Ⅱ-4. Hadron Physics

RIKEN Accel. Prog. Rep. 49 (2016)

Fragmentation function measurements in Belle††∗1∗2∗3∗4∗5∗6∗7Condensed from the article in Phys. Rev. D92, 092007(2015)RIKEN Nishina Center
Physics department, University of Illinois
Physics department, Indiana University
Department of Physics, Tokyo Institute of Technology
Brookhaven National Laboratory
Department of Physics, University of the Basque Country
Ikerbasque- 113 -10610

50.20 < z1 < 0.25

0.25 < z1 < 0.30

0.30 < z1 < 0.35

0.35 < z1 < 0.40

0.40 < z1 < 0.45

0.45 < z1 < 0.500.50 < z1 < 0.550.55 < z1 < 0.600.60 < z1 < 0.65

0.65 < z1 < 0.700.70 < z1 < 0.750.75 < z1 < 0.800.80 < z1 < 0.850.85 < z1 < 0.90104103d2σ / dz1 dz2 [fb]102107106105104103d2σ / dz1 dz2 [fb]102107106105104

103102d2σ / dz1 dz2 [fb]107

π+π- data

106π+π+ data

105π+K data

0.90 < z1 < 0.95-+π+K data+-++K K data

0.95 < z1 < 1.00

K K data

1041031020.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.2
1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.2
1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.2
1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
z2z2
z2
z2

Fig. 1. Di-hadron cross sections as a function of fractionalenergy z2 in bins of the fractional energy z1 without atopology requirement on the two hadrons. Individual
hadron combinations are π + π − (black), π + π + (blue),π + K − (green), π + K + (pink), K + K − (red) and K + K +(purple) including systematic uncertainties as shaded
areas.

sumption whether di-hadrons originated from the same
parton or different partons has been tested by selecting hadron pairs in the same or opposite hemispheres
when applying an additional thrust criterion. As canbe seen in Fig. 2, same-hemisphere dihadrons decrease
rapidly as soon as the sum of their fractional energies
exceeds unity in agreement that opposite-hemispheredi-hadrons are generally produced off different partons.
-106105
104105104d2σ / dz1 dz2 [fb]π+K 107106

d2σ / dz1 dz2 [fb]π+π- 107106

d2σ / dz1 dz2 [fb]

107

K+K-

105
104

103

103

103

102

102

102

105
104

106
105
104

d2σ / dz1 dz2 [fb]106

d2σ / dz1 dz2 [fb]

10
10
10
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.2
1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.2
1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1π+πz+1 10z27
π+Kz+1 10z27
K+Kz1+ z2
107

d2σ / dz1 dz2 [fb]Fragmentation functions (FFs) describe the transition of highly-energetic, asymptotically free partons
into final state hadrons. They are a quantity whichcannot be obtained from first principles QCD but need
to be extracted from experiments. In turn FFs can beused as a tool to extract information about the nucleon structure for different parton flavors. In particular, FFs are commonly used in polarized semi-inclusive
deep-inelastic scattering and proton-proton collisions
to access the spin structure of the nucleon. The cleanest way to access FFs is in electron-positron annihilation due to the lack of hadrons in the initial state.
However, only charge square weighted sums over all
kinematically availabe quarks and antiquarks are accessible at leading order of the strong coupling αSin e+ e− annihilation. To overcome this partially, instead of detecting a single hadron in the final state,
two hadrons, preferrably in opposite hemispheres asdefined by the thrust axis, have been measured. The
combination of charges and hadron types then gives additional information about the FFs if one assumes thehadrons to be fragmenting off different partons. Forexample, same-sign pions and opposite sign-pions contain different combinations of favored (e.g., u → π + )and disfavored (d → π + ) FFs when considering up anddown type (anti)quarks only.
The di-hadron cross sections have been extracted
from a dataset of 655 fb−1 taken by the Belle experiment at the asymmetric-energy e+ e− collider KEKB.
The data was corrected for particle-misidentification,
momentum smearing, contributions of QED processes
not related to fragmentation (such as τ pair production), acceptence and efficiencies as well as initial statephoton radiation1) . The final cross sections were thenextracted for 6 pion and kaon and charge combinations
with different physics content. The cross sections, differential in the√fractional energies of the two hadrons
z1,2 = 2Eh,1,2 / √s relative to the initial, leading orderparton energies s/2, can be seen in Fig. 1. For thesame hadron types the same sign combinations are generally suppressed in comparison to opposite sign combinations. Additional strangness, especially if likely
being created in the fragmentation process such as forsame sign kaons seems further suppressed. The as-d2σ / dz1 dz2 [fb]R. Seidl,∗1 F. Giordano,∗2 M. Leitgab,∗2 A. Vossen,∗3 H. Li,∗3 W. W. Jacobs,∗3 N. Kobayashi,∗4M. Grosse-Perdekamp,∗2 A. Ogawa,∗5 C. Hulse∗6 and G. Schnell∗6,∗7

106
105

same hemi, T>0.8

opp. hemi, T>0.8

104

103

103

103

102

102

102

any hemisphere

10
10
10
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.2
1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.2
1 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1z1 z2z1 z2
z1 z2

Fig. 2. Stacked di-hadron cross sections as a function of
the diagonal fractional energy (z1 = z2 ) bins for same(grey area) and opposite (blue area) hemispheres andin comparison to no hemisphere and thrust selection(red).

References
1) M. Leitgab et al. [Belle Collaboration], Phys. Rev. Lett.
111, 062002 (2013).