RIKEN Accel. Prog. Rep. 48 (2015)

Ⅱ-4. Hadron Physics

Fragmentation function measurements in Belle

Fragmentation functions allow us to study the process of nearly free partons fragmenting into final state
hadrons as they also exist in visible matter. While
the theory of the strong interaction, QCD, is generally accepted as the force governing all hadronic matter around us, only high energy processes are directlycalculable. Parton distribution functions as well as
fragmentation functions need to be obtained by experiment. Of particular interest is, how a parton of acertain flavor fragments into certain types of hadrons,
how initial parton spin gets translated into the distribution of final state hadrons and how transvserse
momentum is generated relative to the initial parton.
In the Belle experiment one can study these aspects
well since the underlying process of electron-positronannihilation provides a clean initial state without any
hadrons to study the emerging final state hadrons.
However, normally the quark flavor is not directly accessible as both a quark and an antiquark are created
and at least for light flavors (u, d and s quarks) tagging
techniques are not reliable. A first way around thislimitation was already performed in the Collins typeanalysis1) where two charged pions in opposite hemispheres were studied. Having two hadrons in opposite
hemispheres mostly ensures, that one hadron was fragmentating from the quark and another from the antiquark. The ratio of same over opposite charges thenrevealed the differences of favored and disfavored polarized and un-polarized fragmenation functions. Thismethod was extended for pion-kaon and kaon-kaon
combinations to obtain sensitivity of the strange quark
Collins functions as well as disfavored u,d quark tokaon Collins fragmentation functions. Preliminary results have been obtained in 20142) as shown in Fig. 1
and are expected to be published soon.
Furthermore the unpolarized fragmentation funch
tions D1,q(z, s) can be studied in a similar way andfirst results have been prepared for all combinations ofcharged pions and kaons either in opposite hemispheres√or also the same for comparison. Here, z = 2Eh / s
is the fractional energy the √hadron h carries relative
to the initial parton q and s is the center of massenergy. In the thus obtained cross sections as a function of fractional energy z the ratios between sameand opposite sign pion pairs in opposite hemispheres
essentially provide the ratio of dis-favored over favored∗1∗2∗3∗4∗5∗6

RIKEN Nishina Center
Physics department, University of Illinois
Physics department, University of Indiana
Department of Physics, Tokyo Institute of Technology
Department of Physics, University of the Basque Country
IkerbasqueA0

R. Seidl,∗1 F. Giordano,∗2 M. Leitgab,∗2 A. Vossen,∗3 H. Li,∗3 W. Jacobs,∗3 N. Kobayashi,∗4M. Grosse-Perdekamp,∗2 A. Ogawa,∗1 C. Hulse∗5 and G. Schnell∗5,∗60.06

Unlike/Like π π
Unlike/Like π K
Unlike/Like KK

0.2 ≤ z1 < 0.25

0.25 ≤ z1 < 0.3

Belle Preliminary

0.04

0.02

0-0.020.06
0.3 ≤ z1 < 0.42

0.42 ≤ z1 < 1

0.04

0.02

0-0.02
0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

z2

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

z2

Fig. 1. Collins type azimuthal moments as a fucntion of
fractional energy z2 in bins of fractional energy z1 foropposite sign over same sign pion pairs (blue), πK(green) and kaon pairs (purple).

fragmentation from u,d quarks to pions. Favored fragmentation relates to fragmentation into a hadron withvalence content the same as the initial parton (ie uto π + = |ud⟩) and dis-favored fragmentation with valence content not the same (ie d to π + ). First results
have been obtained and are expected to be shown as
preliminary results and be published soon. The expected precision is such, that even the ratios at fractional hadron energies z above 0.8 have still reasonablysmall uncertainties.
In addition an analysis of transverse momenta of one
hadron relative to a second hadron is ongoing whichshould help improve the rather large uncertainties andassumptions of any transvserse momentum dependent
distribution and fragmentation functions. These areneeded for the analysis of quark transversity and Sivers
function data of semi-inclusive deep inelastic scattering and hadron collision experiments. These explicit
transvserse momentum dependent measurements arealso expected to obtain preliminary status this year.
References
1) R. Seidl et al. [Belle Collaboration], Phys. Rev. Lett.
96, 232002 (2006). R. Seidl et al. [Belle Collaboration],
Phys. Rev. D 78, 032011 (2008), [Erratum-ibid. D 86,039905 (2012)]. A. Vossen et al. [Belle Collaboration],
Phys. Rev. Lett. 107, 072004 (2011).
2) F. Giordano [Belle Collaboration], PoS DIS 2014, 212(2014).

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