Transcript Strange Quarks Polarisation from Gluon Anomaly IWHSS

Strange Quarks Polarisation from
Gluon Anomaly
IWHSS-08, Torino, COMPASS
Week, March 31 2008
Oleg Teryaev
JINR, Dubna
Outline





Small gluon polarisation – where is an
axial anomaly (c.f. talk of E. Leader)?
Strange quarks as heavy quarks in
vacuum and inside the nucleon
Strange sea polarisation and higher
twist : scale and SIGN
Heavy strange quarks transversity
Conclusions: Hidden connections in
nucleon spin puzzle !?
Gluon anomaly and its
manifestations




Small gluon polarisation – does it mean
that anomaly contribution disappeared
Not necessary! – also in quarks
EXACT relation (holds for each flavour
separately)
Light quarks – non-, heavy conservation
Heavy quarks polarisation


Non-complete cancellation of mass and anomaly terms
(97)
Gluons correlation with nucleon spin – twist 4 operator NOT
directly related to twist 2 gluons helicity BUT related by QCD
EOM to singlet twist 4 correction f2 to g1
Numerics



Small (intrinsic) charm polarisation
Consider STRANGE as heavy! – 100
times larger – reasonable compatibility
to the data
Current data on f2 – appr 50% larger
Can s REALLY be heavy?!


Strange quark mass close to matching scale
of heavy and light quarks – relation between
quark and gluon vacuum condensates (similar
cancellation of classical and quantum
symmetry violation – now for trace anomal).
BUT - common belief that strange quark
cannot be considered heavy,
In nucleon rather than in vacuum - may be
considered heavy in comparison to small
genuine higher twist – multiscale nucleon
picture
Sign of polarisation



Anomaly – constant and OPPOSITE to
mass term
Partial cancellation – OPPOSITE to mass
term
Naturally requires all “heavy” quarks
average polarisation to be negative IF
heavy quark in (perturbative) heavy
hadron is polarised positively
Heavy Strangeness
transversity


Heavy strange quarks – neglect genuine
higher twist: 0 =
Strange transversity - of the same sign
as helicity and enhanced by M/m!
Conclusions




Anomaly is more alive...
Strange quarks INSIDE nucleons may
be treated as heavy ones
Extra relations between seemingly
independent quantities of different twist
(both accessible by COMPASS).May be
non-unique: c.f. d2 relation to Sivers
function
Hidden connections in N spin structure
Sum rules -II


To simplify – low moments
Especially simple – if only gluonic pole
kept:
Compatibility of SSA and DIS





Extractions of Sivers function: – “mirror” u and d
First moment of EGMMS = 0.0072 (0.0042 –
0.014)
Twist -3g - similar for neutron and proton (0.005)
2
and of the
same sign – nothing like mirror
picture seen –but supported by colour ordering!
Current status: Scale of Sivers function – seems
to be reasonable, but flavor dependence differs
qualitatively.
Inclusion of pp data, global analysis including
gluonic (=Sivers) and fermionic poles
Relation of Sivers function to
GPDs



Qualitatively similar to Anomalous Magnetic
Moment (Brodsky et al)
Quantification : weighted TM moment of
Sivers PROPORTIONAL to GPD E
x f T ( x ) : xE ( x )
(hep-ph/0612205 ):
Burkardt SR for Sivers functions is now
related to Ji SR for E and, in turn, to
Equivalence Principle
  dxx f
q ,G
T
( x)  
q ,G
 dxxE ( x )  0
Sivers function and Extended
Equivalence principle




Second moment of E – zero SEPARATELY for quarks
and gluons –only in QCD beyond PT (OT, 2001) supported by lattice simulations etc.. ->
Gluon Sivers function is small! (COMPASS, STAR,
Brodsky&Gardner)
BUT: gluon orbital momentum is NOT small: total –
about 1/2, if small spin – large (longitudinal) orbital
momentum
Gluon Sivers function should result from twist 3
correlator of 3 gluons: remains to be proved!
Generalization of Equivalence
principle

Various arguments: AGM 0 separately
 for quarks
and gluons – most clear from the lattice
(LHPC/SESAM, confirmed recently)