Guo, ZH (reprint author), Hebei Normal Univ, Dept Phys, Shijiazhuang 050024, Peoples R China.
We study the eta-eta' mixing up to next-to-next-to-leading-order in U(3) chiral perturbation theory in the light of recent lattice simulations and phenomenological inputs. A general treatment for the eta-eta' mixing at higher orders, with the higher-derivative, kinematic and mass mixing terms, is addressed. The connections between the four mixing parameters in the two-mixing-angle scheme and the low energy constants in the U(3) chiral effective theory are provided both for the singlet-octet and the quark-flavor bases. The axial-vector decay constants of pion and kaon are studied in the same order and confronted with the lattice simulation data as well. The quark-mass dependences of m(eta), m(eta') and m(K) are found to be well described at next-to-leading order. Nonetheless, in order to simultaneously describe the lattice data and phenomenological determinations for the properties of light pseudoscalars pi, K, eta and eta', the next-to-next-to-leading order study is essential. Furthermore, the lattice and phenomenological inputs are well reproduced for reasonable values of low the energy constants, compatible with previous bibliography.
National Natural Science Foundation of China (NSFC) 
; Natural Science Foundation of Hebei Province [A2015205205]
; Education Department of Hebei Province [YQ2014034]
; Department of Human Resources and Social Security of Hebei Province [C201400323]
; Doctor Foundation of Hebei Normal University [L2010B04]
; Spanish Government (MINECO)
; European Commission (ERDF) [FPA2010-17747, FPA2013-44773-P, FPA2013-40483-P, SEV-2012-0249, CSD2007-00042]
; MINECO (Spain) [FIS2014-57026-REDT]
; EPOS network of the European Community Research Infrastructure Integrating Activity "Study of Strongly Interacting Matter" (HadronPhysics3) 
Guo, XK,Guo, ZH,Oller, JA,et al. Scrutinizing the eta-eta ' mixing, masses and pseudoscalar decay constants in the framework of U(3) chiral effective field theory[J]. JOURNAL OF HIGH ENERGY PHYSICS,2015(6):175.