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Parton distribution functions and quark orbital motion Petr Závada Institute of Physics, Prague The 6 th Circum-Pan-Pacific Symposium on High Energy Spin Physics July 30 - August 2, 2007 Vancouver BC The 6 th Circum-Pan-Pacific Symposium on High Energy Spin Physics July 30 - August 2, 2007 Vancouver BC

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Introduction Presented results are based on the covariant QPM. Intrinsic motion, reflecting orbital momenta of quarks, is consistently taken into account. Due to covariance, transversal and longitudinal momenta appear on the same level. [P.Z. Phys.Rev.D65, 054040(2002) and D67, 014019(2003)]. In present LO version, no dynamics, but exact kinematics effective tool for separating effects due to dynamics (QCD) and kinematics. This viewpoint well supported by our previous results e.g: sum rules WW, Efremov-Leader-Teryaev, Burkhard-Cottingham the same set of assumptions implies substantial dependence Γ 1 on kinematical effects Calculation g 1 and g 2 from valence distributions – very good agreement with data some new relations between structure functions, including transversity [A.Efremov, O.Teryaev and P.Z., Phys.Rev.D70, 054018(2004) and arXiv: hep-ph/0512034].

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Previous papers: What is the dependence of the structure functions on intrinsic motion of the quarks? In this talk further questions: How can one extract information about intrinsic motion from the structure functions? What is the role of the orbital momentum of quarks, which is a particular case of intrinsic motion? [full version in arXiv: hep-ph/0706.2988 and Eur.Phys.J. C – August2007].

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Model

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Structure functions Input: Input: 3D distribution functions in the proton rest frame Result: Result: structure functions (x=Bjorken x B !)

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F 1, F 2 - manifestly covariant form:

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g 1, g 2 - manifestly covariant form:

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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 is assumed. In this talk m 0 is assumed.

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Comments Structure functions are represented by integrals from probabilistic distributions: This form allows integral transforms: 1) g 1 g 2 or F 1 F 2 (rules mentioned above were example). 2)With some additional assumptions also e.g. integral relation g 1 F 2 can be obtained (illustration will be given). 3)To invert the integrals and obtain G or G from F 2 or g 1 (aim of this talk).

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g 1, g 2 from valence quarks

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Calculation - solid line, data - dashed line (left) and circles (right) E155 g 1 fit of world data by E155 Coll., Phys.Lett B 493, 19 (2000).

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Transversity In a similar way also the transversity was calculated; see. Among others we obtained 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 follows from covariant kinematics! - which follows from covariant kinematics! Obtained transversities were used for the calculation of double spin asymmetry in the lepton pair production in proposed PAX experiment; see. 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)].

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2007: Extraction from the data (for the first time) 2004: Our calculation

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Double spin asymmetry in PAX experiment 1.2.

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Momentum distributions from structure function F 2 Deconvolution of F 2 : Remarks: G measures in d 3 p, P in the dp/M p max =M/2 – due to kinematics in the proton rest frame, p=0 Self-consistency test:

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Momentum distributions in the proton rest frame =0.11 (0.083) GeV/c for u (d) quarks Input q(x) MRST LO 4GeV 2 q val =q-q -

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Momentum distributions from structure function g 1 Deconvolution of g 1 : Since G=G + +G - and G=G + +G - … obtained from F 2,g 1 and represent distribution of quarks with polarization ±. dp/Md3pd3p

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Distribution functions f ± (x) Let us note:but!! (equality takes place only in non-covariant IMF approach)

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Momentum distributions in the proton rest frame 2) q(x) & Δq(x) MRST & LSS LO 4GeV 2 Remark: xΔf q (x) are similar to xq val (x) spin contribution comes dominatly from valence region

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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 (j 2,j z ) only, which are represented by the bispinor spherical waves:

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j=1/2

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Spin and orbital motion, Γ 1 : two ways, one result, Γ 1 : two ways, one result -covariant approach is a common basis

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Comments are controlled by the factor, two extremes: massive and static quarks and 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. massless quarks and -this scenario is clearly preferred for quarks with effective mass on scale of thousandths and momentum of tenths of GeV. important role of the intrinsic quark orbital motion emerges as a direct consequence of the covariant approach

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Proton spin Second scenario: implies, that a room for gluon contribution can be rather sensitive to the longitudinal polarization: For 1/3, 0.3 and 0.2 gluon contribution represents 0, 10 and 40%. Value empirically known 0.2-0.35 does not exclude any of these possibilities. CQSM-chiral quark soliton model:

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Orbital motion of quarks well fits to other motions like orbital motion of electrons… He

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…or like orbital motion of nucleons He

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Orbital motion of quarks He

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Orbital motion of everything… He

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Summary Covariant version of QPM involving quark orbital motion was studied. New (LO) 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 g 1 is reduced correspondingly. Important consequence for the composition of proton spin was suggested.

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Thank you!

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