Fitting The Low-energy Constants Of Pseudoscalar Mesons

In chiral perturbation theory,the chiral Lagrangian of the pseudoscalar mesons has many unknown low-energy constants(LECs).Most of physical quantities are the functions of LECs.Without LECs,most of the theoretical predictions of phys-ical quantities can not be obtained.The traditional global fitting method can give the estimates of LECs by fitting the experimental data directly,but there are some problems:The values of the next-to-leading order LECs L_i~r have great changes be-tween the next-to-leading order and the next-to-next-to-leading order fit;the higher order effects are not considered;there is an overfitting problem;some physical quan-tities have bad convergence;most of the next-to-next-to-leading order LECs aredepended on the boundaries.In order to solve these problems,this thesis proposes two new methods of calcu-lation based on the global fitting method.Method I is the preliminary improvement of the global fitting method,which includes using the expansion of physical quanti-ties,considering the truncation errors,and adding more constraints,but this method has some drawbacks.Method ? combines method I and Monte-Carlo method,some drawbacks in method I are solved.In this method,we obtain a better set of L_i~r,and the ranges of C_i~ r are constrained.This thesis gives a set of better values of L_i~r and obtains the estimates of C_i~r and their linear combinations((?)_i).The values of C_i~r are stable and hardly depended onthe chiral dimension.The values of L_i~r are consistent with those in others literature.27C_i~r is depended on the boundaries,these C_i~r value may be unreliable.More exper-imental inputs and constraints are needed to limit their ranges.The other 11C_i~r is hardly depended on the boundaries,theseC_i~r value are more reliable.The values of C_i~r_i are more accurate and more reliable than C_i~r.If one knows the more exact valuesof some C_i~r,other C_i~r.can be obtained or limited by these values.