### Speaker

Dr
Boris Kostenko
(JINR)

### Description

The proton spin puzzle is known since 1988 after measurements of
quarks' helicity contribution to the proton spin [1]. In
spite of all efforts applied, the problem remains an unresolved
enigma of high-energy physics till now (see [2] and
references therein). It has been recently shown that the confinement
of quarks induces a change of their helicities together with a
simultaneous alteration of orbital momenta, so that the total
angular momentum of each quark is conserved [3]. As a
necessary consequence, a superposition of states with opposite
helicities of quarks should appear. Thus, contribution of quarks
helicities to the proton polarization may be much less than it is
expected on the ground of the conventional picture of entirely free
partons. In principle, this mechanism might be considered as a
solution to the proton spin puzzle.
In present communication, such a scenario is verified on basis of
the Dirac equation written in the cylindrical coordinates. Firstly
a resulting system of differential equations was tried to be solved
numerically with MAPLE assisted standard methods such as
Runge-Kutta-Fehlberg algorithm (the rkf45 procedure) and a
finite difference technique with the Richardson extrapolation (the
bvp procedure). Unfortunally, none of them was able to
reproduce the confinement of quarks in the usual linearly increasing
attractive potential. A method of numerical solution of the system
describing the quarks' helicity flipping as well as their
confinement is proposed in this report.
References
[1]EMC, J. Ashman et al., Phys. Lett. B {\bf 206}, 364 (1988)
[2]PHENIX, A. Adare, et al., Phys. Rev. D {\bf 93}, 011501(R)
(2016)
[3]B. Kostenko, Europ. Phys. J., EPJ Web of Conferences {\bf 138},
8009 (2017)

### Primary author

Dr
Boris Kostenko
(JINR)