(3) x SU(3) chiral expansions generates instabilities upsetting their convergence. We develop a systematic program to cure these instabilities by resumming non-perturbatively vacuum fluctuations of pairs, in order to extract information about SB from experimental observations even in the presence of large fluctuations. We advocate a Bayesian framework for treating the uncertainties due to the higher orders. As an application, we present a three-flavor analysis of the low-energy scattering and show that the recent experimental data imply a lower bound on the quark mass ratio at 95% confidence level. We outline how additional information may be incorporated to further constrain the pattern of SB in the N_f = 3 chiral limit.Received: 2 December 2003, Published online: 3 March 2004J. Stern: stern@ipno.in2p3.fr     

Masses and Sigma Terms of Pentaquarks in Chiral Perturbation Theory

Assuming that the recently θ＋ and other exotic resonances belong to the pentaquark i0 of SU（3）I with J^P = 1/2, we constructed a relativistic effective lagrangian in the frame work of baryon chiral perturbation theory. The masses of pentaquarks under isospin symmetry is determined by calculating the propagator to one loop, where the extended on-mass-shell renormalization scheme is applied. Using the experimental data for masses of θ＋, Ξ and N, we estimated the mass of Σ and the a terms.     

Calculation of η′ Decay Modes Using Chiral Perturbation Theory

In this paper, with the use of Chiral Perturbation theory (χPT), we have studied the η′ decays in to 3π and 2πη, after performing these reactions. The Scattering amplitude and decay width are calculated for different modes up to NLO. The Dalitz plot expansion and parameter fixing for each of them is also calculated. Experimental results are in good agreement with the obtained results. We compare our results with charged and neutral decay parameters with the most recent Particle Data Group results of these observables. At next-to-leading order, our results for decay widths of the charged (neutral) channel are Γ(η′→2πη)=83.6±0.8 (43.0±2.2) keV and Γ(η′→3π)=0.716±0.072 (0.320±0.079) keV. These results are in agreement with several other theoretical determinations and experimental findings.     

Masses and Sigma Terms of Pentaquarks in Chiral Perturbation Theory

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Unitarized Chiral Perturbation Theory in a finite volume: Scalar meson sector

We develop a scheme for the extraction of the properties of the scalar mesons f ₀(600) , f ₀(980) , and a ₀(980) from lattice QCD data. This scheme is based on a two-channel chiral unitary approach with fully relativistic propagators in a finite volume. In order to discuss the feasibility of finding the mass and width of the scalar resonances, we analyze synthetic lattice data with a fixed error assigned, and show that the framework can be indeed used for an accurate determination of resonance pole positions in the multichannel scattering.     

A Functional-Analytic Theory of Vertex (Operator) Algebras,II

For a finitely-generated vertex operator algebra V of central charge c, a locally convex topological completion H ^V is constructed. We construct on H ^V a structure of an algebra over the operad of the power Det ^c/2 of the determinant line bundle Det over the moduli space of genus-zero Riemann surfaces with ordered analytically parametrized boundary components. In particular, H ^V is a representation of the semi-group of the power Det ^c/2 (1) of the determinant line bundle over the moduli space of conformal equivalence classes of annuli with analytically parametrized boundary components. The results in Part I for -graded vertex algebras are also reformulated in terms of the framed little disk operad. Using Mays recognition principle for double loop spaces, one immediate consequence of such operadic formulations is that the compactly generated spaces corresponding to (or the k-ifications of) the locally convex completions constructed in Part I and in the present paper have the weak homotopy types of double loop spaces. We also generalize the results above to locally-grading-restricted conformal vertex algebras and to modules.     

$M_\pi^2$ versus mq: comparing CP-PACS and UKQCD data to Chiral Perturbation Theory

I present a selection of CP-PACS and UKQCD data for the pseudo-Goldstone masses in N _f =2 QCD with doubly degenerate quarks. At least the more chiral points should be consistent with Chiral Perturbation Theory for the latter to be useful in an extrapolation to physical masses. I find consistency with the chiral prediction but no striking evidence for chiral logs. Nonetheless, the consistency guarantees that the original estimate, by Gasser and Leutwyler, of the N _f =2 QCD low-energy scale was not entirely wrong. Received: 4 April 2003, Published online: 11 June 2003     

From Local Perturbation Theory to Hopf and Lie Algebras of Feynman Graphs

We review the algebraic structures imposed on the renormalization procedure in terms of Hopf and Lie algebras of Feynman graphs, and exhibit the connection to diffeomorphisms of physical observables.