Strange Quarks Polarisation from Gluon Anomaly IWHSS-08, Torino, COMPASS Week, March 31 2008

1. Oleg Teryaev JINR, Dubna Strange Quarks Polarisation from Gluon AnomalyIWHSS-08, Torino, COMPASS Week, March 31 2008

2. 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 !?

3. 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

4. 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

5. Numerics Small (intrinsic) charm polarisation Consider STRANGE as heavy! – 100 times larger – reasonable compatibility to the data Current data on f2 – appr 50% larger

6. 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

7. 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

8. Heavy Strangeness transversity Heavy strange quarks – neglect genuine higher twist: 0 = Strange transversity - of the same sign as helicity and enhanced by M/m!

9. 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

10. Sum rules -II To simplify – low moments Especially simple – if only gluonic pole kept:

11. Compatibility of SSA and DIS • Extractions of Sivers function: – “mirror” u and d • First moment of EGMMS = 0.0072 (0.0042 – 0.014) • Twist -3 - similar for neutron and proton (0.005) 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

12. 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 (hep-ph/0612205 ): Burkardt SR for Sivers functions is now related to Ji SR for E and, in turn, to Equivalence Principle

13. 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!

14. Generalization of Equivalence principle Various arguments: AGM 0 separately for quarks and gluons – most clear from the lattice (LHPC/SESAM, confirmed recently)