Spin of the proton and orbital motion of quarks Petr Závada Inst. of Physics, Prague Workshop on Nucleon Form Factors Frascati, 12-14 October, 2005

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. [for details see 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)]. In this talk the obtained spin functions will be discussed: Sum rules for g1,g2. Calculation of the spin functions, comparison with experimental data, discussion on Γ1.

Model Input:

Spin structure functions Output:

Sum rules Basis:

…Sum rules

…Sum rules The rules were obtained from: Relativistic covariance Spheric symmetry One photon exchange

Valence quarks

Calculation - solid line, data - dashed line Valence quarks E155 Calculation - solid line, data - dashed line (left) and circles (right)

g1 - analysis Integrating g1 gives: massless quarks static quarks …so, it seems: more motion=less spin? How to understand it?

Angular momentum Forget structure functions for a moment… Remember, that 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 relativistic spherical waves:

j=1/2

Spin and orbital motion

Spin and orbital motion j=1/2 j=1/2 j=l+s 1≥‹s›/j≥1/3 QM: 1) For p0>m there must be some orbital momentum! 2) For localized particles, there must be p0>m! o r b i t a l m o m e n t u m spin spin m<p0 m=p0

Recent experimental data: Contribution of sea quarks is compatible with zero: HERMES Phys.Rev.Lett. 92, 012005 (2004); Phys.Rev. D71, 012003 (2005). Contribution of gluons is compatible with zero, but with rather big errors: HERMES, SMC, COMPASS Phys.Rev.Lett. 84, 2584 (2000); Phys.Rev. D70, 012002 (2004); hep-ex/0501056

Support for dominant role of the orbital momentum: Models, e.g.: Casu, Sehgal, Phys.Rev.D58, 2644 (1996). Wakamatsu, Watabe, Phys.Rev.D62, 054009 (2000). Jefferson Lab Hall A Collaboration Experimental analysis suggests significant presence of the orbital momentum: Phys.Rev.Lett.92, 012004 (2004); Phys.Rev.C70, 065207 (2004).

PAX experiment: Polarized Drell-Yan process in this reaction is very effective for measuring the transversity, which can be extracted from the double spin asymmetry in μ+μ- pair. This was discussed in the previous papers Efremov, Goeke, Schweitzer, Eur.Phys.J. C35 (2004), 207 Anselmino, Barone, Drago, Nikolaev, Phys. Lett. B 594 (2004) 97 We do the same, but as an input we use the transversity, which is calculated in the model.

Asymmetry corresponding to Useful relations: Asymmetry corresponding to Double spin asymmetry defined as: can be calculated from the transversity distributions: where

Results Our calculation based on the “1st way” - level of quark interference only (solid line) Calculation based on the “2nd way”- interference effects at parton-hadron transition included (dashed line) Calculation based on the quark-soliton model [Efremov…] (dotted line) s=45GeV2, Q2=4-5GeV2

…Results Our calculation based on the “1st way” - level of quark interference only (solid line) Calculation based on “2nd way”- interference effects at parton-hadron transition included (dashed line) Calculation based on the estimation by Anselmino… (dotted line) s=45GeV2, Q2=4GeV2

Statistical errors How many events one needs for discriminating among the curves? If then which means roughly So for one needs at least 104 events in given subsample (bin, interval).

Summary Covariant version of QPM involving intrinsic (orbital) motion was studied. Model reproduces the well known sum rules for g1,g2 : WW, ELT, BC. Spin function g1 depend on intrinsic orbital motion rather significantly, this motion generates orbital angular momentum, which can represent as much as 2/3 j. Calculated g1,g2 from qval are well compatible with the experimental data.