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fragmentation functions are important ingredient for understanding the structure of the hadrons , because they play a crucial role in analyzing the processes involving hadrons . for example
, one needs the unpolarized fragmentation functions to analyze the semi - inclusive processes in the electron - positron scattering , deep - inelastic proton - proton scattering , and so on  @xcite .
furthermore , to extract the chiral - odd transversity parton distribution of the nucleon one needs more complicated fragmentation functions , such as the polarized dihadron fragmentation functions and the collins fragmentation functions . because of their fundamental importance
, those functions have been studied intensively for decades but still not fully understood yet .
the unpolarized fragmentation function @xmath2 represents the probability for a quark @xmath3 to emit a hadron @xmath4 with the light - cone momentum fraction @xmath5 .
it can be written with the light - cone coordinate as follows  @xcite : @xmath6|_{zk^-=p^-}.\ ] ] here , @xmath7=@xmath8 and the correlation @xmath9 is defined as @xmath10 where @xmath11 , @xmath12 indicate the four - momenta for the initial quark and fragmented hadron , respectively .
furthermore , @xmath5 is the longitudinal light - cone momentum fraction possessed by the hadron and @xmath13 denotes a renormalization scale at which the fragmentation process is computed .
all the calculations are carried out in the frame where the @xmath5-axis is chosen to be the direction of @xmath14 . consequently the transverse momentum of the initial quark @xmath15 is zero in this frame . on the other hand , @xmath16\,\bm{p}$ ] , defined as the transverse momentum of the initial quark with respect to the direction of the momentum of the produced hadron , is nonzero .
the integrated fragmentation function satisfies the momentum sum rule : @xmath17 where @xmath4 represents all the fragmented hadrons .
( [ eq : sum ] ) means that all of the momentum of the initial quark @xmath3 is transferred into the momenta of the fragmented hadrons .
empirically , information of @xmath18 has to be extracted from the available high - energy lepton - scattering data by global analysis with appropriate parameterizations satisfying certain constraints  @xcite .    from theoretical points of view
, it is impossible to study fragmentation functions directly by lattice qcd because they are defined in minkowski space .
nevertheless , there have been numerous works for the fragmentation functions based on the effective qcd models so far . in ref .
@xcite , the nambu  jona - lasinio ( njl ) model has been used to calculate the fragmentation functions .
monte - carlo ( mc ) simulations with supersymmetric qcd were also carried out to obtain the fragmentation function up to a very high energy in the center - of - mass frame @xmath19  @xcite .
the collins fragmentation functions , which play an essential role in the transverse - spin physics , have been studied as well in the quark - pseudoscalar ( ps ) meson coupling model  @xcite .
note that dihadron fragmentation functions have been investigated in the same theoretical formalism  @xcite . for brevity
, we will simply call the unpolarized fragmentation functions as the fragmentation functions from now on .    in refs .
@xcite , we have already employed the nonlocal chiral quark model ( nlchqm ) with the explicit flavor su(3 ) symmetry breaking to calculate the elementary fragmentation functions .
this instanton - motivated approaches were used for computing the quark distribution amplitudes , manifesting the nonlocal quark - pseudoscalar ( ps ) meson interactions  @xcite .
nlchqm have been applied to determine various nonperturbative quantities and obtained the results which are in good agreement with experiments as well as lattice qcd ( lqcd ) simulations  @xcite .
the elementary fragmentation functions calculated in refs .
@xcite are the functions in eq.([eq : cor1 ] ) with the following approximation : @xmath20 here @xmath21 denotes the ps meson . in other words
, we just calculate the one - step fragmentation process : @xmath22 .
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we investigate the unpolarized pion and kaon fragmentation functions using the nonlocal chiral - quark model . in this model 
 the interactions between the quarks and pseudoscalar mesons is manifested nonlocally . 
 in addition , the explicit flavor su(3 ) symmetry breaking effect is taken into account in terms of the current quark masses . 
 the results of our model are evaluated to higher @xmath0 value @xmath1 by the dglap evolution . 
 then we compare them with the empirical parametrizations . 
 we find that our results are in relatively good agreement with the empirical parametrizations and the other theoretical estimations .