References - Bogoliubov Laboratory of Theoretical Physics - JINR

AXIAL ANOMALIES, NUCLEON SPIN STRUCTURE AND HEAVY
IONS COLLISIONS.
O.V. Teryaev
BLTP,JINR,141980,Dubna. Russia
Abstract
The axial (related to axial anomaly) and vector currents of heavy quarks are
considered. The special attention is payed to the strangeness polarization mediated
by gluon anomaly and treatment of the strange quarks in a heavy ones in a multiscale
nucleon. It is shown that the straightforward modification of Heisenberg-Euler
effective lagrangian allows to calculate the vector current of strange quarks and
describes an analog of Chiral Magnetic Effect for strange and heavy quarks.
1. Introduction. The spin structure of nucleon is a major problem since EMC Spin
crisis (puzzle) emerged in 80’s.
The first observation [1] was related to the role of gluon anomaly which was interpreted
as a (circular) gluon polarization. The extensive experimental investigations at HERMES,
COMPASS and RHIC, however, did not find the significant polarization. Sometimes this
is described as an ”absence” of anomaly which is quite strange because of the fundamental
character of this phenomenon. Because of this, I am going to discuss the manifestation
of anomaly through strange quarks polarization mediated by very small polarizations of
off-shell gluons.
2. Axial current of strange quarks, gluonic anomaly and strangeness polarization.
The divergence of the singlet axial current contains a normal and an anomalous
piece,
∂ μ j (0)
5μ
�
=2i mq ¯qγ5q −
q
� �
Nfαs
G
4π
a μν � G μν,a , (1)
where Nf is the number of flavours. The two terms at the r.h.s. of the last equation are
known to cancel in the limit of infinite quark mass. This is the so-called cancellation of
physical and regulator fermions, related to the fact, that the anomaly may be regarded as
a usual mass term in the infinite mass limit, up to a sign, resulting from the subtraction
in the definition of the regularized operators.
Consequently, one should expect, that the contribution of infinitely heavy quarks to the
first moment of g1 is zero. This is exactly what happens [2] in a perturbative calculation
of the triangle anomaly graph. One may wonder, what is the size of this correction for
large, but finite masses and how does it compare with the purely perturbative result.
To answer this question, one should calculate the r.h.s. of (1) for heavy fermions. The
leading coefficient is of the order m −2 ,
∂ μ j c 5μ = αs
48πm2∂ c
μ Rμ
147
(2)