Ⅱ-4. Hadron Physics

RIKEN Accel. Prog. Rep. 51 (2018)

Fragmentation function measurements in Belle†
R. Seidl,∗1 F. Giordano,∗2 A. Vossen,∗3 H. Li,∗3 W. W. Jacobs,∗3 M. Grosse-Perdekamp,∗2 C. Van Hulse,∗4
and G. Schnell∗4,∗5

0.20 < z < 0.25

0.25 < z < 0.30

0.30 < z < 0.35

0.35 < z < 0.40

0.40 < z < 0.45

0.45 < z < 0.50

0.50 < z < 0.55

0.55 < z < 0.60

0.60 < z < 0.65

0.65 < z < 0.70

0.70 < z < 0.75

0.75 < z < 0.80mπ π [GeV]mπ π [GeV]mπ π [GeV]mπ π [GeV]

0.80 < z < 0.85

0.85 < z < 0.90

110− 1d2σ / dzdm [µ b/GeV]

10− 210d2σ / dz dm [µ b /GeV]

50d2σ / dz dm [µ b /GeV]

30d2σ / dz dm [µ b /GeV]

10

Various resonances are visible in the extracted crosssections for opposite-sign pion pairs. Using MC their
origin can be resolved as shown in Fig. 2. One can identify various resonances such as the KS0 and ρ mesons aswell as the Cabbibo-suppressed decay of the D0 meson.
In the data also the f0 (980) is clearly visible while itis not well modeled in the MC. Additionally, di-pionsfrom a common origin, such as from η or ω decays
or pions from diﬀerent levels of the same decay chain
can also show up as enhancements. Direct fragmentation with no common ancestors provide the generally smooth and dominant contribution to the massspectra. Similar ﬁgures for other hadron combinations
and details on the correction chain leading from raw
yields to cross sections can be found in the actual publication. For unlike-sign pion-kaon combinations theK ∗ and the D0 decays stand out while for the unlikesing kaon pairs the ϕ0 contributes prominently. For all
like-sign combinations no resonances exist while someenhancements from common decays are visible.

d2σ / dz dm [µ b /GeV]

d2σ / dzdm [µ b/GeV]

Fragmentation functions (FFs) tell us about thetransition of asympotically free, nearly massless partons into conﬁned, massive ﬁnal-state hadrons. They
therefore provide important information on some of
the main open questions in nuclear physics, conﬁnement and chiral symmetry breaking. Furthermore,FFs can be used as a tool to extract parton distribution functions in semi-inclusive DIS and hadronhadron collisions. Belle has previously measured polarization dependent interference fragmentation functions,1) needed to access the quark transversity distribution in a collinear factorization framework. The
related unpolarized baseline FF was not available.
Recently, inclusive di-hadron cross sections were extracted as a function√ of invariant mass and fractionalenergy z = 2Ehh / s for any hadron and charge combination.2) The di-hadrons had to emerge in the same
hemisphere as calculated via the event-shape variablethrust in order to be sensitive to the fragmentation of
predominantly one parton into two hadrons, unlike theprevious di-hadron publication3) which focused moreon single hadron fragmentation. The cross sections forunlike-sign pion pairs can be seen in Fig. 1 where they
are compared to various pythia fragmentation tunes.
The overall fractional energy behavior is generally well
reproduced in the pythia default tune, while the mass
structure above 1 GeV is better described by tunes
with larger fragmentation into higher spin states.

14030
20100.20 < z < 0.25
Direct decays*±

Other±D0ω

KsηΦρ

000*K

0.25 < z < 0.30
common ancestry

Kρ00.30 < z < 0.35

0.35 < z < 0.40

uncorrelated*00

others

K

Other

Ds±

D*0

Fragmentation

D0D±

Data

00.40 < z < 0.45

0.45 < z < 0.50

0.50 < z < 0.55

0.55 < z < 0.60

2520151050980.60 < z < 0.65
0.65 < z < 0.70
0.70 < z < 0.75
0.75 < z < 0.80765mπ π [GeV]mπ π [GeV]mπ π [GeV]mπ π [GeV]
432101.60.80 < z < 0.850.85 < z < 0.900.90 < z < 0.950.95 < z < 1.00
1.4π+π1.210.8mπ π [GeV]mπ π [GeV]mπ π [GeV]mπ π [GeV]
0.6
0.4
0.2
0 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2mπ π [GeV]mπ π [GeV]mπ π [GeV]mπ π [GeV]

10−1Fig. 2. Comparison of unlike-sign di-pion cross sections(data points) as a function of mππ in bins of z withthe relative contribution from various parents in MC.
mπ π [GeV]d2σ / dzdm [µ b/GeV]

10−210110− 1d2σ / dzdm [µ b/GeV]

10− 21010−1

π+π- Data

0.90 < z < 0.95

π+π- PYTHIA default

1mπ π [GeV]mπ π [GeV]

π+π- Belleπ+π- ALEPH
π+π- LEP/Tevatron
π+π- old Bellemπ π [GeV]

10−20.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2mπ π [GeV]mπ π [GeV]mπ π [GeV]mπ π [GeV]

Fig. 1. Unlike-sign di-pion cross sections as a function ofmππ in bins of z (black circles), compared to various
fragmentation tunes in pythia.
mπ π [GeV]

†∗1
∗2
∗3
∗4
∗5

mπ π [GeV]mπ π [GeV]mπ π [GeV]mπ π [GeV]Other fragmentation function measurements are
currently ongoing such as explicit transverse momentum dependent fragmentation functions, Λ polarizingfragmentation4) and various spin dependent fragmentation functions.

0.95 < z < 1.00

π+π- HERMESmπ π [GeV]mπ π [GeV]mπ π [GeV]

Condensed from the article in Phys. Rev. D 96, 032005(2017)RIKEN Nishina Center
Physics department, University of Illinois
Physics department, Indiana University
Department of Theoretical Physics, University of the BasqueCountry UPV/EHU
Ikerbasque- 116 -References
1) A. Vossen et al., [Belle Collaboration], Phys. Rev. Lett.
107, 072004 (2011).
2) R. Seidl et al., [Belle Collaboration], Phys. Rev. D 96,032005 (2017).
3) R. Seidl et al., [Belle Collaboration], Phys. Rev. D 92,092007 (2015).
4) A. Abdesselam et al., [Belle Collaboration], e-Print:
arXiv:1611.06648