We calculate the coefficients in the chiral Lagrangian approximately from QCD based on a previous study of deriving the chiral Lagrangian from the first principles of QCD in which the chiral Lagrangian coefficients are defined in terms of certain Green's functions in QCD. We first show that, in the large-Nc limit, the anomaly part contributions to the coefficients are exactly cancelled by certain terms in the normal part contributions, and the final results of the coefficients only concern the remaining normal part contributions depending on QCD interactions. We then do the calculation in a simple approach with the approximations of taking the large-Nc limit, the leading order in dynamical perturbation theory, and the improved ladder approximation, thereby the relevant Green's functions are expressed in terms of the quark self energy Σ(p 2 ). By solving the Schwinger-Dyson equation for Σ(p 2 ), we obtain the approximate QCD predicted coefficients and quark condensate which are consistent with the experimental values.

The littlest Higgs model is the most economical one among various little Higgs models.In the context of the littlest Higgs model, we study the process e + e − → e + e − H at the ILC and calculate the correction of the littlest Higgs model to the cross section of this process.The results show that, in the favorable parameter spaces preferred by the electroweak precision data, the value of the relative correction is in the range from a few percent to tens percent. In most case, the correction is large enough to reach the measurement precision of the ILC. Therefore, the correction of the littlest Higgs model to the process e + e − → e + e − H might be detected at the ILC which will give an ideal way to test the model.

Parameters of Gasser Leutwyler chiral Lagrangian are proved saturated by dynamical quark self energy Σ(k 2 ) in a gauge invariant, nonlocal, dynamical quark model.

One -loop fermion determinant is discussed for the case in which dynamical chiral symmetry breaking caused by momentum dependent fermion self energy Σ(p 2 ) take place. The obtained series generalizes the heat kernel expansion for hard fermion mass. PACS number(s): 03.65. Db, 11.10Ef, 11.30.Rd, 12.39.Fe In quantum field theory, 1-loop quantum correction of fermions is from fermion deter- m is a hard fermion mass. Ignoring anomaly, the real part of lndet(D + m) in terms of a proper time integral is * Mailing address 1