Oleg Teryaev JINR, Dubna. Strange Quarks Polarisation from Gluon Anomaly IWHSS-08, Torino, COMPASS Week, March 31 2008. 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
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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
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
Small (intrinsic) charm polarisation
Consider STRANGE as heavy! – 100 times larger – reasonable compatibility to the data
Current data on f2 – appr 50% larger
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
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 strange quarks – neglect genuine higher twist: 0 =
Strange transversity - of the same sign as helicity and enhanced by M/m!
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
To simplify – low moments
Especially simple – if only gluonic pole kept:
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
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!
Various arguments: AGM 0 separately for quarks and gluons – most clear from the lattice (LHPC/SESAM, confirmed recently)