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a number of polarized semi - inclusive deep - inelastic scattering ( sidis ) and polarized proton - proton scattering ( pp ) experiments are measuring quark and gluon distributions via qcd analysis . unpolarized hadron fragmentation functions are input quantities for such analyses and currently limit the accuracy with which e.g. parton helicity distributions can be determined .
two recent studies have extracted hadron fragmentation functions from datasets of hadron production in @xmath0  @xcite , and from a combination of @xmath0 , sidis and pp datasets  @xcite . in both studies ,
the authors emphasize the need for a precision hadron multiplicity measurement from @xmath0 annihilation data at low center - of - mass energies , compared to the bulk of existing datasets taken at the large electron - positron collider ( lep ) at cern .
this precision dataset is expected to improve in particular the knowledge of the gluon fragmentation functions .
presented in this section is a precision measurement of hadron multiplicities on about @xmath1 @xmath0 annihilation events taken with the belle experiment at kek , japan , at a center - of - mass energy of @xmath2 gev , @xmath3 mev below the @xmath4 resonance .
the multiplicities are measured in dependence of @xmath5 , the hadron energy relative to half of the center - of - mass energy , on an interval @xmath6 .
the measured hadrons are produced in reactions @xmath7 , where @xmath8 .
the belle detector contains several subsystems which allow for particle identification ( pid ) by imposing cuts on likelihood values extracted from measurements of these subsystems .
the likelihood cut selections yield fairly accurate pid but need to be calibrated in the context of a high precision measurement , such that measured hadron yields can be corrected for particle misidentification .
particle misidentification changes hadron yields up to @xmath9 for pions and up to @xmath10 for kaons , depending on hadron momentum .
the correction is performed through an unfolding technique based on inverse @xmath11 pid probability matrices .
pid probability matrices are obtained from analyzing decays of particles in which the species @xmath12 of the decay products can be determined through purely kinematic means . in such a sample , additional cuts on track pid likelihood variables selecting a species @xmath13 define a subsample of tracks .
comparing the number of cut - selected tracks to the total number of tracks in the sample allows to extract pid probabilities @xmath14 .
complete @xmath11 matrices of pid probabilities are extracted from experimental data for species @xmath15 by analyzing decays of @xmath16 , @xmath17 and @xmath18 particles .
this data - driven pid calibration avoids the dependence on the modeling of belle pid detectors in geant  @xcite . as an example
, figure  [ fig : pidfits ] displays fits of invariant mass distributions @xmath19 from decays @xmath20 .
the kaon candidates in contributions to figure b ) fulfill an additional pid likelihood cut to select pions .
the ratio of the hatched peak areas is equal to the pid probability @xmath21 .
from decays @xmath20 .
figures a ) and b ) show distributions containing negatively - charged kaon candidate tracks with laboratory frame momentum @xmath22 gev / c and laboratory frame azimuthal angle @xmath23 degrees .
figure b ) shows all contributions to figure a ) where the kaon candidate additionally passes pid likelihood cuts to select pions . the pid misidentification of kaons as pions can be extracted from the ratio of the hatched areas , yielding the probability @xmath24 .
]    a )     from decays @xmath20 .
figures a ) and b ) show distributions containing negatively - charged kaon candidate tracks with laboratory frame momentum @xmath22 gev / c and laboratory frame azimuthal angle @xmath23 degrees .
figure b ) shows all contributions to figure a ) where the kaon candidate additionally passes pid likelihood cuts to select pions .
the pid misidentification of kaons as pions can be extracted from the ratio of the hatched areas , yielding the probability @xmath24 . ]
b )    for kinematic regions not accessible to this calibration method , an extrapolation algorithm is used to obtain pid calibration information .
the pid probability matrices from all kinematic areas are inverted and then applied to the measured yields @xmath25 to obtain pid - corrected pion and kaon yields @xmath26 .
all uncertainties of the extracted pid probabilities are propagated through the inversion process using a monte carlo technique and are assigned to the pid - corrected yields as systematic uncertainties .
in addition to particle misidentification , the measured experimental data yields are also corrected for sample purity , kinematical smearing , decay - in - flight , detector interaction / shower particles , detector and tracking efficiencies and analysis acceptance .
the presence of initial state radiation is accounted for as well .
figure  [ fig : collinsplanesandangledef ] a ) shows preliminary negatively charged pion and kaon multiplicities including statistical and systematic uncertainties from about @xmath1 @xmath0 annihilations . in figure
[ fig : prelimplotsreluncerts ] a ) and b ) the relative size of preliminary statistical and systematic uncertainties is given .
final systematic uncertainties will likely remain below @xmath27 ( @xmath28 ) for @xmath29 ( @xmath30 ) spectra for @xmath31 , and will increase with @xmath32 up to @xmath33 ( @xmath34 ) for @xmath29 ( @xmath30 ) spectra through @xmath35 , respectively .
currently , the last systematic studies are being finished and timely journal submission for publication is expected .     normalization uncertainty is not shown .
b ) measurement of the interference fragmentation function : azimuthal modulations @xmath36 of two - pion yields for a @xmath37 @xmath38 , @xmath39 binning , as a function of @xmath39 for all @xmath38 bins . indices @xmath40 and @xmath41 refer to the respective reaction hemisphere . ]
a )     normalization uncertainty is not shown .
b ) measurement of the interference fragmentation function : azimuthal modulations @xmath36 of two - pion yields for a @xmath37 @xmath38 , @xmath39 binning , as a function of @xmath39 for all @xmath38 bins .
indices @xmath40 and @xmath41 refer to the respective reaction hemisphere . ]
b )     normalization uncertainty is not shown . ]
a )     normalization uncertainty is not shown . ]
spin - dependent , chiral - odd fragmentation functions can be used to extract transverse spin quark distributions ( so called transversity distributions ) in the nucleon from polarized sidis and pp scattering experiments .
one candidate for such a chiral - odd function is the interference fragmentation function ( iff ) .
first proposed by collins , heppelman and ladinsky  @xcite , the iff describes the fragmentation of a polarized quark into two hadrons correlated via partial wave interference .
the corresponding observable is an azimuthal dependence in the production cross - section of hadron pairs . at belle
, the product of two iffs can be measured by identifying one hadron pair in either hemisphere in a two - jet event @xmath42 .
the iff does not depend on transverse momenta and therefore its factorization and evolution can be described in a collinear approach .
this makes the iff an attractive alternative compared to the usually used collins fragmentation function ( previously measured for pions at belle , cf .
references  @xcite and  @xcite ) for the extraction of parton transversity distributions .
azimuthal correlations between the planes spanned by two hadron pairs and the interaction plane defined by the incoming lepton momenta and the quark - antiquark momentum axis ( approximated by the thrust axis ) are extracted .
the raw azimuthal yields are normalized to the average hadron pair yield and fitted .
this approach is not susceptible to qcd radiative effects and the @xmath43 azimuthal modulation @xmath44 is directly proportional to the product of two iff @xmath45 , where @xmath46 represents the fractional energy of the hadron pair and @xmath47 its invariant mass .
analysis results on a dataset of @xmath48 containing @xmath49 @xmath50 pairs collected at the @xmath51(@xmath52s ) resonance have been published in reference  @xcite .
figure  [ fig : collinsplanesandangledef ] shows azimuthal modulations rising with the fractional energy of the hadron pair to significant values of up to @xmath53 for highest @xmath32 .
the belle collaboration is currently also pursuing measurements of the kaon collins ff , the kaon and @xmath54 iffs and the di - hadron ff .
in addition , measurements are being prepared to extract the @xmath55 dependence of the unpolarized and the di - hadron ffs .
fragmentation functions ( ffs ) describe the formation of final state particles from a partonic initial state 
 . precise knowledge of these functions is a key ingredient in accessing quantities such as the nucleon spin structure in semi - inclusive deep - inelastic scattering and proton proton collisions . 
 however , fragmentation functions can currently not be determined from first principles quantum chromodynamics and have to be extracted from experimental data . 
 the belle experiment at kek , japan , provides a large data sample for high precision measurements on @xmath0 annihilations allowing for first - time or more precise extractions of fragmentation functions . 
 analyses for extractions of spin - independent ( unpolarized ffs ) as well as spin - dependent fragmentation functions ( interference ffs ) at belle are presented .