52 research outputs found

### Role of diquark correlations and the pion cloud in nucleon elastic form factors

Electromagnetic form factors of the nucleon in the space-like region are
investigated within the framework of a covariant and confining
Nambu-Jona-Lasinio model. The bound state amplitude of the nucleon is obtained
as the solution of a relativistic Faddeev equation, where diquark correlations
appear naturally as a consequence of the strong coupling in the colour
$\bar{3}$ $qq$ channel. Pion degrees of freedom are included as a perturbation
to the "quark-core" contribution obtained using the Poincar\'e covariant
Faddeev amplitude. While no model parameters are fit to form factor data,
excellent agreement is obtained with the empirical nucleon form factors
(including the magnetic moments and radii) where pion loop corrections play a
critical role for $Q^2 \lesssim 1\,$GeV$^2$. Using charge symmetry, the nucleon
form factors can be expressed as proton quark sector form factors. The latter
are studied in detail, leading, for example, to the conclusion that the
$d$-quark sector of the Dirac form factor is much softer than the $u$-quark
sector, a consequence of the dominance of scalar diquark correlations in the
proton wave function. On the other hand, for the proton quark sector Pauli form
factors we find that the effect of the pion cloud and axialvector diquark
correlations overcomes the effect of scalar diquark dominance, leading to a
larger $d$-quark anomalous magnetic moment and a form factor in the $u$-quark
sector that is slightly softer than in the $d$-quark sector.Comment: 30 pages and 40 figure

### Monte-Carlo Approach to Calculating the Fragmentation Functions in NJL-Jet Model

Recent studies of the fragmentation functions using the Nambu--Jona-Lasinio
(NJL) - Jet model have been successful in describing the quark fragmentation
functions to pions and kaons. The NJL-Jet model employs the integral equation
approach to solve for the fragmentation functions in quark-cascade description
of the hadron emission process, where one assumes that the initial quark has
infinite momentum and emits an infinite number of hadrons. Here we introduce a
Monte Carlo (MC) simulation method to solve for the fragmentation functions,,
that allows us to relax the above mentioned approximations. We demonstrate that
the results of MC simulations closely reproduce the solutions of the integral
equations in the limit where a large number of hadrons are emitted in the quark
cascade. The MC approach provides a strong foundation for the further
development of the NJL-Jet model that might include many more hadronic emission
channels with decays of the possible produced resonances, as well as inclusion
of the transverse momentum dependence (TMD), all of which are of considerable
importance to the experimental studies of the transverse structure of hadrons.Comment: 5 pages, 3 figures, Proceedings of "TROPICAL QCD II Workshop

### Collins Fragmentation Function within NJL-jet Model

The NJL-jet model is extended to accommodate hadronization of a transversely
polarized quark in order to explore the Collins effect within a multihadron
emission framework. This is accomplished by calculating the polarized quark
spin flip probabilities after a pseudoscalar hadron emission and the elementary
Collins functions. The model is used to calculate the number densities of the
hadrons produced in the polarized quark's decay chain. The full Collins
fragmentation function is extracted from the sine modulation of the polarized
number densities with respect to the polar angle between the initial quark's
spin and hadron's transverse momentum. Two cases are studied here. First, a toy
model for elementary Collins function is used to study the features of the
transversely polarized quark-jet model. Second, a full model calculation of
transverse momentum dependent pion and kaon Collins functions is presented. The
remarkable feature of our model is that the 1/2 moments of the favored Collins
fragmentation functions are positive and peak at large values of z but decrease
and oscillate at small values of z. The 1/2 moments of the unfavored Collins
functions have comparable magnitude and opposite sign to the favored functions,
vanish at large z and peak at small values of z. This feature is observed for
both the toy and full models and can be attributed to the quark-jet picture of
hadronization. Moreover, the transverse momentum dependencies of the model
Collins functions differ significantly from the Gaussian form widely used in
the empirical parametrizations. Finally, a naive interpretation of the
Schafer-Teryaev sum rule is proven not to hold in our model, where the
transverse momentum conservation is explicitly enforced. This is attributed to
the sizable average transverse momentum of the remnant quark that needs to be
accounted for to satisfy the transverse momentum sum-rule.Comment: 15 pages, 22 figures. v2 - minor changes/additions to conform to the
journal published versio

### Kaon fragmentation function from NJL-jet model

The NJL-jet model provides a sound framework for calculating the
fragmentation func- tions in an effective chiral quark theory, where the
momentum and isospin sum rules are satisfied without the introduction of ad hoc
parameters [1]. Earlier studies of the pion fragmentation func- tions using the
Nambu-Jona-Lasinio (NJL) model within this framework showed good qualitative
agreement with the empirical parameterizations. Here we extend the NJL-jet
model by including the strange quark. The corrections to the pion fragmentation
function and corresponding kaon fragmen- tation functions are calculated using
the elementary quark to quark-meson fragmentation functions from NJL. The
results for the kaon fragmentation function exhibit a qualitative agreement
with the empirical parameterizations, while the unfavored strange quark
fragmentation to pions is shown to be of the same order of magnitude as the
unfavored light quark's. The results of these studies are expected to provide
important guidance for the analysis of a large variety of semi-inclusive data.Comment: 6 pages, 9 figures, Proceedings of "Achievements and New Directions
in Subatomic Physics: Workshop in Honour of Tony Thomas's 60th Birthday

### Dihadron Fragmentation Functions within the NJL-jet Model

Dihadron Fragmentation Functions (DFF) provide a vast amount of information
on the intricate details of the parton hadronization process. Moreover, they
provide a unique access to the "clean" extraction of nucleon transversity
parton distribution functions in semi inclusive deep inelastic two hadron
production process with a transversely polarised target. The NJL-jet model has
been extended for calculations of light and strange quark unpolarised DFFs to
pions, kaons and several vector mesons. This is accomplished by using the
probabilistic interpretation of the DFFs, and employing the NJL-jet
hadronization model in the Monte Carlo simulations that includes the transverse
momentum of the produced hadrons. The strong decays of the vector mesons and
the subsequent modification of the pseudoscalar meson DFFs are also considered.
The resulting pseudoscalar meson DFFs are strongly influenced by the decays of
the relevant vector mesons. This is because of the large combinatorial factors
involved in counting the number of the hadron pairs that include the decay
products. The evolution of the DFFs from the model scale to a typical
experimental scale has also been performed.Comment: 11 pages, 11 figure

### Transverse Momentum Dependent Fragmentation and Quark Distribution Functions from the NJL-jet Model

Using the model of Nambu and Jona-Lasinio to provide a microscopic
description of both the structure of the nucleon and of the quark to hadron
elementary fragmentation functions, we investigate the transverse momentum
dependence of the unpolarized quark distributions in the nucleon and of the
quark to pion and kaon fragmentation functions. The transverse momentum
dependence of the fragmentation functions is determined within a Monte Carlo
framework, with the notable result that the average $P_\perp^2$ of the produced
kaons is significantly larger than that of the pions. We also find that
has a sizable $z$ dependence, in contrast with the naive Gaussian
ansatz for the fragmentation functions. Diquark correlations in the nucleon
give rise to a non-trivial flavor dependence in the unpolarized transverse
momentum dependent quark distribution functions. The of the quarks in
the nucleon are also found to have a sizable $x$ dependence. Finally, these
results are used as input to a Monte Carlo event generator for semi-inclusive
deep inelastic scattering (SIDIS), which is used to determine the average
transverse momentum squared of the produced hadrons measured in SIDIS, namely
$$. Again we find that the average $P_T^2$ of the produced kaons in
SIDIS is significantly larger than that of the pions and in each case \la
P_T^2 \ra has a sizable $z$ dependence.Comment: 13 pages, 17 figures, v2: minor revisions to conform with the
published version in Phys.Rev.

### Effects of charge symmetry breaking on form factors of the pion and kaon

Effects of charge symmetry breaking associated with the $u$ and $d$ quark
mass difference in the elastic form factors of the pion and kaon are presented.
We use a confining version of the Nambu--Jona-Lasinio model. The pion and kaon
are described as a dressed quark and antiquark bound states governed by the
Bethe-Salpeter equation, and exhibit the properties of Goldstone bosons, with
the pion mass difference given by $m_{\pi^{+}}^2 - m_{\pi^{0}}^2 \propto (m_u
-m_d)^2$ as demanded by dynamical chiral symmetry breaking. We found
significant charge symmetry breaking effects for realistic current quark mass
ratios ($m_u/m_d \sim 0.5$) in the quark electromagnetic form factors of the
pion and kaon. We also report the effects of charge symmetry breaking on the
parton distribution functions, which are rather smaller than those found in the
electromagnetic form factors.Comment: 4 pages, 5 figures, accepted version for the QNP2018 proceedings, 8th
International Conference on Quarks and Nuclear Physics (QNP2018), November
13-17, 2018, Tsukuba, Ibaraki, Japa

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