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


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

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Oleg Teryaev

JINR, Dubna

Strange Quarks Polarisation from Gluon AnomalyIWHSS-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

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 -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


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


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)


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