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.     

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.     

Masses and Widths of Light Scalar Mesons in Chiral Perturbation Theory

Based on the diquark model, we assume that the light scalar mesons are q^2q^-2 states rather than qq^-. The chiral effective Lagrangian for the light scalar meson is constructed, and the mass relations are obtained： the isotriplet （a0） and the isosinglet （f0） are the heaviest and are degenerate, the isodoublets （κ） are heavier and the other isosinglet （σ） is the lightest; and 2Mκ^2 = Mα0^2＋ Mσ^2. Using experimental value for a0 and σ mass, we obtain Mκ=794 MeV, which is consistent with the experimental value. Then taking Г（a0^0 →ηπ^0） = 90 MeV and Г（f0→π^0π^0） = 20 MeV, we get the width of σ is： Г（σ0→π^＋π^-）= 150 MeV.     

基于手征微扰理论构建相对论重子-重子相互作用(英文)

介绍了两个近期基于协变手征微扰理论构建领头阶核子-核子和超子-核子相互作用的工作。理论中未知的低能常数通过拟合核子-核子和超子-核子散射实验数据确定。分析发现,在对散射数据的描述上,领头阶相对论手征力可以媲美次领头阶非相对论手征核力。研究表明,构建相对论手征重子-重子相互作用技术上是可行的。得到的相互作用不仅可以为相对论核结构及反应研究提供重要的理论输入,而且可以进一步加深对低能强相互作用的认识。In this paper, we report on two recent studies of relativistic nucleon-nucleon and hyperonnucleon interactions in covariant chiral perturbation theory, where they are constructed up to leading order. The relevant unknown low energy constants are fixed by fitting to the nucleon-nucleon and hyperon-nucleon scattering data. It is shown that these interactions can describe the scattering data with a quality similar to their next-to-leading order non-relativistic counterparts. These studies show that it is technically feasible to construct relativist baryon-baryon interactions, and in addition, after further refinements, these interactions may provide important inputs to ab initio relativistic nuclear structure and reaction studies and help improve our understanding of low energy strong interactions.     

Sigma Terms and Strangeness Contents of Baryon Octet in Modified Chiral Perturbation Theory

In the frame work of chiral perturbation theory, a modified effective Lagrangian for meson-baryon system is constructed, where the SU（3） breaking effect for meson is considered. The difference between physical and chiral limlt decay constants is taken into account. Calculated to one 1ooi） at O（p^3）, the sigma terms and strangeness contents of baryon octet are obtained.     

Chiral extrapolation and determination of low-energy constants from lattice data

We propose analytic approximations of chiral SU(3)$\mathit{SU}(3)$ amplitudes for the extrapolation of lattice data to the physical meson masses. The method allows the determination of NNLO low-energy constants in a controllable fashion. We test the approach with recent lattice data for the ratio FK/Fπ$F_K/F_{\pi }$ of meson decay constants.     

Chiral unitary theory: Application to nuclear problems

In this talk we briefly describe some basic elements of chiral perturbation theory, xPT, and how the implementation of unitarity and other novel elements lead to a better expansion of the T-matrix for meson-meson and meson-baryon interactions. Applications are then done to the ππ interaction in nuclear matter in the scalar and vector channels, antikaons in nuclei and K ⁻ atoms, and how the φ meson properties are changed in a nuclear medium.     

PT-Symmetry, Canonical Decomposition, Perturbation Theory

Let H be any PT-symmetric Schrödinger operator of the type H=- ² +x ² +igW(x), where W is a real polynomial, odd under reflection of all coordinates, gR, acting on L ² ( R ^d ). The proof is outlined of the following statements: PH is self-adjoint and its eigenvalues coincide with the eigenvalues of (H*H). Moreover the eigenvalues of (H*H), known as the singular values of H, can be computed via perturbation theory by Borel summability.     

On Field Theory Methods in Singular Perturbation Theory

Singular and supersingular finite rank perturbations of self-adjoint operators are studied using methods from renormalization theory for quantum fields. It is shown that the ideas from dimensional and Pauli–Villars regulatizations can be applied to determine uniquely certain finite rank supersingular perturbations. Approach is based on the regularization of homogeneous singular quadratic forms.     

Soliton Perturbation Theory for the Compound KdV Equation

The soliton perturbation theory is used to study the solitons that are governed by the compound Korteweg de-Vries equation in presence of perturbation terms. The adiabatic parameter dynamics of the solitons in presence of the perturbation terms are obtained. AMS Codes: 35Q51; 35Q53; 37K10. PACS Codes: 02.30.Jr; 02.30.Ik.     

Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameterγ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rateγ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r=C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results.     

Chiral effective field theory and nuclear forces

We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.     

Perturbation Theory for Isotropic Landau-Lifschitz Equation Based on Inverse Scattering Transformation

The perturbation theory for the Landau-Lifschitz equation for isotropic chain with correction, which is based on the inverse scattering transform (IST), is developed to treat Landau-Lifschitz equation for a spin chain with axis asymmetry. The time-evolution equation of parameters and a formula for the first-order correction is given by treating the equation with axis symmetry as a perturbation to the isotropic equation. PACS numbers 05.45.Yv, 42.65.-k, 42.50.Md.Supported by the National Science Foundation of China under Grant NO. 10474076 and No. 10375041.     

Trace Formulae of Characteristic Polynomial and Cayley-Hamilton＇s Theorem, and Applications to Chiral Perturbation Theory and General Relativity

By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton＇s theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to ehiral perturbation theory and general relativity.     

六次非简谐振子的多尺度微扰理论

应用多尺度微扰理论, 对于弱耦合常数的六次非简谐振子得到了其运动方程的经典和量子情况下的一阶解. 与Taylor级数解不同的是, 无论是在经典和量子解中频率移动出现在各阶表达式中, 因此多尺度微扰理论是优于Taylor级数解的一种处理弱耦合常数非简谐振动的近似方法.