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Structure functions and intrinsic quark orbital motion

Structure functions and intrinsic quark orbital motion. P etr Z ávada Inst. of Physics, Prague. Introduction.

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Structure functions and intrinsic quark orbital motion

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  1. Structure functions and intrinsic quark orbital motion Petr Závada Inst. of Physics, Prague

  2. Introduction • Presented results are based on the covariant QPM, in which quarks are considered as quasifree fermions on mass shell. Intrinsic quark motion, reflecting orbital momenta, is consistently taken into account. [P.Z. Phys.Rev.D65, 054040(2002) and D67, 014019(2003)]. • Recently, this model was generalized to include the transversity distribution [A.Efremov, O.Teryaev and P.Z., Phys.Rev.D70, 054018(2004) and arXiv: hep-ph/0512034]. In this talk: • Relation between structure functions and 3D quark momenta distribution • Important role of quark orbital motion as a direct consequence of the covariant description [full version in arXiv: hep-ph/0609027].

  3. Model

  4. Structure functions • Input: • 3D distribution • functions • Result: • structure • functions • (x=Bjorken xB !)

  5. F1, F2 - manifestly covariant form:

  6. g1, g2 - manifestly covariant form:

  7. Comments • In the limit of static quarks, for p→0, which is equivalent to the assumption p=xP, one gets usual relations between the structure and distribution functions like • Obtained structure functions for m→0 obey the known sum rules: Sum rules were obtained from: 1) Relativistic covariance 2) Spheric symmetry 3) One photon exchange • In this talk m→0is assumed.

  8. Comments Structure functions are represented by integrals from probabilistic distributions: • This form allows integral transforms: • g1↔g2orF1↔ F2 (rules mentioned above were example). • With some additional assumptions also e.g. integral relation g1↔ F2 can be obtained (illustration will be given). • To invert the integrals and obtain G or DG from F2or g1 (main aim of this talk).

  9. g1, g2 from valence quarks

  10. g1, g2 from valence quarks E155 Calculation - solid line, data - dashed line (left) and circles (right) • g1 fit of world data by E155 Coll., Phys.Lett B 493, 19 (2000).

  11. Transversity • In a similar way also the transversity was calculated; see [A.Efremov, O.Teryaev and P.Z., Phys.Rev.D70, 054018(2004)]. Among others we obtained - which followsonly from covariant kinematics! • Obtained transversities were used for the calculation of double spin asymmetry in the lepton pair production in proposed PAX experiment; see [A.Efremov, O.Teryaev and P.Z., arXiv: hep-ph/0512034)].

  12. Double spin asymmetry in PAX experiment 1. 2.

  13. Quark momenta distributions from structure functions 1) Deconvolution of F2 • Remarks: • G measures in d3p, 4pp2MGin the dp/M • pmax=M/2 – due to kinematics in the proton rest frame, ∑p=0 • F2 fit of world data by SMC Coll., Phys.Rev. D 58, 112001 (1998).

  14. Quark momenta distributions … 2) Deconvolution of g1 Remark: DG=G+-G- represents subset of quarks giving net spin contribution - opposite polarizations are canceled out. Which F2 correspond to this subset?

  15. Quark momenta distributions … Calculation: In this way, from F2 and g1 we obtain:

  16. Quark momenta distributions … • Comments: • Shape of ΔF2 similar to F2val • Generic polarized and unpolarized distributions DG, G and G+ are close together for higher momenta • Mean value: • Numerical calculation: • g1 fit of world data by E155 Coll., Phys.Lett B 493, 19 (2000).

  17. Intrinsic motion and angular momentum • Forget structure functions for a moment… • Angular momentum consists of j=l+s. • In relativistic case l,s are not conserved separately, only j is conserved. So, we can have pure states of j (j2,jz) only, which are represented by the bispinor spherical waves:

  18. j=1/2

  19. <s>, Γ1: two ways, one result -covariant approach is a common basis Spin and orbital motion

  20. Comments • for fixed j=1/2 both the quantities are almost equivalent: • more kinetic energy (in proton rest frame) generates more orbital motion and vice versa. • are controlled by the factor , two extremes: • massive and static quarks and • massless quarks and • important role of the intrinsic quark orbital motion emerges as a direct consequence of the covariant approach

  21. Summary Covariant version of QPM involving quark orbital motion was studied. New results: • Model allows to calculate 3D quark momenta distributions (in proton rest frame) from the structure functions. • Important role of quark orbital motion, which follows from covariant approach, was pointed out. Orbital momentum can represent as much as 2/3 j. The spin function g1 is reduced correspondingly.

  22. Sum rules Basis:

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