Ⅱ-4. Hadron Physics

RIKEN Accel. Prog. Rep. 50 (2017)

Fragmentation function measurements in Belle∗1∗2∗3∗4∗5RIKEN Nishina Center
Physics department, University of Illinois
Physics department, Indiana University
Department of Theoretical Physics, University of the BasqueCountryIkerbasque- 117 -25
0.20 < zhh < 0.25

0.25 < zhh < 0.30

0.30 < zhh < 0.35

0.35 < zhh < 0.40

0.40 < zhh < 0.45

0.45 < zhh < 0.50

0.50 < zhh < 0.55

0.55 < zhh < 0.60

0.60 < zhh < 0.65

0.65 < zhh < 0.700.70 < zhh < 0.75

0.75 < zhh < 0.80

2015
10d2σ / dzdm [μ b]501210864d2σ / dzdm [μ b]

203
2.52
1.5
10.5
00.45
0.80 < zhh < 0.85
0.85 < zhh < 0.90
0.90 < zhh < 0.95
0.95 < zhh < 1.00
π+π- rec
0.4
0.35
0.3
π+π+ rec
0.25
0.2
0.15
0.1
0.05
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 2.2m π [GeV]m π [GeV]m π [GeV]m π [GeV]
ππππd2σ / dzdm [μ b]The fragmentation from asymptotically free partons
into conﬁned hadrons is described by fragmentation
functions (FF). Since FFs are nonperturbative objects
they cannot be calculated from ﬁrst principles in QCD
and need to be measured experimentally. Especiallythe electron-positron annihilation process such as studied at the Belle experiment on the KEKB accelerator iswell suited for such measurements since no hadrons exist in the initial state. Once fragmentation functions
are extracted universality and factorization allow its
application to other processes such as semi-inclusive
deep-inelastic scattering or hadron collisions in orderto gain ﬂavor as well as spin information in parton
distribution functions. The transversity distributionfunction, for example, can be accessed using spin dependent di-hadron FFs, also called interference FFs.
Belle has obtained those previously1) but the unpolarized baseline is still missing. In this analysis we
extract di-hadron cross sections for various pion, kaonand charge combinations
diﬀerential in their fractional√energy z = 2Ehh / s relative to the initial parton energy and the invariant mass of the pair. Unlike theprevious publication2) , this analysis concentrates on
two hadrons from the same hemisphere in order to increase the likelihood of both emerging from the same
initial parton. The various corrections reported previously have been adapted to this analysis and results
are already in the Belle-internal refereeing process andare expected to be published soon.
Figure 1 displays the expected sensitivities for dipions as a function of invariant mass and in bins offractional energy. In the opposite-sign pion pairs one
clearly can identify various resonances such as the KS0and ρ mesons as well as the Cabbibo-suppressed decayof the D0 meson. The same-sign pion pair cross sections display a more continuous mass distribution. Allother pion, kaon and charge combinations are similarly
prepared.
Other ongoing measurements include the surprising
discovery of a nonzero Λ baryon polarization originating from an unpolarized parton when correlating itwith the transverse momentum the Λ carries with respect to the thrust axis3) . Preliminary results havebeen shown and the results are currently being ﬁnalized.
Also other explicitly transverse momentum depen-d2σ / dzdm [μ b]R. Seidl,∗1 F. Giordano,∗2 A. Vossen,∗3 H. Li,∗3 W. W. Jacobs,∗3 M. Grosse-Perdekamp,∗2 C. Van Hulse∗4 andG. Schnell∗4,∗5Fig. 1. Expected di-pion cross sections as a function of mππ
in bins of z as expected by fully tracked and reconstructed Belle MC. Same sign pion pairs are displayedby blue squares while opposite-sign pion pairs are displayed by black circles.The green vertical lines represent
the kinematic mass boundaries for each z bin.

dent fragmentation functions are currently being extracted. Two teams extract diﬀerent types of such.
One analysis concentrates on measuring the transverse momentum between two nearly back-to-backhadrons relative to one hadron’s momentum direction while the other analysis studies single hadrons’transverse momenta relative to the thrust axis. Whilethe ﬁrst method is experimentally straightforward,
convolutions of the intrinsic transverse momenta ofboth hadrons complicate the extraction of the intrinsic
transverse momentum dependence. The single hadron
method extracts directly the transverse momentum
but the thrust axis is only approximating the initial
parton’s axis. Both types of analysis are progressing
and are expected to be ready for publication soon.
References
1) A. Vossen et al. [Belle Collaboration], Phys. Rev. Lett.
107, 072004 (2011).
2) R. Seidl et al. [Belle Collaboration], Phys. Rev. D92,092007 (2015).
3) A. Abdesselam et al. [Belle Collaboration], e-Print:
arXiv:1611.06648.