Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

RIKEN Accel. Prog. Rep. 47 (2014)

Dihadron Fragmentation Functions in the NJL-Jet Model†
H. Matevosyan,∗1 W. Bentz,∗2∗3 and A. W. Thomas ∗1[QUARK FRAGMENTATION FUNCTIONS]

†∗1
∗2
∗3

influence on the shape of the DiFFs even at very highvalues of Q2 .
The future development of our model will allow usto extract also the so called interference DiFFs by considering the fragmentation of a transversely polarizedquark, which also play an important role to extractthe transversity distribution functions from measured
SIDIS two-hadron asymmetries.
1.5

0.2 Du  (z, Mh2) dzu - +

Full Final StatePrimary-+

1.00.8

0.5

000.2

0.4

0.6

0.8

Mh2 (GeV 2)

1.0

1.2

1.4Fig. 1. Fragmentation function for u → π + π − calculated
in the NJL-jet model, including only primary (dashedline) and full (solid line) final states.

Model
LO, 4 GeV 2
LO, 100 GeV 2

0.2 Du  (z, Mh2) dz-+

1.0

0.50.8In order to describe the scattering of high energy
electrons on nuclear targets in terms of quark degreesof freedom, the Nambu-Jona-Lasinio (NJL) model isoften used as an effective theory of QCD. For example, this model was successfully applied in Ref.1) to
describe quark distribution and fragmentation functions observed in semi-inclusive deep inelastic scattering (SIDIS) processes. Here we extend the model tothe description of dihadron fragmentation functions(DiFFs), which are expected to play an importantrole for extracting the transversity parton distributionfunctions from SIDIS processes with two final detectedhadrons2) .
The unpolarized DiFFs (Dqh1 h2 (z, Mh2 )) for the process q → h1 h2 depend on the sum of the light-cone
momentum fractions z = z1 + z2 and the invariant
mass squared Mh2 = (P1 +P2 )2 of the produced hadronpair. In order to calculate these functions, we use thequark jet picture, with the elementary fragmentation
functions for q → h calculated in the NJL-jet model3) .
The multihadron emissions from a high energy virtualquark (flavor q = u, d, s) are described by using MonteCarlo techniques, averaging over a sufficiently large
number of events (1010 in the results shown below)
and restricting the total number of primary emitted
hadrons for each fragmentation chain to a predefined
number (equal to eight in the results below). In thisstudy we include the pseudoscalar π, K and vector (ρ,ω, K ∗ and φ) mesons. The strong 2-body and 3-bodydecays of the primary vector mesons to secondary πand K are also included in the simulations, and arevery important to describe the invariant mass spectraof the final π and K pairs.
Fig.1 shows the DiFF for u → π + π − , integrated
over z in the region 0.2 to 0.8, for the cases of primary mesons only (dashed line) and the full final
states including the decay products of the primary vector mesons (solid line). The ρ0 peak around Mh2 ≃2(0.78 GeV) , and the enhancement in the region below 0.4 GeV2 coming from ω → π + π − π 0 with shiftedinvariant mass due to the unobserved π 0 , are clearlyseen in the figure. Fig.2 shows the results obtainedby performing the Q2 evolution in leading order (LO),where we assign a typical NJL-jet scale of 0.2 GeV2
to the model results shown by the solid lines in Figs.
1 and 2. The vector meson decays have an important

00

0.2

0.4

0.6

0.8

1.0

Mh2 (GeV 2)

1.2

1.4

Fig. 2. The solid line is the same as in Fig.1, and the otherlines show the results obtained by the Q2 evolution inleading order (LO) to higher energy scales.
This work was supported by the Australian Research Council(Grants No. FL0992247 and No.CE110001004), the Universityof Adelaide, and the Japanese Ministry of Education, Culture,Sports, Science and Technology (Kakenhi Grant No. 20168769).

References

Condensed from an article by H.H. Matevosyan et al, Phys.
Rev. D 88, 094022 (2013).
University of Adelaide
Department of Physics, Tokai University
RIKEN Nishina Center- 105 -1) H. H. Matevosyan, W. Bentz, I.C. Cloët, A.W.
Thomas, Phys. Rev. D 85, 014021 (2012).
2) R.L. Jaffe, X. Jin, J. Tang, Phys. Rev. Lett. 80, 1166
(1998).
3) T. Ito, W. Bentz, I.C. Cloët, A.W. Thomas, K. Yazaki,Phys. Rev. D 80, 074008 (2009).

1