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A new set of the next-to-leading order (NLO) and the next-to-next-to-leading order (NNLO) low-energy constants $L_i^r$ and $C_i^r$ in chiral perturbation theory is obtained. These values are computed using the new experimental data with a new calculation method. This method combines the traditional global fit and Monte Carlo method together. The higher order contributions are estimated with this method. The theoretical values of the observables provide good convergence at each chiral dimension, except for the NNLO values of the $\pi K$ scattering lengths $a_0^{3/2}$ and $a_0^{1/2}$. The fitted values for $L_i^r$ at NLO are close to their results with the new method at NNLO; i.e., these $L_i^r$ are nearly order-independent in this method. The estimated ranges for $C_i^r$ are consistent with those in the literature, and their possible upper or/and lower boundaries are given. The values of some linear combinations of $C_i^r$ are also given, and they are more reliable. If one knows a more exact value $C_i^r$, another $C_i^r$ can be obtained by these values., Comment: 24 pages, 3 figures

We construct the relativistic chiral Lagrangians for heavy-light mesons $(Q\bar{q})$ to the $\mathcal{O}(p^4)$ order. From $\mathcal{O}(p^2)$ to $\mathcal{O}(p^4)$, there are 17, 67, and 404 independent terms in the flavor $SU(2)$ case and 20, 84, and 655 independent terms in the flavor $SU(3)$ case. The Lagrangians in the heavy quark limit are also obtained. From $\mathcal{O}(p^2)$ to $\mathcal{O}(p^4)$, there are 7, 25, and 136 independent terms in the flavor $SU(2)$ case and 8, 33, and 212 independent terms in the flavor $SU(3)$ case. The relations between low-energy constants based on the heavy quark symmetry are also given up to the $\mathcal{O}(p^3)$ order., Comment: 22 pages

We construct the relativistic chiral Lagrangians with decuplet baryons up to the order $\mathcal{O}(p^4)$ (one loop). For the meson-decuplet-decuplet couplings, there are 1, 13, 55, and 548 terms in the $\mathcal{O}(p^1)$-$\mathcal{O}(p^4)$ order Lagrangians, respectively. For the meson-octet-decuplet Lagrangians, the number of independent terms from $\mathcal{O}(p^1)$ to $\mathcal{O}(p^4)$ are 1, 5, 67, and 611, respectively. For convenience of applications, the $\pi\Delta\Delta$ and $\pi N\Delta$ chiral Lagrangians are picked out. This new form of $\Delta$ Lagrangians is equivalent to the original isovector-isospinor one and we establish relations between these two forms., Comment: 25 pages, 7 tables

We construct the Lorentz-invariant chiral Lagrangians up to the order O(p4) by including Δ(1232) as an explicit degree of freedom. A full one-loop investigation on processes involving Δ(1232) can be performed with them. For the πΔΔ Lagrangian, one obtains 38 independent terms at the order O(p3) and 318 independent terms at the order O(p4). For the πNΔ Lagrangian, we get 33 independent terms at the order O(p3) and 218 independent terms at the order O(p4). The heavy baryon projection is also briefly discussed.

We update our original low-energy constant computations to the $O({p}^{6})$ order, including two and three flavors, the normal and anomalous ones. Following a comparative analysis, the $O({p}^{4})$ order results are considered better. In the $O({p}^{6})$ order, most of our results are consistent with or better than those we have found in the literature, although several are worse.

We present the results of calculations of the $p^4$ and $p^6$ order low-energy constants for the chiral Lagrangian with tensor sources for both two and three flavors of pseudoscalar mesons. This is a generalization of our previous work on similar calculations without tensor sources in terms of the quark self-energy $\Sigma(p^2)$, based on the first principle derivation of the low-energy effective Lagrangian and computation of the low-energy constants with some rough approximations. With the help of partial integration and some epsilon relations, we find that some $p^6$ order operators with tensor sources appearing in the literature are related to each other. That leaves 98 independent terms for $n$-flavor, 92 terms for three-flavor, and 65 terms for two-flavor cases. We also find that the odd-intrinsic-parity chiral Lagrangian with tensor sources cannot independently exist in any order of low-energy expansion., Comment: 29 pages

The electroweak chiral Lagrangian for the topcolor-assisted technicolor model proposed by K. Lane, which uses nontrivial patterns of techniquark condensation and walking, was investigated in this study. We found that the features of the model are qualitatively similar to those of Lane's previous natural topcolor-assisted technicolor prototype model, but there is no limit on the upper bound of the ${Z}^{\ensuremath{'}}$ mass. We discuss the phase structure and possible walking behavior of the model. We obtained the values of all coefficients of the electroweak chiral Lagrangian up to an order of ${p}^{4}$. We show that although the walking effect reduces the $S$ parameter to half its original value, it maintains an order of 2. Moreover, a special hypercharge arrangement is needed to achieve further reductions in its value.

We present results of computing the p{sup 6} order low energy constants in the normal part of chiral Lagrangian both for two and three flavor pseudoscalar mesons. This is a generalization of our previous work on calculating the p{sup 4} order coefficients of the chiral Lagrangian in terms of the quark self-energy {Sigma}(p{sup 2}). We show that most of our results are consistent with those we can find in the literature.

Based on previous studies deriving the chiral Lagrangian for pseudoscalar mesons from the first principle of QCD, we derive an electroweak chiral Lagrangian and build up a formulation for computing its coefficients from a one-doublet technicolor model and a schematic topcolor-assisted technicolor model. We find that coefficients of the electroweak chiral Lagrangian for the topcolor-assisted technicolor model are divided into three parts: direct TC2 interaction part, TC1 and TC2 induced effective ${Z}^{\ensuremath{'}}$ particle contribution part, and ordinary quarks contribution part. The first two parts are computed in this paper. We show that the direct TC2 interaction part is the same as that in the one-doublet technicolor model, while effective ${Z}^{\ensuremath{'}}$ contributions are at least proportional to the ${p}^{2}$ order parameter ${\ensuremath{\beta}}_{1}$ in the electroweak chiral Lagrangian. Typical features of the topcolor-assisted technicolor model are that it only allows positive $T$ and $U$ parameters, the $T$ parameter varies in the range $0\ensuremath{\sim}1/(25\ensuremath{\alpha})$, and the upper bound of $T$ parameter will decrease as long as ${Z}^{\ensuremath{'}}$ mass become large. The $S$ parameter can be either positive or negative depending on whether the ${Z}^{\ensuremath{'}}$ mass is large or small. The ${Z}^{\ensuremath{'}}$ mass is bounded above and the upper bound depends on the value of the $T$ parameter. We obtain the values for all coefficients of the electroweak chiral Lagrangian up to the order of ${p}^{4}$.

The complete list of electroweak chiral Lagrangian for W', Z' and a neutral light higgs with symmetry $SU(2)_1\otimes SU(2)_2\otimes U(1)$ is provided. The bosonic part is accurate up to order of $p^4$, the matter part involving various fermions representation arrangements includes dimension three Yukawa type and dimension four gauge type operators. The universal mixings and masses of gauge boson and fermion are given. Constraints from mass differences for $K^0-\bar{K}^0$, $B_d^0-\bar{B}_{d}^0$, $B_s^0-\bar{B}_{s}^0$ systems and indirect CP violation parameter $|\epsilon_K|$ for $K$ mesons are evaluated., Comment: 40 pages, 8figures